System and method for dynamically determining vehicle loading and vertical loading distance for use in a vehicle dynamic control system

[0001] This application is a divisional of U.S. application Ser. No. 10/966,395 filed on Oct. 15, 2004, now issued as U.S. Pat. No. 7,668,645, herein incorporated by reference.

[0002] The present invention generally relates to a control apparatus for controlling a system of an automotive vehicle in response to sensed dynamic behavior. The present invention more specifically relates to a method and apparatus for determining vehicle loading and a vertical loading distance and/or the impact of such vehicle loading on the roll dynamics of the vehicle.

[0003] Recently, vehicle roll stability control (RSC) schemes, i.e., U.S. Pat. No. 6,324,446, have been proposed to address the issue of friction-induced rollovers. RSC system includes a variety of sensors sensing vehicle states and a controller that controls a distributed brake pressure to reduce a tire force so the net moment of the vehicle is counter to the roll direction.

[0004] During an event causing the vehicle to roll, the vehicle body is subject to a roll moment due to the coupling of the lateral tire force and the lateral acceleration applied to the center of gravity of the vehicle body. This roll moment causes suspension height variation, which in turn results in a vehicle relative roll angle (also called chassis roll angle or suspension roll angle). The relative roll angle is an important variable that is used as an input to the activation criteria and to construct the feedback brake pressure command, since it captures the relative roll between the vehicle body and the axle. The sum of such a chassis roll angle and the roll angle between wheel axle and the road surface (called wheel departure angle) provides the roll angle between the vehicle body and the average road surface, which is one of the important variables feeding back to the roll stability control module.

[0005] Such a chassis roll angle can be calculated as in U.S. Pat. No. 6,556,908 using the lateral acceleration of the center of gravity of the vehicle body, the roll angular acceleration, and the roll angular velocity, together with vehicle parameters such as the sprung mass, the vehicle body roll moment of inertia, the roll stiffness and damping ratio of the suspensions and the anti-roll-bars, and the distance between the center of gravity of the vehicle body and the floor of the vehicle body. The disclosure of U.S. Pat. No. 6,556,908 is hereby incorporated by reference.

[0006] One problem with using these parameters in the computation is that the aforementioned relative roll angle may vary with the vehicle operating conditions. For example, a 150 pound roof loading for a typical SUV with a curb weight of 5000 pounds may cause more than 30% error in relative roll angle calculations if computed assuming no roof load. From the vehicle mass point of view, although a 150 pound roof loading accounts for only a 3% mass variation over the vehicle curb weight, it could account for a 30% error in the chassis roll computation, which is ten times larger. If the above parameters are fixed at certain nominal values in the RSC system, it is conceivable that optimal control performance may not be achieved under a different loading condition. For example, if the relative roll angle is computed with nominal vehicle loading condition assumptions, without considering roof loading, the relative roll angle may be under estimated for vehicles with roof loadings, which results in a reduced control. That is, the control system may not be as effective as desired. On the other hand, if the relative roll angle is computed with maximum roof loading, it may be over estimated for vehicles without roof loadings causing unintended control. That is, the control system may become too sensitive or intrusive. Therefore, in order to improve the overall performance of the RSC system, it may be desirable to estimate and update the vehicle parameters periodically or adaptively adjust in real time based on the detected roof loading.

[0007] Certain schemes for obtaining vehicle parameters have been disclosed. For example, in U.S. Pat. No. 4,548,079, a method is disclosed for determining vehicle mass directly using engine output torque and vehicle acceleration. Similarly, in U.S. Pat. No. 5,490,063, push force is determined from the driveline torque and gear ratio to obtain vehicle mass. In U.S. Pat. No. 6,167,357, instead of calculating vehicle mass directly, a recursive least square (RLS) algorithm is proposed to estimate both vehicle mass and aerodynamic coefficient online. The latter method is considered to be more reliable since it recursively adjusts for estimation error of the previous estimates. Furthermore, the use of vehicle acceleration, which is usually very noisy, is avoided. The mass estimation schemes proposed in the above-cited patents may not accurately indicate changes to parameters that impact the roll dynamics of the vehicle. For example, a 150 pound roof loading on a 5000 pound SUV, i.e., 3% mass change, might be undetectable in the above schemes due to the potential error in the engine torque, which usually is much larger than 3%. Other error sources include the road grade, the tire rolling radius change due to tire pressure drop and due to the vehicle loading variations and the vehicle drag.

[0008] The above schemes focus mainly on large mass variations which may have significant influences on the vehicle longitudinal dynamics and vehicle fuel consumption. They do not differentiate if the vehicle mass change is due to a floor loading or due to a roof loading. However, in our case, the roof loading causes much more significant roll motion parameter changes than does the same amount of floor loading. That is, there is a need to detect not only the amount of loading (maybe small), but also the location of the loading (the vertical and longitudinal distance of the loading with respect to the vehicle floor or the center of gravity of the vehicle body, for example).

[0009] That is, the prior art does not address vehicle inertia and mass properties with respect to the vehicle body roll and lateral dynamics. The estimation methodologies suggested in the literature have been considering the vehicle longitudinal dynamics and are not appropriate for an RSC system where the lateral and roll dynamics are more important than longitudinal dynamics.

[0010] Furthermore, the other parameters that affect vehicle body roll and lateral dynamics, such as the roll stiffness and damping in the suspensions and the total center of gravity height of the vehicle body with respect to the vehicle floor, the roll moment of inertia, have not been estimated and/or considered in the prior art.

[0011] Therefore, there is a need for a technique that can detect or adaptively update the vehicle parameters, including vehicle loading and loading location, the roll moment of inertia, in order to refine and improve a vehicle control system relating to roll stability control functions.

[0012] It is therefore one object of the invention to provide a system for quantitative characterization of the chassis roll of a vehicle that may be used in conjunction with the roll stability control (RSC) system of the vehicle to determine accurate vehicle roll trending of vehicles with varying inertia parameters due to various loading conditions, adaptively adjust the computation of the chassis roll angle, and/or adaptively adjust the activation criteria for the roll stability control function. More specifically, the present invention seeks to determine the roll condition of a vehicle in response to an additional mass and height of the mass onboard the vehicle so as to determine if a small mass change onboard the vehicle may significantly impact the roll dynamics of the vehicle, such as in the case of a change in the vehicle's roof load. The control system of the vehicle can then make a determination as to how to command appropriate actuators onboard the vehicle in an increasing control sense to thereby more aggressively correct a potential rollover condition, or in a desensitizing control sense to thereby reduce the amount of actuator actuation so as to correct potential false or inappropriate actuator activation.

[0013] In one aspect of the invention, a method of controlling a vehicle includes the step(s) of determining a roll gradient, a roll acceleration coefficient, and/or a roll rate coefficient. That is, the roll acceleration coefficient, the roll gradient, and the roll rate coefficient may be used simultaneously, or in various combinations thereof, to control a safety system on the vehicle.

[0014] In a further aspect of the invention, a method of controlling a safety device on a vehicle includes the steps of determining a composite parameter called a roll gradient, determining another composite parameter called a roll acceleration coefficient, determining an added mass and a height of the added mass on the vehicle from the roll gradient and the roll acceleration coefficient, and controlling the safety device or system in response to and/or according to the added mass and its height on the vehicle.

