Reduction of Computational Burden of Adaptively Updating Control Filter(s) in Active Systems

This invention relates to the area of active control methods and apparatus for control of noise and vibration. Specifically, the invention relates to means and apparatus for adaptively updating one or more control filters used in active noise and/or vibration control systems.

Active vibration isolation and sound isolation systems inject active forces and/or acoustic noise to effectively cancel noise and/or vibration at one or more defined locations. Hereafter, in the description, the plural will be used as meaning one or more. The noise and/or vibration emanates from a source of disturbance such as an engine. These active systems utilize microprocessors to calculate the appropriate response to eliminate, or at least to substantially minimize, mechanical vibration or ambient noise levels. Typical examples of active systems include systems which reduce noise and/or vibration experienced within an aircraft cabin or within an automobile passenger compartment. Generally, these active control systems are responsive to at least one input or reference signal and/or an error sensor signal. Typical devices for supplying these reference and error signals include microphones, accelerometers, force sensors, and the like.

Examples of active systems are taught in U.S. Pat. Nos. 4,677,676 and 4,677,677 to Eriksson, the disclosures of which are hereby incorporated by reference herein. Further examples include U.S. Pat. Nos. 4,417,098, 4,153,815 and 4,122,303 to Chaplin et al., 4,232,381 to Rennick et al., 4,083,433 to Geohegan, Jr. et al., 4,878,188 to Ziegler, Jr., 4,562,589 and 4,473,906 to Warnaka et al., 5,170,433 to Elliott et al., 4,689,821 to Salikuddin et al., 5,174,552 to Hodgson, and 5,133,527 to Chen et al. In these types of active systems, the algorithm used for control can be least mean square (LMS), Filtered-X LMS, Filtered-U, Newton's Raphson method, or other like gradient descent methods. For background, the Filtered-x LMS algorithm is described herein.

In active control systems, control filters such as finite impulse response (FIR) filters or infinite impulse response (IIR) filters are used. For example, a filtered-x system will include at least one control filter and at least one x-filter. The x-filter models the frequency response of the plant whereas the control filter transforms the input or reference signal into an output signal for driving an output device. In a single-input single-output (SISO) system illustrated in FIG. 1 utilizing the Filtered-x Least Means Square (LMS) algorithm, there is a feed-forward control filter A.sub.N,k and an x-filter C.sub.M. The x-filter information R.sub.k and error signal e.sub.k information from an error sensor are used in an update calculation method utilizing an equation such as: A.sub.k+1 =A.sub.k -.mu.e.sub.k R.sub.k. The result of the update calculation method is used to adaptively update the coefficients or taps of the feed-forward control filter A.sub.N,k as indicated by the arrow. The Filtered-x LMS algorithm is fully described in "Adaptive Signal Processing" by B. Widrow and S. D. Steam, 1985.

FIG. 2 illustrates an active control system of the prior art which includes on-line identification of the x-filter model. This method is fully described in relation to FIG. 20 of U.S. Pat. No. 4,677,676 to Eriksson. Utilizing the numerals used in the '676 patent for reference, the Eriksson invention provides an active attenuation system and method for attenuating an undesirable acoustic wave by producing a canceling output acoustic wave from an output transducer 14. The key is that the invention models the feedback path 20, error path 56 and the output transducer 14 in an on-line fashion. In essence, the pre-training step previously required was eliminated, such that the active system may update itself for changes in the dynamic system due to temperature, etc.

The acoustic system is modeled by adaptive filter model 40 provided by filters 12 and 22 and having a model input at 42. The model 40 outputs a correction signal at 46 to the output transducer 14 to introduce a correction signal to drive the error signal 44 to zero. The auxiliary noise source 140 introduces noise into the adaptive filter model 40. The noise source is a low level random uncorrelated noise source. Model 142 models the error path 56 on-line. A copy of S'E' is copied to 144 and 146 to compensate for the output transducer 14 and the error path 56. The error signal 44 is used with the output of the copy 144 and 146 at junctions 72 and 76 to provide update signals to the A and B filters. The novel feature of this invention is that it requires no calibration, no pre-training of weights, and no start-up procedure as all updates are achieved on-line.

