Braking estimation device, anti-lock brake controller, and braking pressure controller

[0002] 1. Field of the Invention

[0003] The present invention relates to a diagnostic apparatus for a dynamic system, and more particularly, to an apparatus for very accurately diagnosing faults in a dynamic system, the air pressure of a tire, and conditions around the tire by vibrating the dynamic system through use of vibration means provided in the diagnostic apparatus and on the basis of internal disturbance caused by a fault in the thus-vibrated dynamic system even in a case where the amount of external disturbance is small.

[0004] Further, the present invention relates to a braking pressure estimation device which estimates master cylinder pressure, mean braking pressure, and a micro-vibration component in the braking pressure on the basis of wheel speed information and without use of a braking pressure sensor, by taking note of the gain characteristics of a wheel speed and the braking pressure in a case where the braking pressure is minutely vibrated at a resonance frequency of a vibration system comprised of a vehicle body, a wheel, and a road surface. Still further, the present invention relates to an anti-lock brake controller which employs the braking pressure estimation device, as well as to a braking pressure controller capable of continually controlling braking pressure in a smooth manner.

[0005] 2. Related Art

[0006] (Conventional Apparatus for Diagnosing a Dynamic System)

[0007] Japanese Patent Application Laid-open (JP-A) No. 7-98268 describes the following technique as an apparatus for diagnosing a dynamic system.

[0008] In the technique disclosed in the foregoing unexamined patent application, a total disturbance vector—which is the sum of an external disturbance vector exerted on a dynamic system from outside and an internal disturbance vector caused by a fault in the dynamic system—is estimated on the basis of a response output vector from the dynamic system. Further, an internal state quantity vector of the dynamic system is estimated. A component relevant to internal disturbance is separated from the total disturbance vector by calculation of the correlation between the thus-estimated total disturbance vector and the internal state quantity vector. Then, a part of the dynamic system corresponding to the thus-separated component relevant to the internal disturbance is specified as a fault.

[0009] The foregoing technique enables location of an area of the dynamic system to be examined through use of one observer, as well as estimation of the absence or presence of a fault in the area and the degree of the fault. As contrasted with a conventional generalized likelihood comparison test method, there is no need for this technique to examine a plurality of areas through use of a plurality of observers disposed so as to correspond to the areas, and hence the technique has an advantage of being capable of accurately sensing a fault with few calculations.

[0010] (Conventional Braking Pressure Estimation Device, and Anti-lock Brake Controller Utilizing the Braking Pressure Estimation Device)

[0011] With regard to a device which controls the braking force of wheels such as an anti-lock brake controller (hereinafter referred to as an ABS controller), the sensing of braking pressure is an important problem, and a higher degree of control of the braking pressure can be expected if the value of the braking pressure is known. As a method for sensing the braking pressure, there is a method of attaching pressure sensors comprising a semiconductor device or the like to each wheel cylinder. However, the pressure sensors are comparatively expensive, and attachment of the pressure sensors to each wheel cylinders is difficult in terms of cost.

[0012] To overcome such a difficulty, there has already been proposed a technique of estimating the wheel cylinder pressure of each wheel on the basis of the result of measurement of the pressure sensor attached to the master cylinder pressure. Japanese Patent Application Laid-open (JP-A) No. 7-186918 describes a braking pressure controller which employs a method of calculating the wheel cylinder pressure of each wheel from a measured supply pressure (e.g., master cylinder pressure) and the time period over which a valve is actuated. This method enables the estimation of the wheel cylinder pressure of each wheel solely by sensing the pressure of the master cylinder through use of one pressure sensor, thereby rendering the braking pressure controller advantageous in terms of cost.

[0013] However, in many widely-available ABS controllers, a pressure sensor is not attached even to the master cylinder. Therefore, even the foregoing wheel cylinder estimation technique that requires the attachment of a pressure sensor to only the master cylinder still adds to the cost. Further, there is needed a remedy for sensor failures in order to ensure the reliability of the pressure sensor, which also adds to the cost.

[0014] Japanese Patent Application Laid-open (JP-A) No. 6-286590 describes a method of estimating master cylinder pressure without use of a pressure sensor.

[0015] The technique described in the foregoing patent application discloses the following three methods for estimating master cylinder pressure.

[0016] (1) Assuming that there is a uniform increase in the master cylinder pressure as a result of a first reduction in hydraulic braking pressure, a variation ΔPm (constant) in the master cylinder pressure is calculated. The master cylinder pressure is corrected through use of the thus—calculated variation ΔPm.

[0017] (2) By utilization of a tendency for the variation in the master cylinder pressure to increase in accordance with a variation ΔS in slip rate so long as the value of the master cylinder pressure is large, the variation ΔPm in the master cylinder pressure is calculated from the variation in the slip rate. Accordingly, as contrasted with the method described in (1) which is based on the assumption that the variation in the master cylinder pressure is constant, degree of accuracy of estimation is improved.

[0018] (3) The variation ΔPm in the master cylinder is calculated from a variation ΔV′_w0in vehicle acceleration and the variation ΔS in the slip rate. The use of the variation ΔV′_w0in vehicle acceleration enables correction of the master cylinder pressure, even when slippage of wheels due to speed reduction has not yet occurred and therefore the master cylinder pressure Pm is low. Accordingly, as contrasted with the method described in (2), this method further improves the accuracy of estimation of master cylinder pressure.

[0019] (Conventional Hydraulic Braking Pressure Controller)

[0020] For an apparatus such as an ABS controller in which the braking force applied to the vehicle is controlled by the hydraulic pressure of the wheel cylinder, not only a reduction in the hydraulic braking pressure at the time of wheel lock, but also smooth continuous control of the hydraulic braking pressure is important.

[0021] The hydraulic braking pressure is controlled by pressure increase and decrease valves (such as those disposed in an ABS actuator shown in FIGS. 23A and 23B) that are controllable from outside by means of an electrical signal, or the like, and are interposed between the master cylinder—whose pressure is related to the depression of a brake pedal given by the driver—and the wheel cylinders which produce pressure for pressing brake pads; i.e., the actual braking force of the vehicle.

[0022] Under normal conditions, the pressure in the master cylinder is directly transmitted to the hydraulic pressure in the wheel cylinders by opening the pressure increase valves of the ABS actuator shown in FIGS. 23A and 23B, as well as by closing the pressure decrease valves of the same. If the hydraulic pressure in the wheel cylinders is excessively high, there is established a state (a pressure decrease mode) in which the pressure increase valve is closed and the pressure decrease valve is opened so that the pressure from the master cylinder is prevented from being transmitted to the wheel cylinders while the hydraulic pressure in the wheel cylinders is released to a reservoir tank. In order to allow the hydraulic pressure in the wheel cylinders to recover from the pressure-reduced state, there is established a state (a pressure hold mode) in which both the pressure increasing and reducing valves are closed to prevent the hydraulic pressure in the wheel cylinders from changing; a state (a pressure increase mode) in which only the pressure increase valve is opened to allow the master cylinder pressure to be directly transmitted to the wheel cylinders is inserted over a short period of time; and the time period of the pressure increase mode is gradually increased.

[0023] In an actual ABS control operation, if wheel lock is detected, the hydraulic pressure in the wheel cylinders is abruptly reduced through the pressure decrease mode which is continued for a comparatively long period of time. Subsequently, the hydraulic pressure is rather gradually increased by repeating the pressure hold mode and pressure increase mode. If wheel lock arises again during the course of an increase in the hydraulic pressure, the valve is controlled in the pressure decrease mode to thereby abruptly decrease the hydraulic pressure in the wheel cylinders. Subsequently, the operation mode is shifted to the pressure hold mode and the pressure increase mode.

[0024] For example, in the technique disclosed in Japanese Patent Application Laid-open (JP-A) No. 3-118263, for each pressure increase and reduction area, the pulse train pattern is switched through use of a plurality of maps as well as the relationship between wheel speed, acceleration/deceleration, and separately-determined target speed, as shown in FIGS. 24A and 24B.

[0025] Further, Japanese Patent Application Laid-open (JP-A) No. 8-34329 describes a technique of controlling mean hydraulic braking pressure on the basis of the operation frequency of a valve and a duty ratio between a pressure increase mode and a pressure decrease mode through use of a valve having only a pressure increase mode and a pressure decrease mode. This technique principally implements the pressure hold mode of a hydraulic braking pressure by actuating a valve at a comparatively high frequency through use of only the valve having a pressure increase mode and a pressure decrease mode. Further, the amplitude of micro-vibrations in the hydraulic braking pressure is controlled by changing the operation frequency of the valve.

[0026] In the foregoing technique described in Japanese Patent Application Laid-open (JP-A) No. 7-98268, a total disturbance vector of a dynamic system is estimated on the basis of a response output from the dynamic system stemming from the disturbance outside the dynamic system. For example, in a dynamic system comprising a suspension system and a wheel, the external disturbance exerted on wheels traveling on an a rough road surface is utilized as an input. Accordingly, in a case where the input stemming from the external disturbance is small such as that obtained when the wheels travel on a smooth road surface, the response output becomes small. Therefore, even if the output value is normalized, the accuracy of sensing of a fault or the accuracy of estimation of air pressure in the tire is reduced by a quantization error or the like.

[0027] In a case where the mean value of external disturbance obtained during a given period of time is zero or nearly zero, the foregoing conventional technique enables highly accurate separation of the component which is relevant to an internal disturbance vector and stems from a fault from a total disturbance vector. However, the statistical property of the external disturbance differs according to the state of a road surface, and sometimes the internal disturbance vector cannot be very accurately isolated.

[0028] Further, even in the case of the method (3) having the highest degree of accuracy among the techniques described in Japanese Patent Application (JP-A) No. 6-286590, since the method employs the variation ΔS in the slip rate, the relationship between the variation ΔS in the slip rate and the variation ΔPm in the master cylinder pressure changes as a result of a variation in the coefficient of friction μ between the tire and the road surface. The calculation of the variation ΔPm in the master cylinder pressure through use of a constant coefficient results in a reduction in the accuracy of estimation according to the state of the road surface.

[0029] In the conventional technique described in Japanese Patent Application Laid-open (JP-A) No. 3-118263, the hydraulic braking pressure is controlled by switching the pulse train pattern between the patterns shown in FIGS. 24A and 24B. For this reason, as shown in FIG. 24C, a vibration arises in the hydraulic pressure in the wheel cylinders at a comparatively low frequency (several hertz). This vibration imparts to the driver's pedal an unpleasant low frequency vibration called kickback and results in a great variation in vehicle behavior at a comparatively low frequency. As a result, the hydraulic braking pressure cannot be controlled smoothly.

[0030] The technique described in Japanese Patent Application Laid-open (JP-A) No. 8-34329 cannot be applied to the anti-lock brake control operation described in Japanese Patent Application Laid-open (JP-A) No. 7-220920 which utilizes the fact that the resonance characteristics of the resonance system comprised of a vehicle body, a wheel, and a road surface change according to the state of grip of the wheel on the road surface, because it is impossible to change the frequency of vibration at the resonance frequency of the system.

[0031] The present invention has been contrived in view of the aforementioned drawbacks, and an object of the present invention is to provide a diagnostic apparatus for a dynamic system which is capable of constantly sensing a fault highly accurately even in a case where there is a small amount of disturbance and of highly accurately diagnosing the air pressure in the tire or the conditions of elements around the tire irrespective of the state of a road surface.

[0032] Another object of the present invention is to provide a braking pressure estimation device capable of stably estimating braking pressure highly accurately irrespective of the state of a road surface and without use of a pressure sensor, as well as an anti-lock brake controller which uses this braking pressure estimation device.

[0033] Still another object of the present invention is to provide a braking pressure controller which reduces unpleasant vibration felt by the driver or a variation in vehicle behavior by continuously controlling a hydraulic braking pressure in a smooth manner.

[0034] To accomplish the aforementioned objects, in accordance with a first aspect of the present invention, there is provided a diagnostic apparatus for a dynamic system to detect a fault in the dynamic system, comprising: vibration means for vibrating the dynamic system through use of a vibration signal unrelated to an internal state quantity vector of the dynamic system; disturbance estimating means for estimating a total disturbance vector which is the sum of an internal disturbance vector stemming from a fault in the dynamic system and a vibration disturbance vector occurring in the dynamic system as a result of vibration; correlation calculation means which calculates the correlation between the total disturbance vector and the internal state quantity vector and isolates a component relevant to internal disturbance from the total disturbance vector; and diagnostic means for diagnosing a fault in the dynamic system on the basis of the component relevant to the internal disturbance which is separated by the correlation calculation means.

[0035] The vibration means is capable of vibrating the dynamic system by use of a white signal (e.g., a so-called M-series signal) or a signal whose frequency is shifted (e.g., a signal which is shifted from a low frequency to a high frequency) as the vibration signal irrelevant to the internal state quantity vector of the dynamic system.