[0015] In another aspect of the invention, a control system for an automotive vehicle includes a roll rate sensor for generating a roll rate signal, a lateral acceleration sensor for generating a lateral acceleration signal, a longitudinal acceleration sensor for generating a longitudinal acceleration signal, and a yaw rate sensor for generating a yaw rate signal. A safety system and the sensors are coupled to a controller. The controller determines an added mass and a height of the added mass on the vehicle from the roll rate, the lateral acceleration, the longitudinal acceleration, and the yaw rate and then controls the safety system on the vehicle in response to the added mass and its height on the vehicle.

[0016] In another aspect of the invention, a method of controlling a safety device on a vehicle includes the steps of determining different roll conditions onboard the vehicle that are differentiated through determining an added mass and a height of the added mass on the vehicle, and then controlling the safety device or system in response or according to the determined roll condition, which may be caused by an aggressive driving maneuver and enhanced by the added mass at its given height on the vehicle.

[0017] One advantage of the invention is that various vehicle loading conditions can be detected and determined very accurately. Such is true even though vehicle loading conditions (for example, roof loadings) are usually a fraction of a vehicle's total mass (for example, 3% to 6% of the vehicle's curb weight), are difficult to detect when using methods largely involving longitudinal vehicle dynamics, and may cause large (for example, more than 30%) changes in the vehicle's chassis roll angle.

[0018] Other advantages and features of the present invention will become apparent when the detailed written description of a preferred embodiment of the invention set forth below is viewed in conjunction with both the attached drawing figures and the appended claims.

[0027] In the following figures, the same reference numerals will be used to identify the same components. The present invention may be used in conjunction with a rollover control system for a vehicle. The present invention may also be used with a deployment device such as an airbag or active roll bar. The present invention will be discussed below in terms of preferred embodiments relating to an automotive vehicle moving in a three-dimensional road terrain. The present invention is described with respect to determining an added mass and height of the mass. As will be described below the added mass and height may not be directly determined, rather by adaptively updating a roll gradient value, roll acceleration coefficient, roll moment of inertia and/or a roll rate coefficient, the effects of added mass and the height may be included in those values. Such values may also be referred to as an “adaptive” roll gradient, an “adaptive” roll acceleration coefficient, an “adaptive” roll moment of inertia and an “adaptive” roll rate coefficient. The various roll parameters may be referred to as adaptively determined, meaning that such values may change due to a changing mass or load over time. That is, such values are not fixed as has been done in previous systems.

[0028] It should also be noted that while one of the roll gradient, roll acceleration coefficient and roll rate coefficient may be adaptively determined, the other two values may not be adaptive.

[0029] Referring to FIG. 1, an automotive vehicle 10 with a safety system of the present invention is illustrated with the various forces and moments thereon during a rollover condition. Vehicle 10 has front right (FR) and front left (FL) wheel/tires 12A and 12B and rear right (RR) wheel/tires 13A and rear left (RL) wheel/tires 13B, respectively. The vehicle 10 may also have a number of different types of front steering systems 14a and rear steering systems 14b, including having each of the front and rear wheels configured with a respective controllable actuator, the front and rear wheels having a conventional type system in which both of the front wheels are controlled together and both of the rear wheels are controlled together, a system having conventional front steering and independently controllable rear steering for each of the wheels, or vice versa. Generally, the vehicle has a weight represented as Mg at the center of gravity of the vehicle, where g=9.8 m/s² and M is the total mass of the vehicle.

[0030] As mentioned above, the system may also be used with safety systems including active/semi-active suspension systems, anti-roll bar, or airbags or other safety devices deployed or activated upon sensing predetermined dynamic conditions of the vehicle.

[0031] The sensing system 16 is coupled to a control system 18. The sensing system 16 may comprise many different sensors including the sensor set typically found in a roll stability control or a rollover control system (including lateral accelerometer, yaw rate sensor, steering angle sensor and wheel speed sensor which are equipped for a traditional yaw stability control system) together with a roll rate sensor and a longitudinal accelerometer. The various sensors will be further described below. The sensors may also be used by the control system in various determinations such as to determine a lifting event, determine a height and position of a mass, etc. The wheel speed sensors 20 are mounted at each corner of the vehicle and generate signals corresponding to the rotational speed of each wheel. The rest of the sensors of sensing system 16 may be mounted directly on the center of gravity of the vehicle body, along the directions x,y and z shown in FIG. 1. As those skilled in the art will recognize, the frame from b₁,b₂ and b₃ is called a body frame 22, whose origin is located at the center of gravity of the car body, with the b₁ corresponding to the x axis pointing forward, b₂ corresponding to the y axis pointing off the driving side (to the left), and the b₃ corresponding to the z axis pointing upward. The angular rates of the car body are denoted about their respective axes as ω_x for the roll rate, ω_y for the pitch rate and ω_z for the yaw rate. Calculations may take place in an inertial frame 24 that may be derived from the body frame 22 as described below.

[0032] The angular rate sensors and the accelerometers may be mounted on the vehicle car body along the body frame directions b₁,b₂ and b₃ which are the x-y-z axes of the sprung mass of the vehicle.

[0033] The longitudinal acceleration sensor is mounted on the car body located at the center of gravity, with its sensing direction along Maxis, whose output is denoted as a_x. The lateral acceleration sensor is mounted on the car body located at the center of gravity, with its sensing direction along b₂axis, whose output is denoted as a_y.

[0034] The other frame used in the following discussion includes the road frame, as depicted in FIG. 1. The road frame system r₁r₂r₃ is fixed on the driven road surface, where the r₃ axis is along the average road normal direction computed from the normal directions of the four-tire/road contact patches.

[0035] In the following discussion, the Euler angles of the body frame b₁b₂b₃ with respect to the road frame r₁r₂r₃ are denoted as θ_xbr and θ_ybr, which are also called the relative Euler angles (i.e., relative roll and relative pitch angles, respectively).

[0036] Referring now to FIG. 2, roll stability control system 18 is illustrated in further detail having a controller 26 used for receiving information from a number of sensors which may include a yaw rate sensor 28, a speed sensor 20, a lateral acceleration sensor 32, a vertical accelerometer sensor 33, a roll angular rate sensor 34, a steering wheel (hand wheel) angle sensor 35, a longitudinal acceleration sensor 36, a pitch rate sensor 37, steering angle (of the wheels or actuator) position sensor 38, suspension load sensor 40 and suspension position sensor 42. It should be noted that various combinations and sub-combinations of the sensors may be used.

[0037] Lateral acceleration, roll orientation and speed may be obtained using a global positioning system (GPS). Based upon inputs from the sensors, controller 26 may control a safety device 44. Depending on the desired sensitivity of the system and various other factors, not all the sensors 28-42 may be used in a commercial embodiment. Safety device 44 may control an airbag 45 or a steering actuator 46A-46D at one or more of the wheels 12A, 12B, 13A, 13B of the vehicle. Also, other vehicle components such as a suspension control 48 may be used to adjust the suspension to prevent rollover.

[0038] Roll angular rate sensor 34 and pitch rate sensor 37 may sense the roll condition or lifting of the vehicle based on sensing the height of one or more points on the vehicle relative to the road surface. Sensors that may be used to achieve this include but are not limited to a radar-based proximity sensor, a laser-based proximity sensor and a sonar-based proximity sensor. The roll rate sensor 34 may also use a combination of sensors such as proximity sensors to make a roll rate determination.