In multiple-input multiple-output (MIMO) systems such as described in U.S. Pat. No. 5,216,722 to Popovich and U.S. Pat. No. 5,216,721 to Melton, the disclosures of which are hereby incorporated by reference herein, a feed-forward control filter is associated with each reference sensor/output device pair. Also, there is one x-filter associated with each output device/sensor pair. The coefficients or tap weights of each feedforward control filter must be calculated and updated in real time.

A typical MIMO system would have N.sub.a output devices, N.sub.s error sensors, and N.sub.r reference sensors. As a result, there will be (N.sub.a .times.N.sub.r) control filters and (N.sub.a .times.N.sub.s) x-Filters. For example, systems utilizing 16 error sensors, 16 reference sensors, and 16 output devices, such as might be found in a typical MIMO system, there will be 256 control filters and 256.times.-filters. Each of the x-filter models may be developed on-line or off-line by pre-training and represents an estimate of the impulse response between each corresponding error sensor and output device. A matrix of information from the reference sensors is input into the x-filters. The x-filter output information is then used, along with the error sensor matrix information, to calculate the updated coefficients for each of the feed-forward control filters according to an update method. Again, this is known as adaptively updating the control filter tap weights.

Typically, the x-filters are such that they model the plant over the entire frequency range of interest. Because of this, a large stream of frequency response information is developed to model the plant over this wide frequency range. These data streams may include hundreds of samples. As a result, the amount of information provided to the update calculation from the x-filters can be enormous. This results in the need for very fast, expensive microprocessors, or multiple microprocessors or CPU's to provide the required computing power to be able to update the control filter coefficients adequately. Because the computational burden for MIMO systems is so large, typically the control filters are only updated in a round-robin fashion.

In other words, not all the control filters are updated each update cycle in MIMO systems. For example, only two control filters may be updated each update cycle, and a different two control filters are updated the next cycle. As should be apparent, the computational burden becomes very large for MIMO systems, and as a result, adaptively updating of the feed-forward control filters cannot be accomplished very frequently. This causes both the convergence time and the level of noise/vibration cancellation achievable to suffer.

The present invention provides the method and apparatus for reducing the computational burden required to update control filters in an active control system by reducing the size of the filter models that are used for providing information to the update calculation method. For example, in x-filter systems, reducing the length, i.e., the size, of the x-filters allows a system to adapt to changes in the error path more effectively and quickly. In another aspect of the present invention, the reduction technique for reducing the size of the models takes place in an on-line fashion within a reduction block. This method and apparatus has particular applicability for systems having four or less discreet and dominant tones, i.e., tonal systems. However, the apparatus and method may also be used in systems having many tones.

For x-filter systems, this method reduces the length of the x-filters and therefore reduces the computational burden required of the microprocessor to perform the update calculation to update the control filters. These reduced or shortened x-filter models can have up to 25 times fewer values than prior art long x-filter models. This is especially true in tonal systems having a few discreet and dominant tones to be controlled. Fewer values means reduced number of calculations are required to adaptively update the control filters. Because of the shortened length, more updates per unit of time can be achieved, thus providing better control of noise and/or vibration, or in the alternative, allowing the use of smaller and less expensive micro-processors or a smaller number of microprocessors. Of course all of the above making reference to filtered-x feed-forward systems have applicability to feed-back type systems also, as will be described later. Further, the present invention reduction method has applicability in MIMO systems as well.

The key to the present invention is that the long filter models are transformed into shortened or reduced filter models within the reduction block. The reduction method has particular applicability in tonal systems that contain four or less discreet and dominant tones. As a result of the smaller dimensional size, the calculations required to update the coefficients of the control filters are reduced correspondingly. For example, in x-filter systems, the long x-filter models are transformed into short x-filter models which contain the frequency response information only at L frequencies of interest. In most aircraft control systems, there may only be L=2 to L=4 dominant tones of interest. By extracting the frequency response estimates only at these L selected tones, and ignoring the other frequency response information, the length (size) of the x-filters can be dramatically reduced. Typical prior art frequency response models, i.e., long filter models may contain approximately 60 to 100 weights, whereas the reduced filter models may only require approximately 4 to 8 weights.