[0036] FIG. 1 shows the configuration of one example of the dynamic system diagnostic apparatus according to the present invention. A controller 12 also serving as an vibrator for vibrating the dynamic system inputs, as a control input 14, a signal (u+Δu)—which is a sum of a control signal “u” for controlling the dynamic system 10 to a certain internal state and an vibration signal Δu for vibrating the dynamic system 10—to the dynamic system 10 to be diagnosed by a diagnostic apparatus 30.

[0037] The internal state of the dynamic system 10 changes in accordance with the control signal “u” contained in the control input 14, so that a control output 16 changes. Further, the dynamic system 10 is vibrated in the vicinity of the established internal state. In the example shown in FIG. 1, the controller 12 controls the dynamic system 10 through use of the control output 16 as a feedback signal.

[0038] The controller 12 may be designed such that when the control output 16 is small, the controller 12 commences vibration control by means of the vibration signal Δu or increases the vibration signal Δu in order to increase the amplitude of vibration of the dynamic system, and that when the control output 16 is large because of great external disturbance, the controller 12 terminates vibration control by means of the vibration signal Δu.

[0039] In FIG. 1, the dynamic system 10 has “n” internal state quantities (i.e., the degree of the dynamic system is “n”), and the foregoing control signal “u” represents a control input vector 14 which comprises “m” elements and is sent to the dynamic system 10. Reference symbol “y” represents a control output vector 16 which is output from the dynamic system 10 and comprises “p” elements. Further, reference symbol “d” represents an vibration disturbance vector 15 of the dynamic system 10 which is caused by vibration by the vibration signal Δu in the vicinity of the controlled internal state.

[0040] Since the control input vector 14 has “m” elements, the dynamic system 10 is usually constructed in such a way that the vibration signal Δu also comprises “m” elements. With such a configuration, the number of elements contained in the vibration disturbance vector 15 also becomes equal to “m.” In order to highly accurately detect all faults in the dynamic system, the vibrator is desirably constructed in such a way that the vibration disturbance vector 15 comprises “n” elements which are equal in degree to the internal state quantity vector of the dynamic system 10.

[0041] As a result of such a configuration of the vibrator, the vibration disturbance vector 15 affects the dynamic system in the same way as does the vibration disturbance vector when the external disturbance having degree “n” is applied to the dynamic system 10. Even in a case where there is a small degree of external disturbance or no external disturbance at all, faults can be highly accurately detected by increasing a control output from the dynamic system.

[0042] The diagnostic apparatus 30 according to the present invention comprises disturbance estimating means 32, correlation calculation means 34, and diagnostic means 36 and is constructed so as to detect a fault in the dynamic system 10 as internal disturbance.

[0043] The disturbance estimating means 32 is constructed so as to estimate a total disturbance vector “w,” which is a sum of an vibration disturbance vector “d” and an internal disturbance vector of the dynamic system 10, on the basis of at least the internal state quantity vector of the dynamic system 10 (i.e., a vector comprising various elements representing the internal state quantity of the dynamic system 10), as well as to output the thus-estimated total disturbance vector “w” to the correlation calculation means 34.

[0044] In FIG. 1, a control output vector “y” from the dynamic system 10 is input to the disturbance estimating means 32. The disturbance estimating means 32 estimates and calculates an internal state quantity vector “x” of the dynamic system 10 from the control output vector “y” and outputs the thus-calculated internal state quantity vector “x” to the correlation calculation means 34. The estimation and calculation of the internal state quantity vector “x” can be carried out in a case where the control output vector “y” comprises information which enables calculation of elements of the internal state quantity vector “x.” The estimation and calculation of the internal state quantity vector “x” are carried out at the same time the total disturbance vector “w” is estimated. More specifically, a new internal state quantity comprising the total disturbance vector “w” and the state quantity vector “x” shown in Equation (4b), which will be described later, is calculated according to a conventional linear control theory (e.g., “Basic System Theory” by Furuta and Sano, Corona Co., Ltd., 1978, pp. 127 to 137).

[0045] If the amount of information contained in the control output vector “y” is insufficient for estimating the internal state quantity vector “x,” it is desired that a sensor for sensing the internal state quantity be provided in the dynamic system 10, as required, and an output from the sensor be input to the disturbance estimating means 32.

[0046] In a case where the information regarding the internal state quantity vector “x” can be directly determined from the control output vector “y” from the dynamic system 10 or the internal state quantity sensor provided, as required, in the dynamic system 10, it is desired that internal state quantity “x” be directly output to the correlation calculation means 34.

[0047] The correlation calculation means 34 calculates the correlation between the elements of the estimated total disturbance vector “w” and the elements of the internal state quantity vector “x” and separates the component relevant to internal disturbance from the elements of the total disturbance vector “w.” The thus-separated component relevant to the internal disturbance is output to the diagnostic means 36.

[0048] The diagnostic means 36 is formed so as to localize the areas of the dynamic system 10 to be examined on the basis of the thus-separated component relevant to internal disturbance and to determine the state of these areas.

[0049] Preferably, the correlation estimating means 34 is formed so as to calculate the correlation corresponding to a plurality of elements of the total disturbance vector “w” and to separate the component relevant to internal disturbance from the plurality of elements of the total disturbance vector “w.”

[0050] The elements of the thus-separated component relevant to internal disturbance correspond to the faults occurred in the dynamic system 10. For this reason, on the basis of the elements of the thus-separated component relevant to the internal disturbance, the diagnostic means 36 is capable of detecting and locating a fault in the dynamic system 10.

[0051] In such a case, preferably, the diagnostic means 36 is formed so as to comprise a memory section 40—in which are previously stored reference values for diagnosis purposes corresponding to the respective elements of the component relevant to internal disturbance—and a fault locating section 38 which locates a fault in the dynamic system 10 by comparing the elements of the separated component relevant to internal disturbance with the corresponding reference value.

[0052] In a case where the controller 12 controls neither vibration in accordance with the control output 16 nor the dynamic system, the diagnostic apparatus can be formed with a configuration such as that shown in FIG. 2. More specifically, an vibrater 13 which serves solely as vibration means is provided in place of the controller 12, and the disturbance estimating means 32 estimates a total disturbance vector on the basis of the control output 16.

[0053] The dynamic system diagnostic apparatus according to the present invention has the foregoing configuration, and its operation will now be described.

[0054] First, the disturbance estimating means 32 will be described.

[0055] If a fault arises in the dynamic system 10 to be examined, the internal state quantity of the dynamic system 10 shows a response differing from that which is output when the dynamic system 10 is in a normal condition. In a sense, such a response can be considered to be a sum of a response output in answer to vibration disturbance in a normal condition and a certain type of disturbance corresponding to the fault. The disturbance is not exerted to the dynamic system 10 from outside but occurs in the dynamic system 10. The disturbance estimating means 32 estimates the response as total disturbance vector “w,” which is a sum of the internal disturbance stemming from the fault and the vibration disturbance.

[0056] The principle of estimation of disturbance by the disturbance estimating means 32 will now be described. The following description is based on the assumption that external disturbance is considerably smaller than vibration disturbance or does not exist at all.

[0057] First, presume that the dynamic system 10 is represented by the following equation of state.

[0058] x(t)=Ax(t)+Bu(t)+d(t)

[0059] y(t)=Cx(t)  (1)

[0060] Here, x(t) represents an internal state quantity vector of the dynamic system 10 to be examined; u(t) represents a control input vector; y(t) represents a control output vector; and d(t) represents a pure vibration disturbance vector because it ignores external disturbance. Further, matrices A, B, and C represent matrices of constants determined by the structure of the dynamic system 10 to be examined (i.e., parameters of a system constituting the dynamic system to be examined).

[0061] The vibration disturbance vector d(t) is related to an vibration input vector Δu(t) by the following equation.

[0062] d(t)=B·Δu(t)

[0063] Equation (1) is expressed as $\frac{d}{dT}\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ a_{\mathrm{n1}}& a_{\mathrm{n2}}& \cdots & a_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]+\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1m}\\ b_{21}& b_{22}& \cdots & b_{2m}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ b_{\mathrm{n1}}& b_{\mathrm{n2}}& \cdots & b_{nm}\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ ⋮\\ ⋮\\ u_m\end{array}\right]+\left[\begin{array}{c}{d}_1\\ d_2\\ ⋮\\ ⋮\\ ⋮\\ d_n\end{array}\right]\left[\begin{array}{c}{y}_1\\ y_2\\ ⋮\\ ⋮\\ ⋮\\ y_p\end{array}\right]=\left[\begin{array}{cccc}{c}_{11}& c_{12}& \cdots & c_{1n}\\ c_{21}& c_{22}& \cdots & c_{2n}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ c_{\mathrm{p1}}& c_{\mathrm{p2}}& \cdots & c_{\mathrm{cpn}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]$

[0064] The dynamic system 10 to be examined when it is in an anomalous condition can be equivalently expressed through use of variations in matrices A and B (or variations in the parameters). More specifically, given that the matrix A is changed by ΔA(t) and the matrix B is changed by ΔB(t) due to a fault, the object to be examined, or the dynamic system 10, with a fault can be expressed as follows:

[0065] x(t)=Ax(t)+Bu(t)+{ΔA(t)×(t)+ΔB(t)u(t)+d(t)}

[0066] =Ax(t)+Bu(t)+Dw(t)  (2)

[0067] where Dw(t) is represented by the following expression.

[0068] Dw(t)=ΔA(t)×(t)+ΔB(t)u(t)+d(t)  (3)

[0069] where the matrix D represents in which of channels of the dynamic system 10 disturbance arises as a result of a fault. The matrix D is set so as to correspond to the channel in which vibration disturbance enters and to an estimated fault.

[0070] If there are changes in the matrices A and B as a result of a fault, the vibration disturbance d(t) is given by the following expression.

[0071] d(t)=B·Δu(t)+ΔB·Δu(t)

[0072] More specifically, the vibration disturbance d(t) comprises a component ΔB·Δu(t) newly developed as a result of the fault. In terms of diagnosis accuracy, the vibration disturbance d(t) is desirably irrelevant to the influence of the fault. Therefore, the vibration input Δu(t) is made as micro as possible—in which case the term of ΔB·Δu(t) can be ignored—within the range in which the control output “y” is not reduced smaller than a predetermined value.

[0073] If Δu can be observed, u+Δu can be handled as an input for the dynamic system 10. Consequently, vibration input is not required to become micro to such an extent that it can be ignored. In this case, d(t) is external disturbance alone.

[0074] Equations (2) and (3) are represented as the following equation by a general matrix. $\begin{array}{c}\frac{d}{dt}\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ a_{\mathrm{n1}}& a_{\mathrm{n2}}& \cdots & a_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]+\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1m}\\ b_{21}& b_{22}& \cdots & b_{2m}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ b_{\mathrm{n1}}& b_{\mathrm{n2}}& \cdots & b_{nm}\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ ⋮\\ ⋮\\ u_m\end{array}\right]\\ +\left[\begin{array}{cccc}\Delta a_{11}& \Delta a_{12}& \cdots & \Delta a_{1n}\\ \Delta a_{21}& \Delta a_{22}& \cdots & \Delta a_{2n}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ \Delta a_{\mathrm{n1}}& \Delta a_{\mathrm{n2}}& \cdots & \Delta a_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]\\ +\left[\begin{array}{cccc}\Delta b_{11}& \Delta b_{12}& \cdots & {\mathrm{Hb}}_{1m}\\ \Delta b_{21}& \Delta b_{22}& \cdots & \Delta b_{2m}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ \Delta b_{\mathrm{n1}}& \Delta b_{\mathrm{n2}}& \cdots & \Delta b_{nm}\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ ⋮\\ ⋮\\ u_m\end{array}\right]\\ +\left[\begin{array}{c}{d}_1\\ d_2\\ ⋮\\ ⋮\\ ⋮\\ d_n\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ a_{\mathrm{n1}}& a_{\mathrm{n2}}& \cdots & a_{\mathrm{nn}}\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\\ ⋮\\ ⋮\\ ⋮\\ x_n\end{array}\right]\\ +\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1m}\\ b_{21}& b_{22}& \cdots & b_{2m}\\ & ⋮& & \\ & ⋮& & \\ & ⋮& & \\ b_{\mathrm{n1}}& b_{\mathrm{n2}}& \cdots & b_{nm}\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\\ ⋮\\ ⋮\\ ⋮\\ u_m\end{array}\right]+D\left[\begin{array}{c}{w}_1\\ w_2\\ ⋮\\ ⋮\\ ⋮\\ w_n\end{array}\right]\end{array}$

[0075] In this way, the response of state vector from the dynamic system 10 to be examined in a faulty condition can be represented by the sum of a response {Ax(t)+Bu(t)} from the dynamic system 10 in a normal condition and disturbance {Dw(t)}. The disturbance estimating means 32 is configured so as to estimate the disturbance Dw(t).