[0039] Roll rate sensor 34 and pitch rate sensor 37 may also sense the roll condition or lifting based on sensing the linear or rotational relative displacement or displacement velocity of one or more of the suspension chassis components. This may be in addition to or in combination with suspension position sensor 42. The suspension position sensor 42, roll rate sensor 34 and/or the pitch rate sensor 37 may include a linear height or travel sensor, a rotary height or travel sensor, a wheel speed sensor used to look for a change in velocity, a steering wheel position sensor, a steering wheel velocity sensor and a driver heading command input from an electronic component that may include steer by wire using a hand wheel or joy stick.

[0040] The roll condition or lifting may also be sensed by sensing directly or estimating the force or torque associated with the loading condition of one or more suspension or chassis components including a pressure transducer in an act of air suspension, a shock absorber sensor such as a load sensor 40, a strain gauge, the steering system absolute or relative motor load, the steering system pressure of the hydraulic lines, a tire lateral force sensor or sensors, a longitudinal tire force sensor, a vertical tire force sensor or a tire sidewall torsion sensor. The yaw rate sensor 28, the roll rate sensor 34, the lateral acceleration sensor 32, and the longitudinal acceleration sensor 36 may be used together to determine that the wheel has lifted. Such sensors may be used to determine wheel lift or estimate normal loading associated with wheel lift. These are passive methods as well.

[0041] The roll condition of the vehicle may also be established by one or more of the following translational or rotational positions, velocities or accelerations of the vehicle including a roll gyro, the roll rate sensor 34, the yaw rate sensor 28, the lateral acceleration sensor 32, the vertical acceleration sensor 33, a vehicle longitudinal acceleration sensor 36, lateral or vertical speed sensor including a wheel-based speed sensor 20, a radar-based speed sensor, a sonar-based speed sensor, a laser-based speed sensor or an optical-based speed sensor.

[0042] Controller 26 may include a signal multiplexer 50 that is used to receive the signals from the sensors 28-42. The signal multiplexer 50 provides the signals to a wheel lift detector 52, a vehicle roll angle calculator 54, and to a roll stability control (RSC) feedback control command 56. Also, wheel lift detector 52 may be coupled to the vehicle roll angle calculator 54. The vehicle roll angle calculator 54 may also be coupled to the RSC feedback command 56. The RSC feedback command 56 may include a torque controller 57. Vehicle roll angle calculator 54 is described in U.S. Provisional Applications 60/400,376 and 60/400,172, and in U.S. patent application Ser. No. 10/459,697, the disclosures of which are incorporated herein by reference.

[0043] A loading detector 58 may also be included in controller 26. The loading detector 58 may be used to determine an additional mass of the vehicle and a distance of the mass as will be described below.

[0044] In the preferred embodiment, the sensors are located at the center of gravity of the vehicle. Those skilled in the art will recognize that the sensor may also be located off the center of gravity and translated equivalently thereto.

[0045] Safety device 44 may control the position of the front right wheel actuator 46A, the front left wheel actuator 46B, the rear left wheel actuator 46C, and the right rear wheel actuator 46D. Although as described above, two or more of the actuators may be simultaneously controlled. For example, in a rack-and-pinion system, the two wheels coupled thereto are simultaneously controlled. Based on the inputs from sensors 28 through 42, controller 26 determines a roll condition and/or wheel lift and controls the steering position and/or braking of the wheels.

[0046] Safety device 44 may be coupled to a brake controller 60. Brake controller 60 controls the amount of brake torque at a front right brake 62a, front left brake 62b, rear left brake 62c and a rear right brake 62d. Other safety systems such as an antilock brake system 64, a yaw stability control system 66 and a traction control system 68 may also benefit from the knowledge of the roll gradient, roll rate parameter, roll acceleration coefficient, additional mass and position of the mass. This information may impact the control strategy such as modifying the brake force.

[0047] Speed sensor 20 may be one of a variety of speed sensors known to those skilled in the art. For example, a suitable speed sensor may include a sensor at every wheel that is averaged by controller 26. The controller may translate the wheel speeds into the speed of the vehicle. Yaw rate, steering angle, wheel speed and possibly a slip angle estimate at each wheel may be translated back to the speed of the vehicle at the center of gravity. Various other algorithms are known to those skilled in the art. Speed may also be obtained from a transmission sensor. For example, if speed is determined while speeding up or braking around a corner, the lowest or highest wheel speed may not be used because of its error. Also, a transmission sensor may be used to determine vehicle speed.

[0048] Load sensor 40 may be a load cell coupled to one or more suspension components. By measuring the stress, strain or weight on the load sensor a shifting of the load can be determined.

[0049] The roll condition of a vehicle can be characterized by the relative roll angle between the vehicle body and the wheel axle and the wheel departure angle (between the wheel axle and the average road surface). Both the relative roll angle and the wheel departure angle may be calculated in relative roll angle estimation module by using the roll rate and lateral acceleration sensor signals. If both the relative roll angle and the wheel departure angles are large enough, the vehicle may be in either single wheel lifting or double wheel lifting. On the other hand, if the magnitude of both angles is small enough, the wheels are likely all grounded. In case that both of them are not small and the double wheel lifting condition is detected or determined, the sum of those two angles will be used by the feedback control module to compute the desired actuation command for achieving rollover control performance.

[0050] The roll condition of a vehicle can be characterized by rolling radius-based wheel departure roll angle, which captures the angle between the wheel axle and the average road surface through the dynamic rolling radii of the left and right wheels when both of the wheels are grounded. Since the computation of the rolling radius is related to the wheel speed and the linear velocity of the wheel, such rolling-radius based wheel departure angle will assume abnormal values when there are large wheel slips. This happens when a wheel is lifted and there is torque applied to the wheel. Therefore, if this rolling radius-based wheel departure angle is increasing rapidly, the vehicle might have lifted wheels. Small magnitude of this angle indicates the wheels are all grounded.

[0051] The roll condition of the vehicle can be seen indirectly from the wheel longitudinal slip. If during a normal braking or driving torque the wheels at one side of the vehicle experience increased magnitude of slip, then the wheels of that side are losing longitudinal road torque. This implies that the wheels are either driven on a low mu surface or lifted up. The low mu surface condition and wheel-lifted-up condition can be further differentiated based on the chassis roll angle computation, i.e., in low mu surface, the chassis roll angle is usually very small. Hence, an accurate determination of chassis roll is desired.

[0052] The roll condition of the vehicle can be characterized by the normal loading sustained at each wheel. Theoretically, when a normal loading at a wheel decreases to zero, the wheel is no longer contacting the road surface. In this case a potential rollover is underway. Large magnitude of this loading indicates that the wheel is grounded. Normal loading is a function of the calculated chassis roll and pitch angles. Hence, an accurate determination of chassis roll and pitch angles is desired.

[0053] The roll condition can be identified by checking the actual road torques applied to the wheels and the road torques, which are needed to sustain the wheels when they are grounded. The actual road torques can be obtained through torque balancing for each wheel using wheel acceleration, driving torque and braking torque. If the wheel is contacting the road surface, the calculated actual road torques must match or be larger than the torques determined from the nonlinear torques calculated from the normal loading and the longitudinal slip at each wheel.

[0054] The roll condition of a vehicle can be characterized by the chassis roll angle itself, i.e., the relative roll angle θ_xr between the vehicle body and the wheel axle. If this chassis roll angle is increasing rapidly, the vehicle might be on the edge of wheel lifting or rollover. Small magnitude of this angle indicates the wheels are not lifted or are all grounded. Hence, an accurate determination of the chassis roll angle is beneficial for determining if the vehicle is in non-rollover events.