The shortened filter models can be obtained by a relatively simple calculation to be described in detail. Additionally, the shortened or reduced filter updates may be implemented in an on-line fashion such that the reduced filter models can be determined without shutdown and without off-line pre-training. Apparatus are described herein for reducing the filter models in an on-line fashion for both MIMO systems and SISO systems, as well as for feed-forward and feed-back type systems. Further, the on-line reduction method and apparatus may be used for feed-forward systems that utilize a synchronization signal and a waveform generator.

The above-mentioned and further novel aspects and advantages of the present invention will become apparent from the accompanying descriptions of the preferred embodiments and attached drawings.

The accompanying drawings which form a part of the specification, illustrate several embodiments of the present invention. The drawings and description together, serve to fully explain the invention. In the drawings:

FIG. 1 is a block diagram illustration of a filtered-x active attenuation system known in the prior art;

FIG. 2 is a schematic illustration of an active attenuation system with on-line feedback, error path, and output transducer modeling known in the prior art;

FIG. 3 is a schematic illustration of an active attenuation apparatus and system of the present invention including an on-line reduction of the long filter model in a feed-forward system;

FIG. 4A is a schematic illustration of an active attenuation system including on-line reduction of the filter model in a feed-back type control system (lacks a reference sensor);

FIG. 4B is a schematic illustration of an active attenuation system including on-line reduction which includes a reduced filter model in a feed-forward control system which utilizes a waveform generator and synchronization signal; and

FIG. 5 is an illustration of half a MIMO active attenuation system including on-line reduction for determining the reduced filter models in a feed-forward control system; and

In the following, it should be understood that the present invention may be used in systems for controlling acoustic vibrations in air as well as mechanical vibrations in gases, liquids, or solids. In summary, the present invention provides a method and apparatus for transforming a long filter model into a shortened or reduced filter model, thus reducing the computational burden required to update the control filters. The present invention is ideally suited, and is applicable to, tonal active control systems where one to four tones may be present and controlled. The term"tone" refers to the frequency of the mechanical vibration or noise.

FIG. 3 illustrates one embodiment for carrying out the filter model reduction method. In this aspect of the present invention the reduction method is accomplished in an on-line fashion in reduction block 26. The active system 20 is used to cancel either a vibration or a sound and includes an update model 22 wherein the A Filter 32 and B-Filter 34 are adaptively updated to provide an output signal to an output device 25 in order to cancel a disturbance (the disturbing noise or vibration). Optionally, the system 20 may also include on-line identification block 21 including on-line means for extracting an S'E' model 23. The S'E' model 23, i.e., the long filter model, is an estimate of the frequency response of the plant across the frequency range of interest. Basically, this is the long filter model B.sub.K which will be described in the method to follow. This system 20 uses random low-level uncorrelated noise from random noise source 29 to develop the S'E' model 23 on-line. The S'E' model 23 is a model of the error path 27 and the output device 25. However, it should be noted that the S'E' model 23 could be optionally developed off-line by pre-training allowing elimination of identification block 21.

Once obtained, the S'E' model 23 is then copied and used in the novel on-line reduction process of the present invention taking place at reduction block 26. Within the reduction block 26, the input signal 36 is input into the reduced S'E' model 28 and to the S'E' copy 24. The input signal 36 in this embodiment is the signal that goes to both the A Filter 32 and also to the reduction block 26. This convention for the input signal is the same for all of the embodiments to follow. The output from the S'E' model copy 24 is transferred through line 38 and is summed (according to the sign convention shown) with the output from the reduced S'E' model 28 from line 40 at summing junction 42. The output from the summing junction 42 is input into convergence method 44 via line 46. Ideally, once the signal at 46 is zero or near zero, the reduced S'E' model 28 may be copied to reduced S'E' Copy blocks 30 and 30' to be used in the update of the A Filter 32 and B Filter 34 within the update model 22. The error information 41 and the output from the reduced S'E' model copies 30 and 30' are used for update of the A Filter 32 and B Filter 34 models. It should be noted that the update calculation method which calculates the coefficients or weights for the A filter 32 and B filter 34 at adaptation junctions 31 and 33 may be suspended to allow the reduction method of the reduction block 26 to converge and arrive at the reduced S'E' model 28. The reduced S'E' model 28 contains the exact same frequency response as the S'E' model 23, but only at the L number of discreet frequencies of interest, i.e., the tones to be controlled.