[0076] The disturbance is estimated in the following way.

[0077] In a first step, there is formed an extended system of the dynamic system 10 which includes disturbance w(t) in the state thereof. To this end, the following supposition is made with respect to the disturbance w(t), and the disturbance w(t) is added to the state of the dynamic system 10.

[0078] w(t)=0  (4)

[0079] As a result, the extended system of the dynamic system which includes the disturbance w(t) is written as follows; $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}x\\ w\end{array}\right]=\left[\begin{array}{cc}A& D\\ 0& 0\end{array}\right]\left[\begin{array}{c}x\\ w\end{array}\right]+\left[\begin{array}{c}B\\ 0\end{array}\right]uy=\left[\begin{array}{cc}C& 0\end{array}\right]\left[\begin{array}{c}x\\ w\end{array}\right]& \text{(4b)}\end{array}$

[0080] In a second step, the state represented by [xTwT]T in Equation (4b) is estimated and calculated through use of a conventional linear control theory.

[0081] As shown in FIG. 5, the supposition of Equation (4) signifies that disturbance 100 which originally changes continually is approximated such that it changes stepwise as indicted by 110 in FIG. 5. The accuracy of approximation of disturbance improves as the width of each step becomes narrower. The width of the step corresponds to the time period over which the disturbance estimating means 32 estimates disturbance. In practice, the time period over which the disturbance estimating means 32 estimates disturbance can be reduced to a very short period of time compared with the speed at which the disturbance changes. Accordingly, the approximation of disturbance is sufficiently practicable.

[0082] In this way, so long as the extended system can be observed, the disturbance estimating means 32 can estimate an unmeasurable state and the disturbance corresponding to a fault, even in a case where the entire state of the dynamic system to be examined cannot be measured.

[0083] Next, the correlation calculation means 34 will be described.

[0084] As previously described, the total disturbance vector w(t) estimated by the disturbance estimating means 32 is a combination of the internal disturbance caused by a fault in the dynamic system 10 and vibration disturbance “d” occurring in the dynamic system 10 as a result of vibration regardless of whether the dynamic system 10 is in a normal or anomalous condition.

[0085] The vibration disturbance “d” is a vibration caused by a signal irrelevant to the internal state quantity vector and has the feature that a mean value obtained by averaging the vibration disturbance over a given period of time becomes zero when the dynamic system is vibrated through use of a white signal. In consideration of this feature, calculation is performed in the present invention in order to separate from the estimated total disturbance w(t) a component which is relevant to internal disturbance (i.e., variable components ΔA and ΔB of the parameters) and stems from a fault. A representative method of such a calculation is the least square method.

[0086] First, the following expression is defined by Equation (3).

[0087] θ^T=[ΔAΔB], ζ^T=[X^TU^T]  (5)

[0088] {dot over (θ)} which minimizes the following equation $\begin{array}{cc}J\left(\hat{\theta }\right)=\sum _{K=1}^N{\left({\hat{\theta }}^T\zeta \left(k\right)-D\hat{w}\left(k\right)\right)}^2& \left(6\right)\end{array}$

[0089] is calculated from N data items through use of the least square method. Such {dot over (θ)} is obtained by partially differentiating Equation (6) with {dot over (θ)} and by taking the thus-obtained equation as zero, and is expressed as $\begin{array}{cc}\hat{\theta }={\left\{\sum _{K=1}^N\zeta \left(k\right){\zeta }^T\left(k\right)\right\}}^{-1}\left\{\sum _{K=1}^N\zeta \left(k\right)D\hat{w}\left(k\right)\right\}& \left(7\right)\end{array}$

[0090] Further, if Equation (7) is transformed to a recurrence formula, the formula will be written as $\Gamma \left(N\right)=\Gamma \left(N-1\right)-\left\{\Gamma \left(N-1\right)\zeta \left(N\right)\Gamma \left(N-1\right)\right\}/\left\{1+{\zeta }^T\left(N\right)\Gamma \left(N-1\right)\zeta \left(N\right)\right\}$  θ(N)={circumflex over (θ)}(N−1)−{Γ(N−1)ζ(N)}/{1+ζ^T(N)Γ(N−1)ζ(N)}·e(N)

[0091] where e(N)=ζ^T(N){circumflex over (θ)}(N−1)−D{circumflex over (w)}(N); {circumflex over (θ)} corresponds to a directional vector; and ζ corresponds to a basis vector. As a result, the variable components ΔA and ΔB of the parameters can be sequentially estimated.

[0092] Next, a specific example of calculation of correlation is explained with reference to a case where there is no correlation between the vector ζ and the elements. In this case, the component relevant to internal disturbance can be separated from the total disturbance w(t) by calculating the correlation between the total disturbance w(t) and the internal state quantity x(t) irrelevant to vibration disturbance.

[0093] For example, the i-th element of an estimated value of the disturbance vector w(t) is represented by the following equation.

[0094] {circumflex over (W)}_i=Δa_i1X₁+Δa_i2X₂+. . . +Δb_i1U₁+. . . +d_i  (8)

[0095] where {circumflex over (W)}_irepresents an estimated value of disturbance w_i.

[0096] As is evident from Equation (8), the i-th element of the estimated disturbance is a linear combination of a quantity Δaij representing a fault in the dynamic system 10 and elements x1, x2 . . . of the internal state quantity vector x(t).

[0097] In order to determine the quantity of the fault from the i-th element of the estimated disturbance, the cross-correlation between the i-th element of the estimated disturbance and the internal state quantity of the dynamic system 10 is calculated. At this time, the internal state quantity of the dynamic system used for calculation of the cross-correlation may be a value directly measured by a sensor, or the like, provided in the dynamic system 10 or, as previously described, a value estimated by the disturbance estimating means 32.

[0098] First, an explanation will be given of the calculation of a cross-correlation function between the i-th element of the estimated disturbance and the j-th element xj of the internal state quantity vector “x” represented by Equation (8). The cross-correlation function is defined by the following formula.

[0099] C({circumflex over (W)}_i, x_j)ΔCij=Δaijvi

[0100] As previously mentioned, this description is based on the assumption that there is no correlation between the elements of the vibration disturbance vector d(t) and the elements of the internal state quantity vector x.

[0101] The cross-correlation function and the autocorrelation function are represented by the following formulae. $\begin{array}{cc}C\left({\hat{W}}_i,x_j\right)=\frac{1}{N}\sum _{k=1}^N\left({\hat{w}}_i-{\stackrel{\_}{\hat{w}}}_i\right)\left(x_j,{\stackrel{\_}{x}}_j\right)V_{\mathrm{zj}}=\frac{1}{N}\sum _{k=1}^N{\left(x_j,{\stackrel{\_}{x}}_j\right)}^2& \left(9\right)\end{array}$

[0102] The values used in Equation (9) are represented by the following formulae. ${\stackrel{\_}{\hat{W}}}_i=\frac{1}{N}\sum _{k=1}^N{\hat{w}}_i$ ${\stackrel{\_}{X}}_j=\frac{1}{N}\sum _{k=1}^N{X}_j$

[0103] The calculation which employs Equation (8) is based on the assumption that the internal state quantity xj is directly measured through use of a sensor, or the like. In contrast, in a case where the internal state quantity xj is not directly measured, a cross-correlation function is desirably calculated from the value estimated by the disturbance estimating means 32 by the following equation. $\begin{array}{cc}C\left({\hat{W}}_i,x_j\right)=\frac{1}{N}\sum _{k=1}^N\left({\hat{w}}_i-{\stackrel{\_}{\hat{w}}}_i\right)\left({\hat{x}}_j,{\stackrel{\_}{\hat{x}}}_j\right)& \text{(10)}\end{array}$

[0104] where {circumflex over (x)}_jrepresents an estimated value of x_j. $\begin{array}{cc}{\stackrel{\_}{\hat{w}}}_j=\frac{1}{N}\sum _{k=1}^N{\hat{w}}_j{\stackrel{\_}{\hat{x}}}_j=\frac{1}{N}\sum _{k=1}^N{\hat{x}}_j& \text{(11)}\end{array}$

[0105] The disturbance estimating means 32 is capable of estimating the internal state quantity xj of the dynamic system 10 without errors regardless of the existence of a fault, external disturbance, or vibration disturbance. Consequently, even in a case where the cross-correlation function as represented by Equations (10) and (11) is used, there can be obtained a result which is substantially the same as that obtained by use of the directly-measured internal state of the dynamic system.

[0106] Next, the diagnostic means 36 will be described.

[0107] The diagnostic means 36 detects a fault and localizes the position of the fault by means of the correlation function Cij which is calculated by the correlation calculation means 34 and represents a component relevant to internal disturbance. More specifically, the diagnostic means 36 can detect a variable component Δaji of the parameter by dividing the correlation function Cij by the autocorrelation vxj of the state to thereby normalize the correlation function Cij. This is expressed as follows: $\Delta a_{\mathrm{ij}}=\frac{\sum _{k=1}^N\left({\hat{w}}_i-{\stackrel{\_}{\hat{w}}}_i\right)\left({\hat{x}}_j,{\stackrel{\_}{\hat{x}}}_j\right)}{\sum _{k=1}^N{\left(x_j-{\stackrel{\_}{x}}_j\right)}^2}$

[0108] When the mean value is taken as zero, the above formula becomes equivalent to Equation (7), which is based on the assumption that there is no correlation between elements of the vector ζ.

[0109] For example, the dynamic system 10 to be examined comprises constituent element I and constituent element II. It is assumed that the parameter expressing the constituent element I is provided at the first row-first column position of the matrix A of the dynamic system expressed by the equation of state (1), and that the parameters expressing the constituent element II is provided at the first row-first column position and the first row-second column position of the matrix A. At this time, if the correlation function C12, or Δa12, takes on any value, it is immediately determined that a fault is present in the constituent element II. If the correlation function C12 takes on no value, and the function C11, or Δa11, takes on any value, it is determined that a fault is present in the constituent element I.

[0110] As described above, according to the present invention, a fault occurring in any of the constituent elements constituting the dynamic system 10 is reliably detected, and the location of the fault can be correctly detected.

[0111] For a conventional technique for calculating a quantity corresponding to a fault from a residual between a state estimated by an observer and a directly measured state, it is impossible to localize the fault by means of a simple calculation such as the calculation of a correlation, because the relationship between the residual and the fault is not simple (i.e., the relationship cannot be represented by a simple equation such as Equation (8)).

[0112] According to the design of the disturbance estimating means 32, the present invention may take the following modes.

[0113] In a first mode, the entire internal state quantity x(t) of the dynamic system 10 can be measured through use of a sensor, or the like, and the disturbance estimating means 32 is formed so as to estimate only the total disturbance vector w(t). In this case, the degree of the disturbance estimating means 32 is required to correspond only to the degree of disturbance, and hence the disturbance estimating means 32 has the advantages of simple configuration and the highest degree of fault detection.

[0114] In a second mode, there may be a case where the internal state quantity x(t) of the dynamic system 10 can be partially measured or can be estimated by the disturbance estimating means without measurement. In such a case, the disturbance estimating means 32 is formed so as to estimate and calculate the total disturbance vector w(t) and the internal state quantity which cannot be measured or is not measured.

[0115] In this case, there is no need to measure a part of the internal state quantity of the dynamic system 10, thereby eliminating need for the sensor. The disturbance estimating means 32 estimates the internal state quantity which cannot be measured, as well as the quantity of disturbance. By use of the thus-estimated quantity in the calculation of a correlation, a fault can be measured in substantially the same way where the entire internal state of the dynamic system 10 is measured.

[0116] A third mode is directed to a case where a part of the internal state quantity x(t) of the dynamic system 10 cannot be measured, and the disturbance estimating means 32 estimates and calculates the total disturbance vector w(t) and the entire internal state quantity x(t) including an unmeasurable internal state quantity.

[0117] Even in this case, as in the second mode, the sensor can be eliminated, and a fault can be localized in substantially the same way where the overall internal state quantity of the dynamic system 10 is measured.

[0118] This mode has an advantage that the design of the disturbance estimating means 32 is slightly simplified compared with that in the second mode.

[0119] The calculation required for the first through third modes will be described in detail. First, as previously described with reference to the first mode, the overall internal state quantity of the dynamic system 10 is measured.