[0055] The roll condition of a vehicle can also be characterized by the roll angle between the wheel axle and the average road surface, this is called wheel departure angle. If the roll angle is increasing rapidly, the vehicle has lifted wheel or wheels and aggressive control action needs to be taken in order to prevent the vehicle from rolling over. Small magnitude of this angle indicates the wheels are not lifted.

[0056] The center of gravity C is also illustrated with nominal mass M. A roll axis is also illustrated at a distance D from the center of gravity. a_y is the lateral acceleration.

[0057] Referring now to FIG. 3, the relationship of the various angles of the vehicle 10 relative to the road surface 11 is illustrated. In the following, a reference road bank angle θ_bank is shown relative to the vehicle 10 on a road surface. The vehicle has a vehicle body 10a and wheel axle 10b. The wheel departure angle θ_wda is the angle between the wheel axle and the road. The relative roll angle θ_xr is the angle between the wheel axle 10b and the body 10a. The global roll angle θ_x is the angle between the horizontal plane (e.g., at sea level) and the vehicle body 10a.

[0058] Another angle of importance is the linear bank angle. The linear bank angle is a bank angle that is calculated more frequently (perhaps in every loop) by subtracting the relative roll angle generated from a linear roll dynamics of a vehicle (see U.S. Pat. No. 6,556,908 which is incorporated by reference herein), from the calculated global roll angle (as in U.S. Pat. No. 6,631,317 which is incorporated by reference herein). If all things were slowly changing without drifts, errors or the like, the linear bank angle and reference road bank angle terms would be equivalent.

[0059] Referring now to FIGS. 4 and 5, an automotive vehicle 10 is illustrated with various parameters illustrated thereon. A change in mass ΔM is illustrated relative to nominal center of gravity C₀. The center of gravity moves to C and the added mass ΔM is added thereto. The change in mass or load ΔM is positioned at a distance H above the load floor 80. The nominal center of gravity C₀ is located at position h above the load floor 80. The distance between the new center of gravity and the nominal center of gravity C₀ is ΔH.

[0060] The longitudinal acceleration is denoted by a_x whereas the longitudinal velocity is denoted v_x. The lateral acceleration and lateral velocity is denoted by a_y,v_y respectively. The steering wheel angle is denoted by δ_w. The wheelbase of the vehicle is denoted by the symbol WB.

[0061] Referring now to FIG. 6, controller 26 is illustrated in further detail. Controller 26 receives the various sensor signals, for example, the roll rate, lateral acceleration, longitudinal acceleration and yaw rate from the respective sensor signals. From the sensor signals, the loading height and amount of loading, the roll gradient, roll rate parameter, roll acceleration coefficient and roll inertia may be determined. These terms may be used to generate a vehicle roll angle compensation term and a roll stability control gain/threshold compensation term. Instead of determining the load and height of the load, an adaptive roll acceleration coefficient and an adaptive roll gradient that inherently have the load and height of the load therein may be determined. As mentioned above, these values in prior systems were fixed without regard to loading. Here they are adaptively determined to correspond to the loading condition. For example, these terms may increase the sensitivity of the system due to a higher center of mass. As will be further described below, the controller uses the roll rate signal and performs a derivative in box 84 to generate the roll acceleration signal {dot over (ω)}_x, which is then filtered by the first filter 86 to generate the variable X, which is provided to a conditionality averaging box 88. The lateral acceleration signal is filtered in the second filter 90 and provided to the conditionality averaging box 88 illustrated as Y. The longitudinal acceleration is filtered in the third filter number 92 and provided to conditionality averaging box 88. As will be further described below, the conditional averaging box generates signals that are coupled to a least squares fit determination 98 which provides variables α and β. The α and β variables are provided to a loading/loading height detection block 100. The conditional averaging block and least squares fit block 98 illustrate a first conditional least square method illustrated by box 99. The loading/loading height detection block 100 generates a vehicle roll angle compensation term 102 and an RSC control gain/threshold compensation term 104.

[0062] Referring now to FIG. 7, the operation of the controller 26 is described in further detail. In step 102, the various sensors such as the roll rate sensor, the lateral acceleration sensor, longitudinal acceleration sensor and yaw rate sensor are read.

[0063] The roll signal for control is calculated as the (θ_x−θ_refbank), i.e., the subtraction of the reference bank angle from the global roll angle. The roll signal for control may be used to control the roll stability control system or other system or device.

[0064] As mentioned above, the various errors not limited to integration, calculation and drift may enter into the various signals at various times. Thus, in certain situations the wheel departure angle or the reference bank angle may not be accurate. The following description describes how these values can be updated in response to wheel lift/wheel grounded values.

[0065] In step 104, the roll gradient, roll acceleration coefficient computation and a roll rate parameter are determined.

[0066] There are two roll angle computations in the roll stability control: one is the relative roll angle as computed in U.S. Pat. No. 6,556,908 and the other is the global roll angle computation as computed in U.S. Pat. No. 6,631,317. U.S. Pat. Nos. 6,556,908 and 6,631,317 are incorporated by reference herein. The relative roll angle is a function of the lateral acceleration a_y, the roll acceleration {dot over (ω)}_x, the roll rate ω_x, the roll gradient α and the roll acceleration coefficient β and a roll rate coefficient η. That is,
θ_xr=ƒ(a_y,{dot over (ω)}_x;α,β,η,ω_x)   (1)

[0067] In z-transformation,
θ_xr=αT_roll(z)a_y−βT_roll(z){dot over (ω)}_x   (2)
where T_roll(z) is a filter which reflects the linear roll model of the vehicle, i.e., it includes the roll stiffness and damping effect due to suspension dynamics. Based on the roll dynamics, the following is true:

[0068] ${\theta }_{\mathrm{xr}}+\frac{D_{\mathrm{roll}}}{K_{\mathrm{roll}}}{\stackrel{.}{\theta }}_{\mathrm{xr}}=\alpha a_y+\beta {\stackrel{.}{\omega }}_x$

[0069] Performing a Laplace transform to convert this equation into the frequency domain equation, leads to the following computation

• • [0070] θ_xr(s)=T_roll(s)(αa_y(s)+β{dot over (ω)}_x(s)) where the transfer function T_roll is

[0071] $T_{\mathrm{roll}}\left(s\right)=\frac{1}{1+\eta s}$
with the roll rate coefficient η is defined as

[0072] $\eta =\frac{D_{\mathrm{roll}}}{K_{\mathrm{roll}}}$

[0073] Using the algorithm shown in U.S. Pat. No. 6,631,317, the global roll angle θ_x (the roll angle of the vehicle body with respect to sea level) can be obtained through an anti-drift integration of the Euler roll angle velocity (which is different from the roll angular rate) and a roll reference signal through a steady-state recovery filter. On level ground when the vehicle does not have wheels in the air, such a calculated global roll angle is the same as the chassis roll angle when the vehicle roll dynamics is within its linear range (for example, the cornering acceleration of the vehicle is under 0.35 g).