In the FIG. 3 embodiment, the apparatus obtains the input signal 36 from a reference sensor (not shown) for sensing a source of input disturbance and providing an input signal indicative of the input disturbance. The input disturbance causes at least one of a vibration and noise to occur within a control volume (not shown). An output device 25 is used to provide a canceling output for locally canceling at least one of said vibration and noise at the defined location of the control volume. An error sensor (not shown) for sensing a residual combination of at least one of noise and vibration due to the canceling output and the input disturbance produces an error signal 41. An update model 22 is provided for transforming said input signal 36 into a canceling output which is transmitted to the output device 25. The control filter(s) 32 and 34 include a plurality of control filter weights to be updated. An x-filter S'E' model 23 is used for providing a frequency response estimate of the dynamic system or plant which is used in the reduction method. Finally, means are provided in reduction block 26 for shortening the x-filter S'E' model 23 such that the shortened or reduced filtered-x model 28 has a smaller number of coefficients that match the frequency response of a plant at a finite number L of distinct disturbance frequencies. The smaller number of coefficients are used in an update-calculation method at junctions 31 and 33 which may incorporate a method such as filtered-x LMS, for adaptively updating the control filter weights of the control filter(s) 32 and 34. As a result of the fewer calculations needed, the updates to the A Filter 32 and B Filter 34 may be made more often or smaller CPU's may be utilized.

The computational reduction is accomplished by a reduction method taking place in reduction block 26 whereby first an estimate of the plant or frequency response is obtained, i.e., the S'E' model 23. This estimate is referred to in this method as the long x-filter model B.sub.K. This can be done by exposing the system to an impulse function, random noise, or sine sweep and recording the response in an off-line or on-line fashion. The off-line procedure is known as pre-training and generates a model of the frequency response of the plant over a wide frequency range.

Further, the long x-filter model B.sub.K may be initially obtained and also updated by on-line techniques, such as in on-line identification block 21, where low level random uncorrelated noise from random noise source So 29 is input to the dynamic system and the frequency response is recorded. On-line updating is preferred for systems which the plant varies as a function of time, temperature, etc. Off-line pretraining may be appropriate where the system response characteristics are unchanging. For prior art filtered-x LMS systems, the output of the long x-filter model r.sub.k is then used directly in an update calculation method to calculate the updated feed-forward control filter weights.

In the present invention, rather than using the output information r.sub.k from the long x-filter B.sub.K directly, where the long filter model B.sub.K has a length K, the long x-filter model B.sub.K is transformed by a reduction method or technique into a reduced or shortened x-filter model D.sub.M which has a length of M. In particular, in tonal systems where the method is preferable, there are a discreet number of dominant tones, where M<K and typically, M<<K.

The method of transformation will be illustrated with respect to a single input single output (SISO) system, but has equal applicability to MIMO systems where a distinct number of dominant tones are to be controlled. It should be noted that the advantage of the present invention method and apparatus will diminish as the number of frequencies of interest increases. The output vector Y.sub.J consists of J consecutive samples from the long x-filter model B.sub.K is described as

where:

yk=individual sample output

and Y.sub.J is obtained through on-line or off-line methods. Y.sub.J could then be used to calculate the shortened or reduced filter model 28 according to the following