[0120] In this case, a mean value of the disturbance vector defined by Equation (8) is expressed by the following equation. $\begin{array}{c}{\stackrel{\_}{\hat{w}}}_i=\Delta a_{\mathrm{i1}}\frac{1}{N}\sum _{k=1}^N{x}_i+\Delta a_{\mathrm{i2}}\frac{1}{N}\sum _{k=1}^N{x}_2+\dots +\Delta b_{\mathrm{i1}}\frac{1}{N}\sum _{k=1}^1{u}_1+\dots +\frac{1}{N}\sum _{k=1}^1{d}_1\\ =\Delta a_{\mathrm{i1}}{\stackrel{\_}{x}}_1+\Delta a_{\mathrm{i2}}{\stackrel{\_}{x}}_2+\dots +\Delta b_{\mathrm{i1}}{\stackrel{\_}{u}}_{\mathrm{i1}}+\dots +{\stackrel{\_}{d}}_1\end{array}$

[0121] Accordingly, in a case where the entire internal state quantity of the dynamic system can be measured, the cross-correlation function between the estimated disturbance vector and the internal state quantity xj is written as follows: $\begin{array}{cc}\begin{array}{c}c\left({\hat{w}}_i,x_j\right)=\frac{1}{N}\sum _{k=1}^N\left({\hat{w}}_i-{\stackrel{\_}{\hat{w}}}_i\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\\ =\Delta a_{\mathrm{i1}}\frac{1}{N}\sum _{k=1}^N\left(x_1-{\stackrel{\_}{x}}_1\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\\ +\Delta a_{\mathrm{i2}}\frac{1}{N}\sum _{k=1}^N\left(x_2-{\stackrel{\_}{x}}_2\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\\ +\dots +\Delta a_{\mathrm{i1}}\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\\ +\dots =\Delta b_{\mathrm{i2}}\frac{1}{N}\sum _{k=1}^N\left(u_1-{\stackrel{\_}{u}}_1\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\\ +\frac{1}{N}\sum _{k=1}^N\left(d_1-{\stackrel{\_}{d}}_1\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\end{array}& \text{(12)}\end{array}$

[0122] Provided that no correlation exists between the quantities of state of the dynamic system, the terms included in Equation (12) are represented by the following formula. $\frac{1}{N}\sum _{k=1}^N\left(x_1-{\stackrel{\_}{x}}_1\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\cong 0$ $\frac{1}{N}\sum _{k=1}^N\left(x_2-{\stackrel{\_}{x}}_2\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\cong 0$ $⋮$ $\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left(x_j-{\stackrel{\_}{x}}_j\right)=\frac{1}{N}\sum _{k=1}^N{\left(x_j-{\stackrel{\_}{x}}_j\right)}^2\Delta V_{\mathrm{xj}}\ne 0$

[0123] Further, assuming that there is no correlation between the state of the dynamic system xj and the vibration disturbance, the following equation holds. $\frac{1}{N}\sum _{k=1}^N\left(d_1-{\stackrel{\_}{d}}_1\right)\left(x_j-{\stackrel{\_}{x}}_j\right)\cong 0$

[0124] As a result, the value of the correlation function is finally expressed by the following equation. $C\left(w_i,x_i\right)\cong \Delta a_{\mathrm{ij}}\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left(x_j-{\stackrel{\_}{x}}_j\right)=\Delta a_{\mathrm{ij}}{V}_{\mathrm{xj}}$ $V_{\mathrm{xj}}=\frac{1}{N}\sum _{k=1}^N{\left(x_j-{\stackrel{\_}{x}}_j\right)}^2$ $x_j=\frac{1}{N}\sum _{k=1}^N{x}_j$

[0125] As in the second and third modes, when the cross-correlation function is calculated from the value estimated by the disturbance estimating means 32, the calculation is expressed by the following formula. $\begin{array}{c}c\left({\hat{w}}_1,{\hat{x}}_j\right)=\frac{1}{N}\sum _{k=1}^N\left({\hat{w}}_i-{\stackrel{\_}{\hat{w}}}_i\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\\ =\Delta a_{\mathrm{i1}}\frac{1}{N}\sum _{k=1}^N\left(x_1-{\stackrel{\_}{x}}_1\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\\ +\Delta a_{\mathrm{i2}}\frac{1}{2}\sum _{k=1}^N\left({\hat{x}}_2-{\stackrel{\_}{x}}_2\right)\left(x_j-{\hat{x}}_j\right)\dots \\ +\Delta a_{\mathrm{i1}}\frac{1}{2}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left({\hat{x}}_j-\stackrel{\_}{\hat{x}}\right)+\dots \\ +\Delta b_{\mathrm{i1}}\frac{1}{2}\sum _{k=1}^N\left(u_1-{\stackrel{\_}{u}}_1\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)+\dots \\ +\frac{1}{N}\sum _{k=1}^N\left(d_1-{\stackrel{\_}{d}}_1\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\end{array}$

[0126] Assuming that no correlation exists between the quantities of state of the dynamic system, the terms included in Equation (13) are represented as follows: $\frac{1}{N}\sum _{k=1}^N\left(x_1-{\stackrel{\_}{x}}_1\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\cong 0$ $\frac{1}{N}\sum _{k=1}^N\left(x_2-{\stackrel{\_}{x}}_2\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\cong 0$ $⋮$ $\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\Delta V_{\mathrm{xj}}\ne 0$ $⋮$ $\frac{1}{N}\sum _{k=1}^N\left(d_1-{\stackrel{\_}{d}}_1\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\cong 0$

[0127] Consequently, the value of the above correlation function is expressed by the following equation. $\begin{array}{c}C\left({\hat{w}}_{\mathrm{i1}},{\hat{x}}_j\right)\cong \Delta a_{\mathrm{ij}}\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left({\hat{x}}_j-{\stackrel{\_}{\hat{x}}}_j\right)\\ =\Delta a_{\mathrm{ij}}{v}_{\mathrm{zj}}\end{array}$ $v_{\mathrm{xj}}=\frac{1}{N}\sum _{k=1}^N\left(x_j-{\stackrel{\_}{x}}_j\right)\left({\hat{x}}_j-{\stackrel{\_}{x}}_j\right)$ ${\stackrel{\_}{\hat{x}}}_j=\frac{1}{N}\sum _{k=1}^N{\hat{x}}_j$

[0128] Even by use of the thus-obtained correlation function, a fault and the location of the fault can be detected in a similar manner to that employed previously.

[0129] In a case where the control output becomes sufficiently large because of application of large external disturbance d′, the controller 12 suspends the vibration control performed on the basis of the vibration signal Δu. In this case, a fault and the location of the fault can be detected solely by replacing the vibration disturbance “d” in the foregoing equation with external disturbance d′.

[0130] In the diagnosis based on the previously-described principle, the disturbance estimating means for estimating the disturbance stemming from a fault as one state is used as the fault detection means. As a result, there are no fault detection speed/fault detection sensitivity trade-offs, and hence the fault detection speed and the fault detection sensitivity are both remarkably improved. Further, there is no need to use a plurality of observers corresponding to the number of faults, and a fault in an object to be examined can be localized with a high degree of sensitivity without measuring the entire state of the object, as required.

[0131] Further, since the relationship between the estimated disturbance and the location of the fault can be expressed by simple numerical equations, the external disturbance can be easily separated from the internal disturbance stemming from a fault by executing a simple calculation such as the calculation of a correlation between the estimated disturbance and the internal state quantity of the object, thereby enabling localization of the fault.

[0132] In this case, the internal state quantity used for calculation of a correlation can be represented by not only the internal state quantity of the object directly measured solely by a sensor, but also the internal state quantity of the object estimated by the disturbance estimating means at the same time it estimates disturbance, as required. As a result, detailed detection of a fault becomes feasible even when the entire internal state quantity of the object is not measured.

[0133] Diagnostic Apparatus

[0134] [Description of the Invention]

[0135] Next, an explanation will be given of a case where the foregoing principle of the apparatus for diagnosing a dynamic system is applied to an apparatus for diagnosing the air pressure in the tire.

[0136] With reference to the previously-described dynamic system diagnostic apparatus shown in FIG. 1, the tire air-pressure diagnostic apparatus according to the present invention will be described in more detail.

[0137] In the present invention, the dynamic system 10 to be examined is a system comprising a suspension system and a wheel. If there are variations in the air pressure in a tire, the internal state quantity of the system differs from that obtained when the air pressure is normal. In a sense, the response output from the system when there are variations in the air pressure in the tire can be considered to be a sum of the response output from the system when the air pressure is normal and the internal disturbance corresponding to the variation in the air pressure. If this disturbance, or a total disturbance vector, is estimated by use of the disturbance estimating means 32, variations in the air pressure in the tire can be detected.

[0138] It is assumed that the dynamic system 10 comprising a suspension system and a wheel is expressed by the following equation of state. The following description is based on the assumption that the wheels receive a small degree of disturbance or no disturbance from the road surface. This situation corresponds to a case where the vehicle is traveling over a road in good condition.

[0139] X=Ax+Bu+d

[0140] y=Cx  (14)

[0141] where reference symbol “x” represents an internal state quantity vector of the system 10; “u” represents a control input; and “y” represents a control output vector (an internal state quantity vector) directly detected by and output from the system 10. Further, reference symbol “d” represents vibration disturbance caused through vibration. Matrices A, B, C are matrices of constants determined by physical parameters of the system 10.

[0142] The vibration disturbance “d” is related to an vibration input Δu according to the following equation.

[0143] d=B·Δu

[0144] Here, in a case where the suspension system is an active suspension system, the control input “u” can be handled as the quantity of actuation of the active suspension system. In this case, the quantity of actuation (u+Δu)—which is the sum of the quantity of actuation “u” and the quantity of vibrating actuation Δu for vibrating the active suspension system—is input to the active suspension system.

[0145] In other cases, the control input “u” can be handled as a mean braking force instruction sent to a control solenoid valve which applies braking force to the wheel cylinder of the wheel. In this case, an instruction (u+Δu)—which is the sum of a mean braking force instruction “U” and an vibration instruction Δu for vibrating the braking force—is input to a control solenoid valve. This method can be applied to both the active suspension system and a conventional passive suspension system.

[0146] As a matter of course, in the case of the active suspension system, the active suspension system and the braking force can be vibrated at the same time.

[0147] FIG. 3 shows the configuration of the tire air-pressure diagnostic apparatus in a case where vibration is controlled by means of braking force.

[0148] The tire air-pressure diagnostic apparatus shown in FIG. 3 is equipped with a braking force controlling means 190—which controls the braking force exerted on wheels—in lieu of the controller 12 shown in FIG. 1. The braking force control means 190 applies mean braking force Pm to the wheels in response to the braking force instruction “u,” as well as minutely vibrated braking force Pv to the wheels in response to a micro-vibration braking force instruction Δu which is irrelevant to the internal state quantity of the system 10. As a result, the braking force is minutely vibrated to the braking force Pv in the vicinity of the mean braking force Pm, and the vibration disturbance “d” is imparted to the system 10.

[0149] The braking force instruction “u” output from the braking force control means 190 is converted into the braking force Pm—which is actually exerted on the wheels—by way of transmission characteristics 192 and is input to the disturbance estimating means 32. The transmission characteristics 192 are represented by a transmission function H of a mechanism for converting the braking force instruction “u” into the actual braking force Pm.

[0150] The braking force control means 190 receives the control output 16 and determines whether or not to vibrate the braking force according to the value of the control output 16 in response to the micro-vibration braking force instruction Δu. In a case where the braking force control means 190 does not determine whether or not to vibrate the braking force according to the control output 16, the tire air-pressure diagnostic apparatus is arranged so as to have a configuration such as that shown in FIG. 4. More specifically, an output terminal of the dynamic system which outputs a control output is not connected to the braking force control means 190.

[0151] The braking force control means 190 can be configured such that even in a case where the mean braking force Pm is not applied to the wheels (i.e., u=0, Pm=0), vibration of the braking force according to the micro-vibration braking force instruction Δu is possible. The detailed configuration of the braking force control means 190 will be described later (FIGS. 20 to 21).

[0152] The present invention will be separately described with reference to a case where the system 10 receives an input “u” and to a case where the system 10 does not receive the input “u.”

[0153] (Taking a system input into consideration)

[0154] In this case, variations in the air pressure in the tire, or the like, are converted into variations in physical parameters of the system 10. These variations can be expressed through use of variations in the matrix A. More specifically, if the matrix A is shifted by only ΔA by means of variations in the air pressure, the system after occurrence of variations in the air pressure is expressed as follows: $\begin{array}{c}x=\mathrm{Ax}+\mathrm{Bu}+\left(\Delta \mathrm{Ax}+d\right)\\ =\mathrm{Ax}+\mathrm{Bu}+\mathrm{Dw}\end{array}$

[0155] where Dw is expressed by the following equation.

[0156] Dw=ΔAx+d  (15)

[0157] From Equation (15), it is understood that variations in the air pressure in the tire induce new disturbance ΔAx. Reference symbol D designates a matrix consisting of 0 and 1 and is set according to a channel—into which vibration disturbance enters—and to the source of disturbance stemming from variations in the parameter of the system 10.

[0158] As described above, a response of state vector output from the system when there are variations in the air pressure in the tire can be expressed as the sum of the response output when the air pressure is normal and the disturbance Dw (t). The disturbance estimating means 32 is configured so as to estimate the disturbance “w.”