[0074] Therefore, on level ground when the vehicle does not have wheels in the air and the vehicle has moderate cornering acceleration, the algorithm used to compute global roll angle as in U.S. Pat. No. 6,631,317 is a function of the roll rate ω_x, the yaw rate ω_z, the relative roll angle θ_xr and the relative pitch angle θ_yr
θ_x=g(ω_y,ω_z,θ_xr,θ_yr)   (3)

[0075] In z-transformation, such a computation can be expressed as in the following format
θ_x=T_adi(z)[ω_x+ω_zθ_yr]+T_ssc(z)θ_xr   (4)
where T_adi(z) is the so-called steady-state recovery filter which is used to recover the good low frequency portion of the roll angle removed by the anti-drift-integration filter. Here the relative roll angle (chassis roll angle) θ_xr is used to recover the true steady state value of the roll angle.

[0076] Notice that on level ground if the vehicle is driven without wheel lifting and with moderate cornering acceleration, the relative roll angle and the global roll angle are equal. Therefore, from equations (1) and (3) or (2) and (4), the relationships between the roll gradient α, the roll acceleration coefficient β, and the roll rate coefficient η may be found.

[0077] Although the computation of the roll gradient α and the roll acceleration coefficient β is the main focus of this disclosure, the roll rate coefficient η can be similarly determined. It can be adaptively determined independent of the determination α and β, or simultaneously determined together with α and β. Likewise α and β can be independently determined.

[0078] Substituting (2) into (4), the following is obtained
θ_x=T_adi(z)[ω_x+ω_zθ_yr]+α·T_ssc(z)T_roll(z)a_y−βT_ssc(z)T_roll(z){dot over (ω)}_x   (5)
where the relative pitch θ_yr is a function of the longitudinal acceleration and the pitch acceleration as in the following (see U.S. Pat. No. 6,556,908 for detail)
θ_yr=m( a_x,{dot over (ω)}_y;κ,λ)   (6)
and which can be further written as
θ_yr=κT_pitch(z)a_x+λT_pitch(z){dot over (ω)}_y   (7)
where T_pitch(z) is a filter which reflects the linear pitch model of the vehicle, i.e., it includes the pitch stiffness and damping effect due to the vehicle suspension dynamics. T_pitch(z) is different for vehicle deceleration and acceleration, i.e.,

[0079] $\begin{array}{cc}{T}_{\mathrm{pitch}}\left(z\right)=\{\begin{array}{cc}{T}_{\mathrm{pitchacc}}\left(z\right)& \mathrm{if}{a}_x>0\\ T_{\mathrm{pitchdec}}\left(z\right)& \mathrm{if}{a}_x\le 0\end{array}& \left(8\right)\end{array}$
and the same is true for the pitch gradient κ and the pitch acceleration coefficient λ

[0080] $\begin{array}{cc}\kappa =\{\begin{array}{cc}{\kappa }_{\mathrm{acc}}& \mathrm{if}{a}_x>0\\ {\kappa }_{\mathrm{dec}}& \mathrm{if}{a}_x\le 0\end{array}\lambda =\{\begin{array}{cc}{\lambda }_{\mathrm{acc}}& \mathrm{if}{a}_x>0\\ {\lambda }_{\mathrm{dec}}& \mathrm{if}{a}_x\le 0\end{array}& \left(9\right)\end{array}$

[0081] If the pitch angular rate ω_y is not available, the above relative pitch θ_yr can be approximated as in the following
θ_yr≈κT_pitch(z)a_x   (10)
which is acceptably accurate at low frequency region (pitch acceleration term only provides high frequency contents).

[0082] By equating (2) and (5) on level ground, θ_x=θ_xr, the following equation is obtained
αX−βY=U   (11)
where
X=T_roll(z)(1−T_ssc(z))a_y
Y=T_roll(z)(1−T_ssc(z)){dot over (ω)}_x
U=T_adi(z)[ω_x+ω_zθ_yr]  (12)

[0083] The following is a summary of the computation algorithm.

[0084] In step 106, the filtered lateral acceleration X is determined in the following iterative equation
X_k=d₁₁X_k-1+d₁₂X_k-2+d₁₃X_k-3+n₁₁a_yk+n₁₂a_yk-1+n₁₃a_yk-2+n₁₄a_yk-3   (13)
where d_{1i ,n1i} for i=1,2,3,4 are the involved first set of the filter coefficients.

[0085] In step 108, the filtered roll acceleration Y as is determined in the following iterative equation
Y=d₁₁Y_k-1+d₁₂Y_k-2+d₁₃Y_k-3+n₁₁{dot over (ω)}_xk+n₁₂{dot over (ω)}_xk-1+n₁₃{dot over (ω)}_xk-2+n₁₄{dot over (ω)}_xk-3   (14)

[0086] In step 110 the filtered roll angle velocity, which is the sum of the roll rate and the product of the relative pitch and yaw rate, may be calculated in the following iterative algorithm
U=d₂₁U_k-1+d₂₂U_k-2+d₂₃U_k-3+n₂₁R_k+n₂₂R_k-1+n₂₃R_k-2+n₂₄R_k-3   (15)
where R_k is the total roll angle velocity at the kth time instant on level ground, i.e.,
R_k=ω_xk+ω_zkθ_yrk   (16)
where d_2i,n_2i for i=1,2,3,4 are the involved 2^nd set of the filter coefficients. If the approximation (10) is used, the total roll velocity on level ground can be approximated as in the following
R_k≈ω_xk+κω_zkT_pitch(z)a_xk   (17)

[0087] Using the calculated filtered value X_k,Y_k and U_k at each sampling instant k, equation (11) can be used to potentially compute the unknown parameters of the roll gradient α, the roll acceleration coefficient β if the roll rate coefficient η is determined independent of the determination of α and β. A more complicated method is needed in order to obtain α, β and η simultaneously. One method to compute the unknown values α and β in equation (11) is the so-called least-square method.

[0088] Since equation (11) is true when the vehicle is driven on level ground and the vehicle does not have any wheel in the air (4 tires are contacting the road), a conditional least-square (CLS) method is used. Two CLS's may be used. The first CLS method conduct α and β parameter updating after a fixed number of conditional samples, while the second method updates α and β and resets a covariance matrix at each conditional sample.

[0089] Referring to FIG. 6A, the second conditional least square method is illustrated by box 250. Blocks 84, 86, 90 are the same as in FIG. 6. This embodiment, however, uses a relative pitch signal instead of the longitudinal acceleration signal. The relative pitch signal and yaw rate signal are multiplied in block 252. The output of block 252 is added to the roll rate in addition to block 95′ and filtered in block 96′. The filtered signals from blocks 86, 90, 96′ are provided to a conditional covariance block 254. The block 254 output is provided to roll gradient, roll acceleration coefficient least square updating block 256, which provides an output to block 100.

[0090] Since α and β are related to the inertia parameters of the vehicle body roll motion, only if the vehicle roll mode is fully excited α and β can be identified correctly through least-square methods. Hence, under the steady-state driving condition, the least-square identification is not conducted. Therefore, a further condition reflecting vehicle roll dynamic condition is needed. Considering the driver's steering input could induce roll dynamics, one of such conditions can be characterized using the steering wheel angle velocity, i.e., only if
|{dot over (δ)}_w|≧δ_wνmin
the CLS method will be conducted, δ_w is the measured steering wheel angle, δ_wνmin is a threshold (for example, 20 degree per second).