However, in practice, one would extract B.sub.K first, which is an estimate of the plant. Then, an equivalent shortened or reduced x-filter model D.sub.M would be constructed from the long x-filter model B.sub.K. First, the matrix ›H.sub.J,K ! would be generated by extracting a collection of inputs at 36. ›H.sub.J,K ! represents a Hankel matrix which is a collection of row vectors, each row being a buffer of input data. In a feed forward system, the data may be collected from the reference sensor (not shown). In a feed-back type system, the input includes the error information. It should be understood that any appropriate input may be used to construct the Hankel Matrix. K represents the length of the long filter model B.sub.K. Next, ›H.sub.J,M ! would be extracted, as a subset of ›H.sub.J,K !. This is accomplished by taking the M left-most columns of the ›H.sub.J,K ! matrix. Next, one would complete or perform an inverse of ›H.sub.J,M !. The inverse is denoted ›H.sub.J,M.sup.+ !. Methods of developing inverses are known, such as taught in Matrix Computations by Golub and Van Loan, Johns Hopkins University Press, 1983.

As mentioned above, the solution may be arrived at by calculating Y.sub.J as follows:

where:

The solution to the equation above is the vector of coefficients z.sub.k of the short x-filter D.sub.M which can model the output response only at the L distinct, unique, and dominant tones present in the reference signal x.sub.k.

Two forms of the generalized solution which require a pseudo inverse operation are as follows:

These two forms are known as pseudo inverse methods where the generalized inverse (superscript+) is used to describe all solutions including cases where the actual inverse does not exist. When an actual solution does exist, for example, when ›H.sub.J,M ! is non-singular, the shortened x-filter model D.sub.M and the B.sub.K long x-filter model will produce exactly the same output for the same input, but only at the L frequencies or dominant tones present in the reference signal x.sub.k. L is a user selected input that depends on the number of dominant tones present in the disturbance.

For the first form, once ›H.sub.J,M.sup.+ ! and ›H.sub.J,K ! are computed, their product is multiplied by B.sub.K. Updates to ›H.sub.J,M.sup.+ ! and ›H.sub.J,K ! are needed only when there is a change to the system. The short model D.sub.M contains far fewer than K terms present in the long x-filter model B.sub.K for tonal systems. The first form is more desirable. The final step is to calculate the control filter weights for updating the A and B Filters 32 and 34, preferably according to a gradient descent update method based upon D.sub.M and the error signal e.sub.k. In general, the ideal relationship for a tonal system is found to be where:

The second form may also be used but is more computationally intensive.

In particular, the present invention is a reduction method for reducing the computational burden of an active control system which uses any gradient descent control algorithm and which uses an estimate of the plant such as S'E' model 23. The reduction method has particular utility in systems using a filtered-x LMS algorithm. The method involves the steps of extracting an input signal x.sub.k at 36 , such as in a feed-forward system, indicative of characteristics of a source of disturbance. Next, an error signal 41 having magnitude e.sub.k indicative of a residual disturbance at a selected location is extracted.

The reference signal x.sub.k is fed into a feed-forward control filter 32 for generating a control signal u.sub.k. The output signal u.sub.k is fed to an output device 25 to cancel the disturbance, that is, to minimize the magnitude e.sub.k of error signal 41. It is notable that the B Filter 34 may not be needed if the feed-back path 35 is not significant. The feed-forward control filter 32 within the update model 22 has a plurality of control filter weights which are adaptively updated according to an update calculation method taking place at 31. The update-calculation method may be filtered-x LMS or the like.

The transformation step taking place at reduction block 26 involves transforming the long x-filter S'E' model 23 having a length of K into a shortened or reduced x-filter model 28 having a length of M, where M is less than K. Typically, the long filter model B.sub.K (the S'E' model 23) will model the plant over a wide frequency range, for example, from 100 Hz to 400 Hz and may include 60-100 w weights. The shortened x-filter model may only include 2-6 weights if the input only contains one or two tones to be canceled. Inputting the input signal 36 into said shortened x-filter model 28 generates output 40.