[0159] The disturbance estimating means 32 is configured in two steps as shown below.

[0160] In the first step is formed an extended system of the system whose state includes the disturbance w(t). To this end, the following supposition is made with regard to the disturbance w(t), and the disturbance w(t) is added to the state of the system 10 to be examined.

[0161] w=0

[0162] As a result, the extended system of the system 10 which includes the disturbance “w” is expressed by the following equation. $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}x\\ w\end{array}\right]=\left[\begin{array}{cc}A& D\\ 0& 0\end{array}\right]\left[\begin{array}{c}x\\ w\end{array}\right]+\left[\begin{array}{c}B\\ 0\end{array}\right]u& \text{(16)}\\ y=\left[C0\right]\left[\begin{array}{c}x\\ w\end{array}\right]& \end{array}$

[0163] In the second step, the estimating means 32 for estimating the state [xTwt] expressed by Equation (16) is configured through use of conventional linear control theory. The disturbance “w” is estimated by means of the thus-designed estimating means 32.

[0164] As has already been explained, the assumption of Equation (23) signifies that the disturbance w(t) which changes continually is approximated such that it changes stepwise as indicated by 110 in FIG. 5.

[0165] The disturbance estimating means 32 having the foregoing configuration can estimate an unmeasurable state and the disturbance corresponding to a fault even in a case where the entire internal state quantity vector x of the system 10 cannot be measured.

[0166] As is obvious from Equation (15), the disturbance estimated by the estimating means 32 is the sum of the vibration disturbance “d” stemming from vibration and the internal disturbance ΔAx occurring in the system 10 as a result of variations in the air pressure in the tire. Equation (15) is expressed as a vector; for example, the first element of this vector is expressed by the following equation.

[0167] [Dw]₁=ΔD₁₁X₁+ΔD₁₂X₂+ . . . +Δa_1jX_j+ . . . +d₁  (17)

[0168] where Δa_1jis the first row-jth column element of the matrix ΔA.

[0169] The disturbance estimating means 32 will be described specifically on the basis of Equation (17).

[0170] In Equation (17), assume that Δa₁₁is an element stemming from variations in the air pressure in the tire, and other elements stem from variations in components other than the air pressure in the tire. In this case, it is understood that the internal disturbance stemming from variations in the air pressure in the tire depends on the state quantity x1. More specifically, in this case, the state quantity which affects the system 10 as a result of variations in the air pressure in the tire is x1.

[0171] In order to detect only the component—which is relevant to internal disturbance stemming from variations in the air pressure in the tire—by eliminating the vibration disturbance “d” from the disturbance [Dw]1 estimated by the estimating means 32, the cross-correlation between the estimated disturbance [Dw]1 and the internal state quantity x1 is calculated. The cross-correlation is calculated by means of the correlation calculation means 34. Provided that the cross-correlation calculated at this time is C([Dw]1, w1), the value represented by the following expression is obtained. $\begin{array}{cc}C\left(\left[\mathrm{Dw}\right]1,\mathrm{x1}\right)=\Delta a_{11}\frac{1}{N}\sum _{k=1}^N{\left(x_1-{\stackrel{\_}{x}}_1\right)}^2& \text{(18)}\end{array}$

[0172] where {overscore (χ)}₁is a mean value represented by $\frac{1}{N}\sum _{k=1}^N{x}_1,$

[0173] and N is the number of samples used for the calculation of a correlation.

[0174] As previously described, the term related to the vibration disturbance and the term related to the internal disturbance stemming from variations in components other than the air pressure are irrelevant to the internal state quantity x1. Accordingly, only the internal disturbance corresponding to variations in the air pressure in the tire can be extracted from the estimated disturbance “w” by calculation of the correlation expressed by Equation (18).

[0175] The thus-calculated correlation function takes on a value corresponding to the frequency component of internal disturbance stemming from only variations in the spring constant of the tire from among various frequency components included in the estimated disturbance “w.” Accordingly, the amount of variation in the spring constant can be detected from the values calculated by the correlation function.

[0176] The correlation function expressed by Equation (18) can be represented by the product of item Δa₁₁representing variations in the spring constant and the autocorrelation function of the state quantity represented by the following equation. For example, the diagnostic means 36 can quantitatively detect the amount of variation Δa₁₁in the spring constant by dividing the cross-correlation function by the autocorrelation function of state quantity. $\frac{1}{N}\sum _{k=1}^N{\left(x_1-{\stackrel{\_}{x}}_1\right)}^2$

[0177] The diagnostic means 36 determines that the air pressure is anomalous when the thus-detected amount of variation Δa₁₁in the spring constant reaches the amount of variation in the spring constant corresponding to the air pressure in the tire determined to be anomalous.

[0178] (Where there is no input to the system 10)

[0179] An explanation will now be given of a case where there is no input to the system 10, and the system 10 is only minutely vibrated.

[0180] In this case, the dynamic system 10 comprising the suspension system and the wheels is expressed by the following equation of state.

[0181] x=Ax+d

[0182] y=Cx.

[0183] Where “x” designates a state quantity vector of the system 10; “y” designates an output vector measured directly by means of a sensor of the system; and “d” designates vibration disturbance. The matrices A, B, and C are matrices of constants determined by physical parameters of the system 10. The system 10 is different from the active suspension system in that there is no input “u,” expressed by Equation (14), to the system 10.

[0184] Given that the matrix A is shifted by ΔA because of variations in air pressure, the system after the air pressure has changed is expressed by the following equation. $\begin{array}{cc}\begin{array}{c}x=\mathrm{Ax}+\left(\Delta \mathrm{Ax}+d\right)\\ =\mathrm{Ax}+\mathrm{Dw}\end{array}& \text{(19)}\end{array}$

[0185] where Dw is represented as

[0186] Dw=ΔAx+d  (20)

[0187] From Equations (19) and (20), the extended system of the system 10 which includes the disturbance “w” is expressed by the following equation. $\frac{d}{dt}\left[\begin{array}{c}x\\ w\end{array}\right]=\left[\begin{array}{c}\mathrm{AD}\\ 00\end{array}\right]\left[\begin{array}{c}x\\ w\end{array}\right]$ $y=\left[\begin{array}{cc}C& 0\end{array}\right]\left[\begin{array}{c}x\\ w\end{array}\right]$

[0188] The system including the disturbance observer 32 is completely the same in configuration and operation as the active suspension system, with the exception of the input “u.”

[0189] As described above, even in a case where there is no input to the system 10, as in the conventional suspension system, an anomaly in the air pressure in the tire can be detected.

[0190] The foregoing dynamic system diagnostic apparatus can also be applied to the diagnosis of the state of components around a tire (e.g., the damping force of a damper used in the suspension system, the eccentric state of a tire, the state of a wheel, the wear of the tire, and foreign objects cut into the tire).

[0191] As has been described above, according to a first aspect of the invention, since there is provided means for vibrating the dynamic system, the control output can be increased even when there is a small degree of external disturbance. As a result, there is yielded an advantage of the ability to highly accurately diagnose a fault or variations in the air pressure in the tire.

[0192] Further, according to the present invention, the dynamic system is vibrated with a signal irrelevant to a state quantity of the dynamic system, and hence there is yielded an advantage of the ability to constantly maintain a high degree of accuracy of fault detection compared with a diagnosing apparatus which utilizes external disturbance as an input.

[0193] To accomplish the aforementioned object, according to a second aspect of the present invention, there is provided a braking force estimation device, comprising; a first input means for receiving a wheel speed; a second input means for receiving a physical quantity which indicates the slipping ability of a wheel; braking pressure estimating means for estimating a mean braking pressure from an wheel speed and the physical quantity.

[0194] In the second aspect of the present invention, the braking pressure estimating means estimates a mean braking pressure from the wheel speed and the physical quantity. The physical quantity includes, the gradient of friction coefficient between the road surface and the wheel with respect to a slip speed, the gradient of braking force with respect to a slip speed, and the gradient of braking torque with respect to a slip speed.

[0195] As described above, in a second aspect of the present invention, the mean braking pressure is estimated from the wheel speed and the physical quantity. The coefficient of friction reaches its peak value when the physical quantity is zero regardless of the state of the road surface. In the present invention, regardless of the state of the road surface, the mean braking pressure can be stably estimated highly accurately without use of a pressure sensor.

[0196] According to a third aspect of the present invention, there is provided a braking force estimating device, comprising: first input means for receiving a wheel speed input; second input means for receiving a resonance gain which is a ratio of a micro amplitude of the wheel speed at a resonance frequency with respect to a micro amplitude of a braking pressure at the time of vibration of the braking pressure at the resonance frequency of a resonance system including a vehicle body, a wheel, and a road surface; a third input means for receiving a pressure increase/decrease time required to achieve a mean braking pressure with respect to a given master cylinder pressure or a physical quantity associated with the pressure increase/decrease time; braking pressure estimating means for estimating the mean braking pressure from the input wheel speed and a resonance gain on the basis of a model in which the gradient of braking torque with respect to a slip speed is proportional to the resonance gain; master cylinder pressure estimating means for estimating a master cylinder pressure on the basis of the mean braking pressure estimated by said braking pressure estimating means and the pressure increase/decrease time required to achieve the mean braking pressure or the physical quantity associated with the pressure increase/decrease time; and micro amplitude estimating means for estimating the micro amplitude of the braking pressure on the basis of the master cylinder pressure estimated by said master pressure estimating means and of the pressure increase/decrease time required to achieve the mean braking pressure or the physical quantity associated with the pressure increase/decrease time.

[0197] In the third aspect of the present invention, the braking pressure estimating means estimates a mean braking pressure from the input wheel speed and the resonance gain on the basis of a model in which the gradient of braking torque with respect to the slip speed is proportional to the resonance gain. Subsequently, the master cylinder pressure estimating means estimates master cylinder pressure on the basis of the estimated mean braking pressure and the pressure increase/decrease time required to achieve the input mean braking pressure or the physical quantity associated with the pressure increase/decrease time. The micro amplitude estimating means estimates the micro amplitude of the braking pressure on the basis of the master cylinder pressure estimated by the master cylinder pressure estimating means and of the pressure increase/decrease time required to achieve the input mean braking pressure or the physical quantity associated with the pressure increase/decrease time.

[0198] The pressure increase/decrease time required to achieve the mean braking pressure include a pressure increase time and a pressure decrease time of the valve which is controlled so as to apply the mean braking force. For example, the physical quantity associated with the pressure increase/decrease time includes a mean braking pressure (i.e., a mean braking pressure reference value which will be described later) corresponding to the pressure increase/decrease time and under which pressure the micro amplitude of the braking pressure becomes constant while the master cylinder pressure is constant.

[0199] As described above, in the third aspect of the present invention, master cylinder pressure is estimated from the mean braking pressure estimated on the basis of a model in which the friction-torque gradient is proportional to the resonance gain. The coefficient of friction reaches its peak value when the friction-torque gradient is zero regardless of the state of the road surface. In the present invention, regardless of the state of the road surface, the master cylinder pressure can be stably estimated highly accurately without use of a pressure sensor.

[0200] According to a fourth aspect of the present invention, there is provided an anti-lock brake controller comprising: wheel speed detection means for detecting a wheel speed; resonance gain calculation means for calculating a resonance gain which is the ratio of the micro amplitude of the wheel speed at a resonance frequency with respect to the micro amplitude of a braking pressure at the time of vibration of the braking pressure at the resonance frequency of a resonance system including a vehicle body, a wheel, and a road surface; braking pressure estimating means for estimating a mean braking pressure from the wheel speed detected by said wheel speed detection means and the resonance gain calculated by said resonance gain calculation means on the basis of a model in which the gradient of braking torque with respect to a slip speed is proportional to the resonance gain; master cylinder pressure estimating means for estimating master cylinder pressure on the basis of the mean braking pressure estimated by said braking pressure estimating means and a pressure increase/decrease time required to achieve the mean braking pressure or a physical quantity associated with the pressure increase/decrease time; micro amplitude estimating means for estimating the micro amplitude of the braking pressure on the basis of the master cylinder pressure estimated by said master pressure estimating means and the pressure increase/decrease time required to achieve the mean braking pressure or the physical quantity associated with the pressure increase/decrease time and for outputting the estimated micro amplitude of the braking pressure to said resonance gain calculation means; control means for controlling the pressure increase/decrease time required to achieve the mean braking pressure in such a way that the resonance gain calculated by said resonance gain calculation means matches or substantially matches a reference gain; and reference means for outputting to the master cylinder pressure estimating means the pressure increase/decrease time which is required to achieve the mean braking pressure and is controlled by said control means or the physical quantity associated with the pressure increase/decrease time.