[0091] In step 114, the conditional sum of the products or cross products of the above filtered variables are determined over a significant large number N of the conditional samples. This is performed using the following iterative algorithm if the first CLS method is used

[0092] $\begin{array}{cc}\mathrm{if}\left({\stackrel{.}{\delta }}_w\ge {\delta }_{\mathrm{wv}\min }\&\mathrm{level}\mathrm{ground}\text{}\&\mathrm{no}\mathrm{wheel}\mathrm{lifting}\text{}\&s\le N\right)\{a_{{11}_{s+1}}=a_{{11}_s}+X_k^2{a}_{{21}_{s+1}}=a_{{21}_s}-X_k{Y}_k{a}_{{22}_{s+1}}=a_{{22}_s}+Y_k^2{b}_{1_{s+1}}=b_{1_s}+X_k{U}_k{b}_{2_{s+1}}=b_{2_s}-Y_k{U}_{k}s=s+1\}& \left(18\right)\end{array}$

[0093] Notice that the time instant denoted by k is different from the CLS updating instant denoted by s. Only if the conditions are satisfied all the time, then s=k. N in (18) is the total number of conditional samples used for CLS, which could have value ranged from 1000 to 80,000.

[0094] Step 114 is performed for the conditional sample when the road is a level ground. The level ground can be identified if there is an indication that the vehicle is not on a significantly banked road. Therefore, checking road bank can be used for this purpose, for example, using the method disclosed in U.S. Pat. No. 6,718,248. The level ground can also be checked through a flatness index (as the one calculated in U.S. Pat. No. 6,718,248), or a road profile detection (see U.S. Pat. No. 6,718,248), or a rough comparison between the global roll angle and the nominal chassis roll angle.

[0095] In step 116, the nominal values for α₀ and β₀ of the roll gradient and roll acceleration coefficient are calculated. They can also be obtained by using test data from the vehicle with nominal loading condition and nominal configuration.

[0096] In step 118, the roll gradient α and the roll acceleration coefficient β are computed as in the following

[0097] $\begin{array}{cc}\mathrm{if}s=N\{D=\min \left(\max \left(a_{{11}_N}-\frac{a_{{21}_N}^2}{\max \left(a_{{22}_N,}{a}_{\min }\right)},-a_{\min }\right),a_{\min }\right);\alpha =\min \left(\max \left(\left(b_{1_N}-\frac{a_{{21}_N}{b}_{2_N}}{\max \left(a_{{22}_N},a_{\min }\right)}\right)D^{-1},\underset{\_}{\alpha }\right),\stackrel{\_}{\alpha }\right);\beta =\min \left(\max \left(\left(\begin{array}{c}\frac{a_{{11}_N}{b}_{2_N}}{\max \left(a_{{22}_N},a_{\min }\right)}-\\ \frac{a_{{21}_N}{b}_{1_N}}{\max \left(a_{{22}_N},a_{\min }\right)}\end{array}\right)D^{-1},\underset{\_}{\beta }\right),\stackrel{\_}{\beta }\right);s=0;a_{{11}_s}=0;a_{{21}_s}=0;a_{{22}_s}=0;b_{1_s}=0;b_{2_s}=0;\}& \left(19\right)\end{array}$
where a_min is a small number (for example, 0.0001), which is used to remove division by zero in the implemented computation; α and α are the respective lower and upper bounds of the roll gradient, which can be calculated as
α=α₀−Δα
α=α₀+Δα  (20)
and α₀ is the nominal value of the roll gradient (obtained through vehicle testing for the vehicle with nominal loading), Δα is the allowed variation of the roll gradient; β and β are the respective lower and upper bounds of the roll acceleration coefficient, which can be obtained as
β=β₀−Δβ
β=β₀+Δβ  (21)
and β₀ is the nominal value of the roll acceleration coefficient (for vehicle with nominal loading), Δβ is the allowed variation of the roll acceleration coefficient. If the second CLS method is used, the roll gradient α and the roll acceleration coefficient β can be calculated in block 256 through the following iterative algorithm. First, a 2 by 2 matrix variable V_s+1 at the (s+1)th conditional time instant is calculated from its past value V_s and the calculated filtered values of X_k and Y_k as in the following

[0098] $\begin{array}{cc}\mathrm{if}\left({\stackrel{.}{\delta }}_w\ge {\delta }_{\mathrm{wv}\min }\&\mathrm{level}\mathrm{ground}\text{}\&\mathrm{no}\mathrm{wheel}\mathrm{lifting}\&s\le N\right)\{\mathrm{if}\left(s=0\right)\left\{V_0=\left[\begin{array}{cc}{v}_0& 0\\ 0& v_0\end{array}\right];\right\}{V}_{s+1}=V_s-g\frac{V_s\left[\begin{array}{cc}{X}_k^2& -X_k{Y}_k\\ -X_k{Y}_k& Y_k^2\end{array}\right]V_s}{1+\gamma \left[\begin{array}{cc}{X}_k& -Y_k\end{array}\right]{V_s\left[\begin{array}{cc}{X}_k& -Y_k\end{array}\right]}^T};\}& \left(22\right)\end{array}$
where g, γ and ν₀ are three positive numbers, and the time instant k denotes the regular time instant and the time instant s is the conditional time instant. Equation (22) is also called the covariance resetting in the normalized least square algorithm.

[0099] The roll gradient and the roll acceleration coefficient are calculated using the 2 by 2 matrix V_s, and the calculated filtered values X_k, Y_k and U_k, as in the following

[0100] $\begin{array}{cc}\mathrm{if}\left({\stackrel{.}{\delta }}_w\ge {\delta }_{\mathrm{wv}\min }\&\mathrm{level}\mathrm{ground}\text{}\&\mathrm{no}\mathrm{wheel}\mathrm{lifting}\&s\le N\right)\{\left[\begin{array}{c}{\alpha }_{s+1}\\ {\beta }_{s+1}\end{array}\right]=\left[\begin{array}{c}{\alpha }_s\\ {\beta }_s\end{array}\right]-g\frac{{S_s\left[\begin{array}{cc}{X}_k& -Y_k\end{array}\right]}^T{U}_k}{1+\gamma \left[\begin{array}{cc}{X}_k& -Y_k\end{array}\right]{S_s\left[\begin{array}{cc}{X}_k& -Y_k\end{array}\right]}^T};s=s+1;\}& \left(23\right)\end{array}$

[0101] The calculated values are also limited to within their feasible sets as in the following
α_s−1=sat(α_s+1,α₀−Δα,α₀+Δα)
β_s+1=sat(α_s+1,β₀−Δβ,β₀+Δβ)   (24)

[0102] Notice that during the time instant where the conditions for (22) and (23) do not hold, the computations are frozen to the last values. That is if the following conditions are not true at a time instant k

[0103] $\begin{array}{cc}\left({\stackrel{.}{\delta }}_w\ge {\delta }_{\mathrm{wv}\min }\&\mathrm{level}\mathrm{ground}\text{}\&\mathrm{no}\mathrm{wheel}\mathrm{lifting}\&s\le N\right)& \left(25\right)\end{array}$
then computation in (2), (23) and (24) are not conducted, and the involved variables will keep the values for the last conditional sample s
V_k=V_s;
α_k=α_s;
β_k=β_s.   (26)

[0104] From the calculated roll gradient and the roll acceleration coefficient, the vehicle loading and its distance to the center of gravity of the vehicle body in the vertical direction can be determined in the following in step 122.