This output 40 is then used to converge the reduced filter model 28 by comparison with the output of the S'E' model 23 at the frequencies of interest. Then a copy 30 of the reduced filter model 28 is used to calculate the control filter weights of the feed-forward control filter 32 according to the update-calculation method at 31. The update-calculation method at 31 uses both the shortened x-filter copy 30 output together with the error signal 41. Finally, an output device 25 is driven responsive to the control signal u.sub.k in order to reduce at least one of vibration and sound at a selected location.

The input signal at 36 in this embodiment is generated by a sensor such as at least one of a microphone, accelerometer, force transducer, and a tachometer, or the like. The error signal 41 in this embodiment may be generated by a sensor which can be at least one of a microphone, accelerometer, force transducer, or the like. Finally, the output signal is provided to an output device 25 that may be at least one of a loudspeaker, inertial actuator, active mounting, and electro-mechanical actuator, or the like. This reduction method has particular utility in controlling noise and vibrations from sources having two dominant tones such as an aircraft turbofan engine. The first tone emanates from the low pressure turbine and the second from the high pressure turbine. The method is also useful for controlling 4 dominant tones in a turboprop aircraft.

FIG. 4A illustrates an active system 20' of the feed-back type. It is generally referred to as a feed-back type because there is no reference sensor present or needed in this embodiment. The system and apparatus utilizes the on-line reduction method of the present invention in the environment of a feed-back type system to obtain a reduced S'E' model 28 which is then used in the adaptation process at junctions 31 and 33. The on-line reduction is implemented in conjunction with the feed-back type system taught in U.S. Pat. No. 5,206,911 to Eriksson, the disclosure of which is hereby incorporated by reference herein. As in the feed-forward system of FIG. 3, the system 20' may include on-line identification block 21 for extracting an S'E' model 23 indicative of the error path 27 and the output device 25. Alternatively, the S'E' model 23 may be obtained with off-line pre-training and block 21 may be eliminated. In the FIG. 4A embodiment, the system 20' is identical to the system in FIG. 3 except that the FIG. 4A does not include a reference input, i.e., it is a feed-back type system. The input signal 39 for this embodiment is input into the A Filter 32 of the update model 22 and also to the reduction block 26. Note, the input signal 39 is derived from error signal 41' and the output from the reduced S'E' copy 30'.

The on-line identification block 21, the update model 22, and the reduction block 26 are the same as in FIG. 3. Upon determining the S'E' model 23 and copying it to the S'E' Copy 24, convergence at junction 44 will result in a reduced S'E' model 28 which matches the frequency response of the S'E' model 23 at the distinct frequencies of interest. Therefore, the reduced S'E' model 28 includes less information than the S'E' model 23. This is particularly true if the plant is dynamically dense or complex, for example, where the plant includes many resonances. The reduced S'E' model 28 is then copied to reduced copy models 30 and 30' which are used for adaptively updating the coefficients of the A filter 32 and the B filter 34. The input 39 to the reduction block 26 is the combination of the error signal 41' and the output of the reduced S'E' Copy 30'. The input signal 39 is directed to both the reduction block 26 and the update model 22.

FIG. 4B illustrates an active system 20" including a feed-forward system and apparatus utilizing the on-line reduction technique of the present invention. In this particular embodiment, the feed-forward system includes a waveform generator 48 for generating at least one sinusoidal input signal at 40. The waveform generator 48 receives a synchronization signal 49 which contains the frequency content of the disturbance. This synchronization signal 49 may include multiple dominant and discreet tones. By using on-line reduction block 26, the filter model S'E' 23, which contains frequency response information across the entire range, may be reduced in complexity and size. Therefore, updating of the coefficients of the A filter 32 is less computationally intensive. The method is essentially the same as the FIG. 4A and FIG. 3 embodiments except that the input signal 40 is the output of the waveform generator 48.