[0201] In the fourth aspect, the aforementioned braking pressure estimating device is applied to an anti-lock brake controller. As a result, stable anti-lock braking operation becomes feasible by means of a simply-structured apparatus and without use of a pressure sensor regardless of the state of the road surface.

[0202] According to a fifth aspect of the present invention, there is provided a braking pressure controller comprising: a control valve equipped with a pressure increase valve for increasing the braking pressure exerted on a wheel cylinder and a pressure decrease valve for decreasing the braking pressure; and controlling means for controlling the control valve in such a way as to alternately switch, at a given cycle, between a first state, including a pressure increasing state in which the braking pressure is increased by the pressure increase valve and a pressure holding state in which the braking pressure is held, and a second state, including the state in which the braking pressure is decreased by the pressure decrease valve and, the pressure holding state and for controlling the periods for the pressure increasing state and pressure decreasing state of the control valve.

[0203] In the fifth aspect of the present invention, the first state including a pressure increasing state and the second state including a pressure decreasing state are alternatively switched at a given cycle. The braking pressure is controlled by controlling the pressure increase and decrease time periods in each of the states, thereby enabling continuous control of braking pressure. The cycle at which the states are switched is made constant, and hence the present invention is easily applied to an ABS system which controls anti-lock braking operation on the basis of variations in the resonance characteristics of the braking pressure by minutely vibrating the braking pressure. In the fifth aspect of the present invention, when the braking pressure is to be held, the pressure increase and decrease valves are both closed.

[0204] The braking pressure can be minutely vibrated to such an extent that resultant variations in the braking pressure do not provide the driver with unpleasant feeling by shortening the cycle at which the first and second states are switched (i.e., by increasing the cycle to a high frequency), thereby preventing kickback. As a result, vehicle behavior is not subjected to great variations. In a case where the anti-lock brake controller is applied to an ABS system, ABS control can be improved further.

[0205] The mean braking pressure can be continually controlled without changing the valve configuration which comprises two valves; i.e., a pressure increase valve and a pressure decrease valve, and is used in the current ABS system, thereby not requiring a change in hardware.

[0206] As has been described above, in the second aspect of the present invention, since the master cylinder pressure is estimated from the mean braking pressure estimated on the basis of the model in which the friction-torque gradient is proportional to the resonance gain, the present invention provides an advantage of being capable of stably estimating the master cylinder pressure highly accurately without use of a pressure sensor regardless of the state of the road surface.

[0207] Further, in the third aspect of the present invention, the master cylinder pressure is estimated from the mean braking pressure estimated on the basis of the model in which the friction-torque gradient is proportional to the resonance gain, and the resonance gain used for determining the state of the wheel immediately before wheel lock is calculated from the micro amplitude of the braking pressure obtained on the basis of the master cylinder pressure. As a result, the present invention provides an advantage that highly-accurate stable anti-lock braking operation is enabled regardless of the state of the road surface through use of a device having a simple structure without use of any pressure sensor.

[0208] In the fifth aspect of the present invention, the first state including the pressure increasing state and the second state including the pressure decreasing state are alternatively switched at a given cycle, and the braking pressure is controlled by adjusting the pressure increase and decrease time periods in each of the states. As a result, the present invention provides an advantage of enabling smooth and continuous braking pressure control.

[0209] Still further, in the fourth aspect of the present invention, the cycle at which1 the first and second states are switched is shortened, thereby resulting in still other advantages of suppressing variations in the braking pressure to such an extent as not to provide the driver with unpleasant feeling and of preventing great variations from arising in vehicle behavior. In a case where the anti-lock brake controller is applied to an ABS system, ABS control can be improved to a much greater extent. In addition, the mean braking pressure can be continually controlled without changing the valve configuration including two valves; i.e., a pressure increase valve and a pressure decrease valve, used in the conventional ABS system, thereby not requiring a change in hardware.

[0210] FIG. 1 is a block diagram showing a first example of a diagnostic apparatus of the present invention for a dynamic system;

[0211] FIG. 2 is a block diagram showing a second example of a diagnostic of the present invention for a dynamic system;

[0212] FIG. 3 is a block diagram showing the first example of a diagnostic apparatus of the present invention for a dynamic system composed of a wheel and a suspension system;

[0213] FIG. 4 is a block diagram showing the second example of the diagnostic apparatus of the present invention for a dynamic system composed of a wheel and a suspension system;

[0214] FIG. 5 is a curve showing a method of approximating disturbance used in a first embodiment;

[0215] FIG. 6 is a schematic representation of a suspension system of a vehicle to be diagnosed in accordance with the first embodiment;

[0216] FIG. 7 is a block diagram showing a diagnostic apparatus in accordance with a first mode of the first embodiment for diagnosing the suspension system model shown in FIG. 6;

[0217] FIG. 8 is a block diagram showing a second mode of the diagnostic apparatus in accordance with the first embodiment;

[0218] FIG. 9 is a block diagram showing a third mode of the diagnostic apparatus in accordance with the first embodiment;

[0219] FIG. 10 is a schematic representation showing a dynamic system including an active suspension system and a wheel;

[0220] FIG. 11 is a block diagram showing a diagnostic apparatus in accordance with a second embodiment for diagnosing the dynamic system shown in FIG. 10;

[0221] FIG. 12 is a schematic representation showing a dynamic system including a conventional suspension system and a wheel;

[0222] FIG. 13 is a block diagram showing a diagnostic apparatus in accordance with a fourth embodiment for diagnosing the dynamic system shown in FIG. 12;

[0223] FIG. 14 is a block diagram showing a minimum dimension observer in accordance with the first embodiment;

[0224] FIG. 15 is a dynamic model of the vehicle in accordance with the fourth embodiment;

[0225] FIG. 16 is an equivalent model made by conversion of the dynamic model of the vehicle along the axis of rotation;

[0226] FIG. 17 is a block diagram showing the configuration of the diagnostic apparatus in accordance with the fourth embodiment of the present invention;

[0227] FIG. 18 is a flowchart showing the flow of operation of the diagnostic apparatus (e.g., the diagnosis of air pressure in the tire) in accordance with the fourth embodiment;

[0228] FIG. 19 is a graph showing a difference in vibration characteristics between the dynamic system in a normal condition and the dynamic system in an anomalous condition in accordance with the fourth embodiment;

[0229] FIG. 20 is a block diagram showing the configuration of braking force control means of the dynamic system in accordance with the fourth embodiment;

[0230] FIG. 21 is a block diagram showing an vibration instruction signal generation section of the braking force control means of the dynamic system in accordance with the fourth embodiment;

[0231] FIG. 22 is a diagrammatic representation showing the processing performed by an FFT calculation section and an vibration characteristics detection section of the diagnostic apparatus in accordance with the fourth embodiment;

[0232] FIG. 23A is a schematic representation showing an ABS actuator including one 3-position valve;

[0233] FIG. 23B is a schematic representation showing an ABS actuator including two 2-position valves;

[0234] FIG. 24A is a plot showing pulses for opening or closing a pressure increase valve;

[0235] FIG. 24B is a plot showing pulses for opening or closing a pressure decrease valve;

[0236] FIG. 24C is a plot showing variations in hydraulic wheel cylinder pressure with time when the pressure increase and decrease valves are controlled by means of the foregoing pulses;

[0237] FIG. 25A is a timing chart showing the relationship between hydraulic braking pressure and the pressure increasing, decreasing and holding instructions for the valve in an ordinary situation;

[0238] FIG. 25B is a timing chart showing the between hydraulic braking pressure and the pressure increasing, decreasing and holding instructions for the valve in a case where pressure-increase time t_iis longer than pressure-decrease time t_r;

[0239] FIG. 25C is a timing chart showing the between hydraulic braking pressure and the pressure increasing, decreasing and holding instructions for the valve in a case where pressure-increase time t_iis shorter than pressure-decrease time t_r;

[0240] FIG. 26A is a graph showing the characteristics of a hydraulic braking pressure with respect to the pressure increase and decrease time periods, and particularly, the characteristics of a mean braking pressure;

[0241] FIG. 26B is a graph showing the characteristics of a hydraulic braking pressure with respect to the pressure increase and decrease time periods, and particularly, the micro amplitude characteristics of the braking pressure;

[0242] FIG. 27A is a graph showing the characteristics of a hydraulic braking pressure with respect to the master cylinder pressure, and particularly, the characteristics of a mean braking pressure;

[0243] FIG. 27B is a graph showing the characteristics of a hydraulic braking pressure with respect to the pressure increase/decrease time, and particularly, the micro amplitude characteristics of the braking pressure;

[0244] FIG. 28 is a block diagram showing estimation of hydraulic braking pressure in accordance with a fifth embodiment;

[0245] FIG. 29 is a graph showing the relationship between slip speed Δω and a coefficient of friction μ and a gradient of the friction of coefficient μ in relation to the slip speed Δω;

[0246] FIG. 30A is a graph showing the pressure increase and decrease time periods for maintaining the constant micro amplitude of the braking pressure, and particularly, the relationship between a mean braking pressure and pressure increase time;

[0247] FIG. 30B is a graph showing the pressure increase and decrease time periods for maintaining the constant micro vibration of the braking pressure, and particularly, the relationship between the mean braking pressure and pressure decrease time;

[0248] FIG. 31 is a plot showing the relationship between the slip speed Δω, braking torque Tb, and the gradient of the braking torque T_b;

[0249] FIG. 32 is a block diagram showing the configuration of an anti-lock brake controller in accordance with the fifth embodiment;

[0250] FIG. 33 is a block diagram showing an example of configuration of a mean braking pressure estimation section constituting the braking pressure estimation apparatus in accordance with the fifth embodiment;

[0251] FIG. 34 is a block diagram showing an example of configuration of a master cylinder pressure estimation section constituting the braking pressure estimation apparatus in accordance with the fifth embodiment;

[0252] FIG. 35 is a block diagram showing an example of configuration of a braking pressure micro amplitude estimation section constituting the braking pressure estimation apparatus in accordance with the fifth embodiment;

[0253] FIG. 36 is a block diagram showing an example of configuration of a resonance gain calculation section constituting the anti-lock brake controller in accordance with the fifth embodiment;

[0254] FIG. 37 is a block diagram showing an example of configuration of a PI controller constituting the anti-lock brake controller in accordance with the fifth embodiment;

[0255] FIG. 38 is a block diagram showing a signal for instructing the actuation of the valve of the ABS actuator constituting the anti-lock brake controller in accordance with the fifth embodiment;

[0256] FIG. 39A is a graph for explaining the result of operation of the anti-lock brake controller in accordance with the fifth embodiment, showing variations in wheel speed ω_wand vehicle speed ω_uwith time;

[0257] FIG. 39B is a graph for explaining the result of operation of the anti-lock brake controller in accordance with the fifth embodiment, showing variations in a slip rate S with time;

[0258] FIG. 39C is a graph for explaining the result of operation of the anti-lock brake controller in accordance with the fifth embodiment, showing variations in actual wheel cylinder pressure P_band in estimated mean braking pressure P_mwith time; and

[0259] FIG. 39D is a graph for explaining the result of operation of the anti-lock brake controller in accordance with the fifth embodiment, showing variations in a resonance gain G_dand a reference gain G_swith time.

[0260] An example of application of the present invention to detection of a fault in an active suspension control system in a vehicle will now be described as a first embodiment.

[0261] FIG. 6 shows a specific example of a dynamic system 10 shown in FIG. 1 to be examined in the first embodiment. This dynamic system 10 represents a vibration model of a single wheel suspension unit of the vehicle. In the drawing, a wheel 41 is represented by a combination of an unsprung mass section expressed by a parameter m1 and a spring section of the wheel (or tire) expressed by a spring constant k1. Reference numeral 42 designates a vehicle body having a spring constant m2; 46 designates a gas spring having a spring constant k2; 48 designates a damper having a damping constant Dm; and 56 designates the amount of displacement with reference to the road surface. Further, reference numeral 52 designates unsprung displacement represented by a variable x1; 50 designates sprung displacement represented by a variable x2; 54 designates relative displacement (i.e., x1−x2) represented by a variable “y”; and 44 designates a control force generator which produces active control force “f” required for control operation, from the quantity of actuation “u” output from a controller for controlling the suspension unit.

[0262] At the time of diagnosis of the dynamic system 10, the quantity of actuation (u+Δu) made by addition of another quantity of actuation Δu for vibration purposes to the quantity of actuation “u” is input to the control force generator 44. The control force generator 44 produces active control force (f+Δf) which is the sum of the active control force “f” and vibration control force Δf. As a result, the vehicle body 42 and the wheel 41 are vibrated by the vibration control force Δf around the area displaced by the control force “f.” Further, a white signal or a frequency-shifted signal is used as the quantity of actuation Δu. It is assumed that the displacement occurring in the dynamic system 10 as a result of vibration control force Δf is taken as x0. This value x0 is given by the following equation.