[0105] From FIG. 4, M_s is the vehicle body mass and the height of the center of gravity C₀ of the car body is denoted as h which is measured in the vertical direction with respect to the vehicle floor. A loading of mass ΔM is added to the vehicle. The distance between the center of gravity of this mass relative to the vehicle floor is denoted as H. The center of gravity C of the vehicle body is likely to change due to the added mass ΔM. The distance between C₀ and C is denoted as ΔH. Then ΔH must satisfy the following relationship

[0106] $\begin{array}{cc}\Delta H=\frac{\Delta M}{M_s+\Delta M}\left(H-h\right)& \left(27\right)\end{array}$
that is, the unknown ΔH can be readily obtained from the added mass ΔM, the height of the added mass H, the center of gravity height h of the vehicle body and the vehicle mass M_s prior to the addition of the mass ΔM.

[0107] The total roll inertial momentum of the vehicle body with respect to the final center of gravity C can be expressed as
I_xc=I_xc^M+I_xc^ΔM   (28)
where
I_xc^M=I_xc0+M_sΔH²
I_xc^ΔM=ΔM(H−h−ΔH)²   (29)

[0108] By inserting equation (27) into equation (29), equation (28) can be expressed as the following

[0109] $\begin{array}{cc}{I}_{\mathrm{xc}}=I_{\mathrm{xc}0}+\frac{M_s\Delta {M\left(H-h\right)}^2}{M_s+\Delta M}& \left(30\right)\end{array}$

[0110] The nominal roll gradient and the roll acceleration coefficient is α₀ and β₀. Then

[0111] $\begin{array}{cc}{\alpha }_0=\frac{M_{s}h}{K_{\mathrm{roll}}}{\beta }_0=\frac{I_x}{K_{\mathrm{roll}}}& \left(31\right)\end{array}$
where K_roll denotes the roll stiffness due to suspension and anti-roll bar. Using those nominal values and the calculated values α and β, the loading mass and the loading distance satisfy the following

[0112] $\begin{array}{cc}\Delta \mathrm{MH}=K_{\mathrm{roll}}\left(\alpha -{\alpha }_0\right)=A\frac{\Delta {{\mathrm{MM}}_s\left(H-h\right)}^2}{M_s+\Delta M}=K_{\mathrm{roll}}\left(\beta -{\beta }_0\right)=B& \left(32\right)\end{array}$

[0113] From the relationship in equation (32), the following estimations may be determined

[0114] $\begin{array}{cc}\{\begin{array}{c}H=h+\frac{B}{2A}+\sqrt{\frac{1}{4}{\left(\frac{B}{A}\right)}^2+h\left(\frac{B}{A}\right)+{\left(\frac{B}{M_s}\right)}^2}\\ \Delta M=\frac{\alpha }{h+\frac{B}{2\alpha }+\sqrt{\frac{1}{4}{\left(\frac{B}{A}\right)}^2+h\left(\frac{B}{A}\right)+{\left(\frac{B}{M_s}\right)}^2}}\end{array}& \left(33\right)\end{array}$

[0115] In step 124, the height H of the added mass (ΔM) from the vehicle floor based on the first equation of (33) is determined.

[0116] In step 126, the added mass ΔM is determined based on the second equation of (33) by using the calculated height H of the added mass.

[0117] In step 128, a safety system such as a roll stability control system is controlled in response to the added mass and the height of the added mass. The safety system may also be controlled directly from the roll gradient and roll rate parameter, both of which may be adaptive. The safety system may also include the roll acceleration coefficient, which may also be adaptive as a factor in addition to the adaptive roll gradient and adaptive roll rate parameter. A vehicle roll angle compensation term may be determined such as that shown above. The vehicle roll angle compensation term may sensitize the roll angle computation for earlier deployments. The amount of roll compensation will depend on the particular vehicle and the characteristics of such things as the suspension and configuration of the vehicle. A roll stability control gain/threshold compensation term may also be generated. The threshold may be changed to allow earlier deployment if an added mass at a predetermined height is determined in steps 124 and 126. The amount of compensation will likely be determined experimentally based on the vehicle configuration.

[0118] Thus, as can be seen, the roll signal for control may be adjusted according to the vehicle loading and its height. On the other hand if the vehicle has a significant amount of loading, i.e., the calculated loading exceeds a threshold L_max
ΔM≧L_max   (34)
and at the same time the height of the mass exceeds another threshold H_max
H≧H_max   (35)
then in addition to the adjusted computation of roll signal for control (through the adjustment of the chassis roll angle using the new roll gradient and roll acceleration coefficient), all the gains for the feedback control used for commanding the actuators are set to a set of values G_RLMAX tuned for larger roof loadings, or adaptively adjusted in high values based on the amount of ΔM. In this way, when the vehicle has double wheel lift, the proper amount of actuation will be requested so the vehicle achieves robust roll stability control function during rollover event involving vehicles with large roof loadings.

[0119] If the vehicle has a significant loading, i.e., ΔM≧L_max, but the loading is a floor loading, that is, the height of the loading is smaller than a lower threshold H_min
H≦H_min   (36)
all the gains for the feedback control used for commanding the actuators are set to a set of values G_FLMAX tuned for larger floor loadings.

[0120] If the vehicle has a significant loading, i.e., ΔM≧L_max, but the loading height is between the roof and floor, i.e., H is between a lower threshold H_min (possibly zero) and the higher threshold H_max
H_min≦H≦H_max   (37)
all the gains for the feedback control used for commanding the actuators are set to the following values adjusted based on the detected loading height as in the following

[0121] $\begin{array}{cc}{G}_H=G_{\mathrm{FLMAX}}+\frac{H-H_{\min }}{H_{\max }-H_{\min }}\left(G_{\mathrm{RLMAX}}-G_{\mathrm{FLMAX}}\right)& \left(38\right)\end{array}$

[0122] If the vehicle has a roof loading which is below the maximum allowed roof loading L_max but above the lower bound of a valid roof loading L_min, i.e.,
L_min≦ΔM≦L_max   (39)

[0123] Assume all the nominal gains for feedback (for the vehicle with nominal loading) are denoted as G_nom, then the control gains will be adjusted based on the detected roof loading as in the following

[0124] $\begin{array}{cc}{G}_{\Delta M}=G_{\mathrm{nom}}+\frac{\Delta M-L_{\min }}{L_{\max }-L_{\min }}\left(G_{\mathrm{RLMAX}}-G_{\mathrm{nom}}\right)& \left(40\right)\end{array}$

[0125] The roll gradient itself can also be directly used to adjust control gains. If the vehicle has a significant increase of roll gradient, i.e., α≧α_min, then all the gains for the feedback control used for commanding the actuators are set to the following values adjusted based on the detected roll gradient as in the following

[0126] $\begin{array}{cc}{G}_{\alpha }=G_{\alpha \mathrm{MIN}}+\frac{\alpha -{\alpha }_{\min }}{{\alpha }_{\max }-{\alpha }_{\min }}\left(G_{\alpha \mathrm{MAX}}-G_{\alpha \mathrm{MAX}}\right)& \left(41\right)\end{array}$

[0127] where α_min is the roll gradient corresponding to a vehicle without roof loading and α_max is the roll gradient corresponding to the vehicle with maximum roof loading allowed.

[0128] Notice that the control gain adjustments other than the above listed linear interpolation methods are possible. Also, notice that the dead-bands and thresholds used in roll stability feedback control can also be similarly adjusted based on the loading height H and/or the loading ΔM, or the roll gradient, or the roll moment of inertia calculated as in (30).