FIG. 5a and 5b illustrates the present invention reduction method for transforming the long filter model into a reduced filter model is also applicable in a MIMO system 120. The description of this complex multi-channel system will reference only portions of the diagram, as much of the diagram is symmetric and duplicative. Like reference numerals have been utilized to signify like components as compared to the FIGS. 3, 4A, and 4B embodiments. The Figures of FIG. 5a and FIG. 5b are connected at points indicated by A, B, C, D, E, and F. In the FIG. 5a and 5b MIMO embodiment, each of the S'E' models is an estimate for the actual frequency response indicated as SE.sub.11, SE.sub.12, SE.sub.21, and SE.sub.22. For example, the SE.sub.11 nomenclature used is indicative of the frequency response between the first output device S and the first error sensor e.sub.1. Further, the numeral 1 or 2 following RA indicates the sensor r.sub.1 for subscript 1 and r.sub.2 for subscript 2. The numeral 1 or 2 following RB indicates actuator s.sub.1 for subscript 1 and s.sub.2 for subscript 2. Output device s.sub.1 may take the form of an actuator, speaker or other cancellation device.

In a MIMO system of FIG. 5a and 5b the reduction method includes obtaining at least one input signal such as r.sub.1 as is present in line 136 indicative of characteristics of at least one source of disturbance such as an input noise. Further, at least one error signal such as e'.sub.1 indicative of at least one residual disturbance (such as output noise) at least one location is extracted. The active system 120 also includes at least one output device such as s.sub.1. The at least one input signal at 136 is input into at least one control filter 132 within an update model 122. The control filters are denoted as A.sub.11, A.sub.21, A.sub.12 and A.sub.22, and B.sub.11, B.sub.21, B.sub.12 and B.sub.22. The at least one control filter 132 generates at least one control signal. The at least one control filter 132 also has a plurality of control filter weights which are adaptively updated by an update-calculation method such as at 131. Again, the preferred method is filtered-x LMS or the like.

At least one long filter model 123 such as S'E'.sub.11 may be determined in an on-line fashion by on-line identification block 121 which represents at least one frequency response of said system. This may be also be accomplished by off-line identification or pre-training. The at least one long filter model 123 which has a length of K is then transformed into at least one shortened or reduced filter model 128, such as RA.sub.1 S'E'.sub.11 which has a length of M, where M is less than K. In particular, it is preferable that 2L.ltoreq.M<K. This is true of MIMO and SISO systems.

The transformation for the S'E'.sub.11 long filter model as it relates to r.sub.1 takes place in reduction block 126. The reduction method used is identical to that described in relation to the FIG. 3 embodiment. Upon convergence of the reduction model in block 126, the reduced model is copied to the update model 122 to be used in the update process for updating the A.sub.11 control filter 132. The reduction method is also performed for the remainder of the frequency response models S'E'.sub.12, S'E'.sub.21, and S'E'.sub.22 as they relate to r.sub.1. This occurs in upper A reduction Block 150 within upper reduction block 152. The reduction of the B Filter models relating to actuator s.sub.1 is required in MIMO systems. These reductions take place in the Upper B reduction block 151 within upper reduction block 152 using input signal 157. Likewise, the reductions relating to sensor r.sub.2 take place in Lower A reduction block 154 and Lower B reduction block 155 in lower reduction block 156. MIMO systems, which use the reduction techniques of the present invention are particularly useful for tonal cancellation systems where the multiple tones are to be canceled. By way of example and not by limitation, the system may include four or less dominant tones to be canceled. Upon generating the at least one shortened filter model 128, at least one input signal r.sub.1 is input into said at least one shortened filter model 128 to generate at least one shortened filter output.

Next, the control filter weights of said at least one control filter 132 are calculated according to said update-calculation method based upon said at least one shortened filter output and said at least one error signal. Finally, at least one output device, such as speaker s.sub.1 is driven responsive to said at least one control signal in order to reduce at least one of vibration and sound at said at least one location, such as within the duct shown.

It should be understood that this reduction method has applicability to MIMO systems where mechanical vibration is attempted to be controlled at a defined location by use of active mounts, actuators or the like.

While several embodiments of the present invention have been described in detail, various modifications, alterations, changes and adaptations to the aforementioned may be made without departing from the spirit and scope of the present invention defined in the appended claims. It is intended that all such modifications, alterations, changes and adaptations be considered part of the present invention.