[0263] x0−Δy=Δx1−Δx2

[0264] Since the first embodiment is based on the assumption that the vehicle travels over a road in good condition, the displacement 56 with reference to the road surface is smaller than the displacement x0. Accordingly, external disturbance is ignored (the same applies to other embodiments which will be described below).

[0265] From the drawing, the equation of state 1-1 is represented as follows; $\frac{d}{dt}\left[\begin{array}{c}y\\ \stackrel{.}{y}\\ x_2\\ {\stackrel{.}{x}}_2\\ f\end{array}\right]=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\\ -a& -\mathrm{Dm}-b& k_1/m_1& 0& -b\\ 0& 0& 0& 1& 0\\ k_2/m_2& \mathrm{Dm}/m_2& 0& 0& 1/m_2\\ 0& 0& 0& 0& -1/T\end{array}\right]\left[\begin{array}{c}y\\ \stackrel{.}{y}\\ x_2\\ {\stackrel{.}{x}}_2\\ f\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ 1/T\end{array}\right]u+\left[\begin{array}{c}0\\ k_1/m_1\\ 0\\ 0\\ 0\end{array}\right]x_0$

[0266] where T represents the response time of the control force generator 44; i.e., a time lag between the quantity of actuation “u” and the active control force “f.” Further, “a” and “b” are expressed as

[0267] a=k1/m1+k2/m1+k2/m2

[0268] b=1/m1+1/m2.

[0269] Presumable faults in the first embodiment are an anomaly in the air pressure in a broken tire, an anomalous pressure in the gas spring 46, and a fault in the damper 48. These faults are handled as variations in the respective parameters k1, k2, and Dm. A disturbance observer 32 is formed on the basis of the foregoing vibration model 10.

[0270] More specifically, the parameters k1, k2, Dm exist in the second and fourth elements in the right side of Equation (2-2). Accordingly, the channel along which the internal disturbance stemming from a presumable fault enters the actuation unit is set to these two areas. The channel is set according to the matrix D expressed by Equation (2). In this case, the channel is desirably set in a manner as represented by the following expression. $\begin{array}{cc}{D}_w=\left[\begin{array}{cc}0& 0\\ 1& 0\\ 0& 0\\ 0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{w}_2\\ w_4\end{array}\right]=\left[\begin{array}{c}0\\ w_2\\ 0\\ w_4\\ 0\end{array}\right]& \text{(21)}\end{array}$

[0271] The extended system represented by Equation (4b) is formed through use of the matrix D, and the disturbance observer 32 shown in FIG. 7 is formed.

[0272] In the first embodiment is formed the disturbance observer 32 according to three modes shown below.

[0273] The first mode is a case where all of the sprung displacement x2, sprung speed, relative displacement “y,” relative speed, and active control force “f” in the suspension model 10 can be measured. In this mode, there is no need for the disturbance observer 32 to estimate the internal state quantity of the dynamic system. The sprung speed and relative speed are respectively expressed by the following equations.

[0274] Sprung speed=x₂

[0275] Relative speed=y

[0276] The second mode is a case where only the sprung displacement x2 and the relative displacement “y” can be measured, and the disturbance observer 32 estimates the unmeasurable internal state quantity of other elements in the suspension system (e.g., the sprung speed and the relative speed in this case).

[0277] The third mode is a case where only the sprung displacement x2 and the relative displacement y can be measured, and the disturbance observer 32 estimates the entire internal state quantity of the suspension system including the sprung displacement and the relative displacement.

[0278] The disturbance observer 32 used for each of the foregoing modes and a diagnostic apparatus 30 employing this disturbance observer 32 will be described in detail hereinbelow.

[0279] First Mode

[0280] FIG. 7 shows a block diagram of the diagnostic apparatus 30 used for the first mode. In the drawing, reference 10 designates the dynamic system (a suspension system for a single wheel) shown in FIG. 6; 12 designates a controller for controlling the suspension system; 14 designates the quantity of actuation (u+Δu) output from the controller 12 for controlling the suspension system; and 16 designates the entire internal state quantity of the suspension system measured through use of a sensor (not shown).

[0281] Since the entire internal state quantity of the suspension system is measured through use of the sensor, there is no need for the disturbance observer 32 to estimate a part of, or the entirety of, the internal state quantity of the suspension system, unlike the second and third modes, which will be described later. Reference numeral 17 designates the quantity of actuation “u” input to the disturbance observer 32 from the controller 12. Only the quantity of actuation “u” resulting from subtraction of the vibration input Δu from the quantity of actuation (u+Δu) is input to the disturbance observer 32.

[0282] The disturbance observer 32 in the first embodiment acknowledges, as internal disturbance in the dynamic system 10 to be examined, an anomaly in the air pressure in the tire in the dynamic system 10, an anomaly in the pressure in the gas spring, or a fault in the damper. A total disturbance vector “w”—which is a sum of an vibration disturbance vector and an internal disturbance vector of the dynamic system 10—is estimated from the quantity of actuation 14 of the controller 12 and the entire state quantity 16 of the dynamic system 10, and the thus-estimated total disturbance vector “w” is output to a correlation calculation section 34.

[0283] The correlation calculation section 34 calculates a cross-correlation between the value of the total disturbance vector “w” estimated and calculated by the disturbance observer 32 and the internal state quantity of the dynamic system 10; namely, the sprung displacement, the relative displacement, and the relative speed. At this time, the internal state quantity; i.e., the sprung displacement, the relative displacement, or the relative speed, is irrelevant to vibration disturbance. For this reason, the influence of the vibration disturbance is eliminated from the internal state quantity by calculation of a cross-correlation between the internal state quantity and the estimated value of the total disturbance vector, thereby separating from the internal state quantity the components associated with the internal disturbance stemming from the fault. The result of such calculation can be output to a diagnostic section 36.

[0284] The diagnostic section 36 detects a fault occurring in the dynamic system 10 on the basis of the result of calculation received from the cross-correlation calculation section 34, and localizes a specific location of the fault in the suspension system on the basis of the location of the internal disturbance calculated by the cross-correlation calculation section 34.

[0285] The diagnostic apparatus 30 in accordance with the first embodiment has the aforementioned configuration, and the operation of the diagnostic apparatus 30 will now be described.

[0286] Assume that the presumable fault has arisen in the dynamic system 10 shown in FIG. 6. In such a case, the disturbance observer 32 estimates, from the control input “f” sent to the suspension system 10 and the state of the dynamic system 10, the second and fourth elements w2, w4 of the total disturbance vector previously set according to a fault. At this time, given that lag in the estimation of the disturbance is negligibly small, the estimated value is expressed by the following Equation (22). $\begin{array}{cc}{\hat{w}}_2\cong -\frac{\Delta k_1}{m_1}+\frac{\Delta k_2}{m_1}+\frac{\Delta k_2}{m_2}y-\Delta \mathrm{Dmby}-\frac{\Delta k_1}{m_1}{x}_2+\frac{k_1+\Delta k_1}{m_1}{x}_0& \text{(22)}\\ {\hat{w}}_4\cong \frac{\Delta k_2}{m_1}y+\frac{\Delta \mathrm{Dm}}{m_2}y& \\ {\hat{w}}_1={\hat{w}}_3={\hat{w}}_5=0& \end{array}$

[0287] where {circumflex over (W)}₁, {circumflex over (W)}₂, {circumflex over (W)}₃, {circumflex over (W)}₄, {circumflex over (W)}₅represent estimated values of w₁, w₂, w₃, w₄, and w₅, respectively.

[0288] In Equation (22), Δk1 represents a variation in the parameter stemming from an anomaly in the air pressure in the tire; Δk2 represents a variation in the parameter stemming from an anomaly in the pressure in the gas spring; and ΔDm represents a variation in the parameter stemming from a fault in the damper.

[0289] The thus-estimated total disturbance is a sum of the sum of products—between the variations in the parameters and a variable of state of the suspension system (i.e., the relative displacement “y,” the relative speed of displacement, and the sprung displacement x2)—and the displacement x0 exerted on the suspension system as vibration disturbance.

[0290] On the basis of the estimated total disturbance, the cross-correlation calculation section 34 and the diagnosis section 36 separate the vibration disturbance from the internal disturbance and determines a fault in the following manner.

[0291] First, a correlation function C21 between the estimated value of w2 and the measured value “y,” a correlation function C41 between the estimated value of w4 and the measured value “y,” and a correlation function C42 between the estimated value of w4 and the measured value thereof (i.e., relative speed), are calculated. Although the estimated value of w2 includes vibration disturbance, the influence of displacement stemming from the vibration disturbance irrelevant to the measured value “y” is eliminated by finding the correlation between the measured value “y” and the estimated value of w2. As a result, only the disturbance stemming from the fault is extracted in the form of; e.g, a value of the correlation function C21.

[0292] Next, the fault is localized on the basis of the thus-obtained correlation functions. For example, only the value corresponding to a variation in the gas spring is obtained from the correlation function C41. For this reason, if there is any anomaly in this value, a fault in the gas spring can be localized.

[0293] Similarly, if there is any anomaly in the value of the correlation function C42, the damper is determined to be faulty.

[0294] Finally, an anomaly in the air pressure in the tire is determined by the correlation function C21. If the gas spring is faulty or the air pressure in the tire is anomalous, the correlation function C21 takes on a value. However, a fault in the gas spring is detected by the determination made by the correlation function C41. Hence, if the gas spring is in a normal condition, and there is an anomaly in the value of the correlation function C21, an anomaly in the air pressure in the tire can be determined. If an anomaly in the gas spring and an anomaly in the air pressure in the tire simultaneously arise, it is impossible to distinguish the anomalies from one another. However, such a trouble occurs very rarely, and hence no actual problem arises.

[0295] As described above, the relationship between the estimated value of the total disturbance and the location of a fault can be expressed by a simple mathematical equation in the first embodiment. Consequently, a fault can be localized by executing a simple calculation such as calculation of a correlation between the state of the object to be examined and an estimated value.

[0296] Further, disturbance is imparted to the dynamic system through vibration in the first embodiment even when external disturbance is very small, as in a case where the vehicle travels over a road in good condition. As a result, a reduction in the accuracy of calculation attributable to a reduction in the control output can be prevented. Moreover, as a result of imparting to the dynamic system the vibration disturbance irrelevant to the internal state quantity of the dynamic system, a fault can be highly accurately detected at all times.

[0297] (Second Mode)

[0298] FIG. 8 is a block diagram showing the disturbance observer 32 configured so as to correspond to the previously-described second mode and the diagnostic apparatus 30 employing this disturbance observer 32. The elements which are the same as those shown in FIG. 7 are assigned the same reference numerals, and hence their explanations will be omitted here.

[0299] In the present embodiment, only the sprung displacement x2 and the relative displacement “y” are directly measured, as the internal state quantity of the dynamic system 10, from the dynamic system 10 constituting the vibration model of the suspension system. The internal state quantity of another element in the dynamic system 10; e.g., relative speed, is not directly measured.

[0300] In this case, from the quantity of actuation 14 and the measured value 16, the disturbance observer 32 estimates and calculates the sprung speed, the relative speed, and the active control force among the internal state quantity of the dynamic system 10 which have not yet been measured, as well as the total disturbance vector of the dynamic system 10. The thus-estimated factors are output to the correlation calculation section 36.

[0301] The disturbance observer 32 is designed in the manner as represented by the following equations.