[0129] Combining those control gain, dead-band and threshold adjustments with the quantitative roll angle (for example, the chassis roll) adjustment, a robust roll stability control function can be achieved.

[0130] Notice that based on the afore-mentioned computation of the added mass and its vertical from the vehicle floor, the roll moment of inertia of the vehicle body can be readily calculated as in (30). Alternatively, the roll moment of inertia I_xx can be determined directly by using the equation
M_sa_yh_cg−K_rollθ_xr−D_roll{dot over (θ)}_xr=I_xx{dot over (ω)}_x   (42)
where M_s is vehicle mass, a_y is the measured lateral acceleration, h_cg is the center of mass height above the roll center, K_roll is the roll stiffness of the suspension, θ_xr is the relative roll of the body with respect to the wheels (or ground), D_roll is the roll damping of the suspension, {dot over (θ)}_xr is the relative roll velocity and {dot over (ω)}_x the roll acceleration (obtained by differentiating the roll rate obtained from the roll rate sensor), and I_xx the roll inertia, in kg-m².

[0131] When a_y and θ_xr are zero but {dot over (θ)}_xr and {dot over (ω)}_x are non-zero, then
I_xx=−D_roll{dot over (θ)}_xr/{dot over (ω)}  (43)

[0132] Or, when θ_xr and {dot over (θ)}_xr are zero and the mass, M_s is determined by another means,
I_xx=M_sa_yh_cg/{dot over (ω)}_x   (44)

[0133] Alternatively, the roll response of the vehicle, obtained from the roll rate sensor, can be analyzed in the frequency domain to determine roll gradient and roll acceleration coefficient:

• • [0134] ω_d=the damped natural frequency of the roll motion of the vehicle (Hz)
  • [0135] ω_n=the undamped natural frequency of the roll motion of the vehicle (Hz)
  • [0136] ζ=the damping ratio of the roll motion of the vehicle (unitless)

[0137] Taking the Laplace transform of

[0138] $\begin{array}{cc}{\theta }_{\mathrm{xr}}+\frac{D_{\mathrm{roll}}}{K_{\mathrm{roll}}}{\stackrel{.}{\theta }}_{\mathrm{xr}}=\frac{M_s{h}_{\mathrm{cg}}}{K_{\mathrm{roll}}}{a}_y-\frac{I_{\mathrm{xx}}}{K_{\mathrm{roll}}}{\stackrel{.}{\omega }}_x& \left(45\right)\end{array}$

[0139] and rearranging yields the following by considering {dot over (ω)}_x≈{umlaut over (θ)}_xr when the vehicle does not have large pitch motion or the vehicle does not have large yaw rate:

[0140] $\begin{array}{cc}\begin{array}{c}\frac{{\Theta }_{\mathrm{xr}}\left(s\right)}{A_y\left(s\right)}=\frac{1}{\frac{I_{\mathrm{xx}}}{M_s{h}_{\mathrm{cg}}}{s}^2+\frac{D_{\mathrm{roll}}}{m_s{h}_{\mathrm{cgs}}}s+\frac{K_{\mathrm{roll}}}{m_s{h}_{\mathrm{cgs}}}}\\ =\left(\frac{M_s{h}_{\mathrm{cg}}}{K_{\mathrm{roll}}}\right)\frac{1}{\frac{I_{\mathrm{xx}}}{K_{\mathrm{roll}}}{s}^2+\frac{D_{\mathrm{roll}}}{K_{\mathrm{roll}}}s+1}\end{array}& \left(46\right)\end{array}$
where Θ_xr(s) and A_y(s) are the Laplace transform of the θ_xr and a_y respectively.

[0141] Using a digital fast Fourier transform to construct a frequency response function and determine the magnitude of

[0142] $\frac{{\Theta }_{\mathrm{xr}}\left(s\right)}{A_y\left(s\right)}$

[0143] vs. frequency, the roll gradient is equal to the DC gain (Equation 7 evaluated at s=0).

[0144] The peak of the magnitude of the frequency response function will occur at the damped natural frequency,
ω_d=ω_n√{square root over (1−ζ²)}  (47)
where ω_n is the undamped natural frequency and ζ is the damping ratio. (Alternatively, the damped natural frequency can be determined from “impulse-like” inputs into the suspension (hitting a bump in the road or a pot-hole), and determining the frequency of the roll oscillations.)
From (45)

[0145] $\begin{array}{cc}{\omega }_n=\sqrt{\frac{K_{\mathrm{roll}}}{I_{\mathrm{xx}}}}\Rightarrow \frac{I_{\mathrm{xx}}}{K_{\mathrm{Roll}}}=\frac{1}{{\omega }_n^2}=-\beta & \left(48\right)\\ ϛ=\frac{{\omega }_n{D}_{\mathrm{roll}}}{2K_{\mathrm{roll}}}& \left(49\right)\end{array}$
Substituting Equation (49) into Equation (47) gives

[0146] $\begin{array}{cc}{\omega }_d={\omega }_n\sqrt{1-\frac{{\omega }_n{D}_{\mathrm{roll}}^2}{2K_{\mathrm{roll}}}}& \left(50\right)\end{array}$

[0147] Equation (50) can be solved for ω_n, which can in turn be used to evaluate Equation (48) and solve for the roll acceleration coefficient β.

[0148] Another way to determine roll inertia is to use an indirect empirical approach. First, a mass is determined, then the inertia may be correlated to mass. That is, a first estimate mass is determined via a method such as that described in Invention Disclosure (203-0482) filed as U.S. patent application Ser. No. 10/849,590, the disclosure of which is incorporated by reference herein, or another method. Then the inertia may be obtained per various methods explained below:

[0149] a. Assume inertia changes as mass changes from its base values, M_s—base to the current value, M_s—current as:
I_xx—total=I_xx—base+h₂(M_s—current−M_sbase)   (51)
where h₂ is assumed to be a constant. Based on testing for a vehicle loaded several ways, an average may then be used.

[0150] b. Correlate roll inertia, I_xx, to vehicle mass; e.g., via testing using a vehicle inertial measurement facility to get roll inertia, the mass for various loading conditions and roof loads may be correlated. This is based on the premise that you can only load an SUV so many ways (e.g., mass above curb loading must be placed in vehicle seats and/or on the roof rack). Again, the vehicle mass may be determined via a method described in U.S. patent application Ser. No. 10/849,590 or another method, then use the roll inertia, I_xx, corresponding to that mass obtained from testing.

[0151] The currently estimated mass or roll inertia estimate can be used several ways in the RSC algorithm, including:

[0152] Improved state estimation: Since mass and inertia values are used in the roll, pitch, and yaw angle state estimates, values accurately reflecting the actual vehicle will improve the accuracy, improve RSC control, and reduce the occurrence of false interventions.

[0153] Modified thresholds for activation: For example, a fully loaded vehicle can be less stable in roll. Hence, tighter thresholds on roll angle and roll rate, for example, can be used. This will increase the level of RSC control for the same level of roll angle and velocity for the loaded vehicle.

[0154] c. Increased gains for the RSC PID and/or Transition controllers.

[0155] d. Less stringent entry conditions for PID or Transition control intervention.

[0156] e. Any combination of the above.

[0157] While particular embodiments of the invention have been shown and described, numerous variations and alternate embodiments will occur to those skilled in the art. Accordingly, it is intended that the invention be limited only in terms of the appended claims.