[0302] First, an expanded system of the dynamic system 10 is formed on the basis of Equations (4b), (2), and (21). $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}y\\ y\\ x_2\\ x_2\\ f\\ w_2\\ w_4\end{array}\right]=\left[\begin{array}{ccccccc}0& 1& 0& 0& 0& 0& 0\\ -a& -\mathrm{Dmb}& \frac{k_1}{m_1}& 0& -b& 1& 0\\ 0& 0& 0& 1& 0& 0& 0\\ \frac{k_2}{m_2}& \frac{\mathrm{Dm}}{m_2}& 0& 0& \frac{1}{m_1}& 0& 1\\ 0& 0& 0& 0& \frac{1}{T}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}y\\ y\\ x_2\\ x_2\\ f\\ w_2\\ w_4\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ -\frac{1}{T}\\ 0\\ 0\end{array}\right]u& \text{(23)}\end{array}$

[0303] The measurable state quantities “y” and x2 are separated from the unmeasurable state quantity through use of Equation (23). $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}y\\ x_2\\ \cdots \\ \stackrel{.}{y}\\ {\stackrel{.}{x}}_2\\ f\\ w_2\\ w_4\end{array}\right]=\left[\begin{array}{cccccccc}0& 0& ⋮& 1& 0& 0& 0& 0\\ 0& 0& ⋮& 0& 1& 0& 0& 0\\ \cdots & \cdots & ⋮& \cdots & \cdots & \cdots & \cdots & \cdots \\ -a& -\frac{k_1}{m_1}& ⋮& -\mathrm{Dmb}& 0& -b& 1& 0\\ \frac{k_2}{m_2}& 0& ⋮& \frac{\mathrm{Dm}}{m_2}& 0& \frac{1}{m_2}& 0& 1\\ 0& 0& ⋮& 0& 0& -\frac{1}{T}& 0& 0\\ 0& 0& ⋮& 0& 0& 0& 0& 0\\ 0& 0& ⋮& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}y\\ x_2\\ \cdots \\ \stackrel{.}{y}\\ {\stackrel{.}{x}}_2\\ f\\ w_2\\ w_4\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ \cdots \\ 0\\ 0\\ -\frac{1}{T}\\ 0\\ 0\end{array}\right]u& \text{(3-3)}\end{array}$

[0304] To simplify the expression, Equation (3-3) is transformed in the manner as shown below. $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}{x}_a\\ \cdots \\ x_b\end{array}\right]=\left[\begin{array}{ccc}{A}_{11}& ⋮& A_{12}\\ \cdots & ⋮& \cdots \\ A_{21}& ⋮& A_{22}\end{array}\right]\left[\begin{array}{c}{x}_a\\ \cdots \\ x_b\end{array}\right]+\left[\begin{array}{c}{B}_1\\ \cdots \\ B_2\end{array}\right]u\mathrm{where}{x}_a=\left[\begin{array}{c}y\\ x_2\end{array}\right],x_b={\left[\begin{array}{ccccc}\stackrel{.}{y}& {\stackrel{.}{x}}_2& f& w_2& w_4\end{array}\right]}^T& \text{(4-4)}\end{array}$

[0305] The state quantity xb—which includes total disturbance and is unmeasurable—is estimated through use of the following equation.

[0306] {circumflex over (x)}b=A₂₁x_a+A₂₂{circumflex over (x)}b+B_2u+G{x_a−(A₁₁x_a+A₁₂{circumflex over (x)}b+B₁u)}  (24)

[0307] From Equations (4-4) and (24), an error between a true value xb and an estimated value can be written as

[0308] {circumflex over (x)}_b−xb=A₂₁x_a+A₂₁{circumflex over (x)}_b+B_2u+G{x_a−(A₁₁x_a+A₁₂{circumflex over (x)}_b+B₁u)}−(A₂₁x_a+A₂₂x_b+B₂u)

[0309] =A₂₂({circumflex over (x)}_b−x_b)+G{(A₁₁x_a+A₁₂x_b+B_1u)−(A₁₁x_a+A₁₂{circumflex over (x)}_b+B_1u)}

[0310] =(A₂₂−GA₁₂)({circumflex over (x)}_b−x_b)  (25)

[0311] where {circumflex over (x)}_brepresents an estimate value and Xb represents a true value.

[0312] Consequently, so long as the matrix of real number G is determined in such a way that all the characteristic values of the vector of (A22−GA12) in Equation (25) become negative, the error expressed by Equation (25) converges on zero with time. More specifically, the estimated value converges on a true value.

[0313] Equation (24) can be illustrated such as that shown in FIG. 14. As shown in FIG. 14, the unmeasurable state quantity xb can be estimated through use of the control input “u” and the measurable state quantity xa=[y x2]T.

[0314] As described above, a disturbance observer 32 in the second mode is configured in the form of a minimum dimension observer which estimates the total disturbance “w” and the unmeasurable internal state quantity; e.g., relative speed, from the control input delivered to the suspension system and the measured quantities of internal state x2, y of the suspension system 10. Even in a case where the disturbance observer 32 is formed so as to have the foregoing configuration, the thus-estimated total disturbance can be represented by Equation (22). Consequently, as in the first mode, the diagnosis section 36 can detect and localize a fault as a result of the correlation function being executed by the correlation function calculation section 34.

[0315] More specifically, an estimated value of the relative speed required for correlation calculation is represented by

[0316] Estimated value of {dot over (y)}={circumflex over ({dot over (y)})}

[0317] Accordingly, it is only required that correlation function similar to that performed in the first mode be executed by replacing the relative speed with the estimated value.

[0318] Since the disturbance observer 32 estimates the internal state quantity without any substantial errors even if a fault arises in the dynamic system, a correlation function essentially analogous to that used in the first mode can be obtained even if the correlation is calculated through use of the estimated value in the manner as previously described. After acquisition of the correlation function, the disturbance observer can localize the fault in a manner analogous to that employed in the first mode, and hence its explanation will be omitted here.

[0319] As described above, in the second mode, the state quantity of the dynamic system directly measured through use of a sensor, as well as the internal state quantity of the same estimated by the disturbance observer 32 at the same time it estimated the total disturbance, can be used for calculation of a correlation function in the second mode. Accordingly, even if the entire internal state quantity of the dynamic system 10 to be examined is not directly measured, a fault can be detected in detail.

[0320] (Third Mode)

[0321] FIG. 9 is a block diagram showing the disturbance observer 32 used for the foregoing third mode and the diagnostic apparatus 30 employing the observer 32.

[0322] The third mode is different from the second mode in that the disturbance observer 32 is configured as a complete dimension observer.

[0323] More specifically, the disturbance observer 32 in the third mode is configured so as to estimate the overall disturbance and the entire internal state quantity of the dynamic system 10 from the control input “f” delivered to the suspension system and from the directly-measured internal state quantities x2, y of the dynamic system 10.

[0324] The disturbance observer 32 is designed on the basis of Equations (4b), (2-2), (21), and the following equation. $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}\hat{y}\\ \widehat{\stackrel{.}{y}}\\ {\hat{x}}_2\\ {\widehat{\stackrel{.}{x}}}_2\\ \hat{f}\\ {\hat{w}}_2\\ {\hat{w}}_2\end{array}\right]=\left[\begin{array}{ccccccc}0& 1& 0& 0& 0& 0& 0\\ -a& -\mathrm{Dmb}& \frac{k_1}{m_1}& 0& -b& 1& 0\\ 0& 0& 0& 1& 0& 0& 0\\ \frac{k_2}{m_2}& \frac{\mathrm{Dm}}{m_2}& 0& 0& \frac{1}{m_1}& 0& 1\\ 0& 0& 0& 0& -\frac{1}{T}& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}\hat{y}\\ \widehat{\stackrel{.}{y}}\\ {\hat{x}}_2\\ {\widehat{\stackrel{.}{x}}}_2\\ \hat{f}\\ {\hat{w}}_2\\ {\hat{w}}_2\end{array}\right]+\left[\begin{array}{c}0\\ 0\\ 0\\ 0\\ \frac{1}{T}\\ 0\\ 0\end{array}\right]u+G\left[\left[\begin{array}{c}y\\ x_2\end{array}\right]-\left[\begin{array}{ccccccc}0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0\end{array}\right]\left[\begin{array}{c}\hat{y}\\ \widehat{\stackrel{.}{y}}\\ {\hat{x}}_2\\ {\widehat{\stackrel{.}{x}}}_2\\ \hat{f}\\ {\hat{w}}_2\\ {\hat{w}}_2\end{array}\right]\right]& \text{(5-5)}\end{array}$

[0325] where Λ represents an estimated value, and G represents a matrix of real number having seven rows and two columns.

[0326] Even in this case, a differential equation related to an error between an estimated value and a true value used in Equation (25) is formed, and the matrix of real number G is determined in such a way that all the characteristic value of the vector of the foregoing equation become negative. Although greater absolute values of the characteristic values are more desirable, they are desirably set to about −300 to −700 rad/s.

[0327] In this way, an estimated value represented by the following equation can be calculated from the control input “u” and the estimated values y, x2.

[0328] estimated value [{circumflex over (y)}{circumflex over (y)}{circumflex over (x)}₂{circumflex over (x)}₂{circumflex over (𝑓)}{circumflex over (w)}₂{circumflex over (w)}₄]^τ

[0329] The thus-estimated total disturbance is represented by Equation (22), and hence the correlation function is calculated in a manner analogous to that employed in the first mode. The estimated values of the relative displacement and the relative speed are used for calculation of the correlation function. After the correlation function has been calculated, a fault is localized in a manner analogous to that employed in the first mode.

[0330] As described above, a fault can be localized by use of simple calculation in the third mode. In addition, the disturbance observer 32 employed in the third mode is configured in the form of a complete dimension observer, and hence the procedures required for its configuration are simpler than those required for the minimum dimension observer used in the second mode.

[0331] A second embodiment of the present invention will now be described.

[0332] FIG. 10 shows a specific example of the dynamic system 10 to be examined in the second embodiment which comprises an active suspension system and wheels. The members corresponding to those shown in FIG. 6 are assigned the same reference numerals, and their explanations will be omitted here.

[0333] Such an active suspension system is usually provided with a pressure sensor 60aas a member required for active control of the suspension system. The pressure sensor 60ais provided in the control force generator 16 so as to be able to measure the active control force “f.” Further, acceleration sensors 60band 60care provided for detecting an anomaly in the air pressure in the tire. Both the acceleration sensors 60band 60care provided at the upper end and at the lower end of the suspension spring, respectively, so as to be able to detect the acceleration of vertical vibrations.

[0334] In such a dynamic system 10, the equation of state represented by Equation (16) is specifically expressed in the following form. $\begin{array}{cc}\frac{d}{dt}\left[\begin{array}{c}{\stackrel{.}{x}}_2\\ {\ddot{x}}_2\\ \stackrel{.}{y}\\ \ddot{y}\\ f\end{array}\right]=\left[\begin{array}{ccccc}0& 1& 0& 0& 0\\ 0& 0& \frac{k_2}{m_2}& 0& \frac{-1}{m_{2}T}\\ 0& 0& 0& 1& 0\\ -\frac{k_1}{m_1}& 0& -a& 0& \frac{b}{T}\\ 0& 0& 0& 0& \frac{-1}{T}\end{array}\right]\left[\begin{array}{c}{\stackrel{.}{x}}_2\\ {\ddot{x}}_2\\ \stackrel{.}{y}\\ \ddot{y}\\ f\end{array}\right]+\left[\begin{array}{c}0\\ \frac{-1}{m_{2}T}\\ 0\\ \frac{-b}{T}\\ \frac{1}{T}\end{array}\right]u+\left[\begin{array}{c}0\\ 0\\ 0\\ \frac{k_1}{m_1}\\ 0\end{array}\right]x_0& \text{(26)}\end{array}$

[0335] where a=k₁/m₁+k₂/m₁+k₂/m₂, b=1/m₁+1/m₂, and T represents lag time between the quantity of actuation “u” and the active control force “f.”

[0336] FIG. 11 is a block diagram of the dynamic system in accordance with the second embodiment. As previously mentioned, the suspension system 10 to be examined is configured so as to receive the quantity of actuation (u+Δu) from the controller 12 and to handle the following vector contained in Equation (26) as the internal state quantity.

[0337] x=[{dot over (x)}₂{umlaut over (x)}₂{dot over (y )}{umlaut over (y )}𝑓]^τ

[0338] Of the elements included in the internal state quantity vector “x,” sprung acceleration is directly detected by the acceleration sensor 60bshown in FIG. 10, and sprung speed is calculated by integration of the sprung acceleration. Relative acceleration is calculated from a difference between the unsprung acceleration detected by the acceleration sensor 60cand the sprung acceleration. Further, relative speed is calculated by integration of the relative acceleration. Assume that calculation sections which perform the foregoing calculations are incorporated into the suspension system 10 in accordance with the second embodiment at all times. Accordingly, the output from the suspension system 10 represents the internal state quantity vector included in Equation (26); i.e.,

[0339] x=[{dot over (x)}₂{umlaut over (x )}₂{dot over (y)}{umlaut over (y)}𝑓]^τ

[0340] The controller 12 in accordance with the second embodiment receives the thus-output internal state quantity vector “x” as an input and calculates and outputs the quantity of actuation (u+Δu) used as an input signal of the active suspension system 10.

[0341] The diagnostic apparatus 30 that diagnoses the active suspension system 10 comprises the disturbance observer 32, the correlation calculation section 34, and the diagnostic section 36.

[0342] The disturbance observer 32 is formed so as to receive the output “u” from the controller 12 and the internal state quantity vector “x” output from the active suspension system 10 and estimates and calculates variations in a spring constant k1 of the tire as internal disturbance occurring in the active suspension system 10.

[0343] From the internal state quantity vector “x” output from the active suspension system 10, a state quantity detection section 60 extracts the state quantity which affects the active suspension system 10 as a result of a variation in the air pressure in the tire (i.e., relative speed in this embodiment).

[0344] The correlation calculation section 34 comprises a cross-correlation calculation section 70, a normalization section 72, and an autocorrelation section 74.

[0345] The cross-correlation calculation section 70 calculates and outputs a cross-correlation between the total disturbance estimated by the disturbance observer 32 and the relative speed.

[0346] The autocorrelation calculation section 74 calculates the autocorrelation function of the relative speed.