Active noise and vibration control system accounting for time varying plant, using residual signal to create probe signal

An active noise and vibration control system is constructed such that the residual signal from the residual sensor is fed back into the controller and used to generate the probe signal. Measurements of the residual signal are used to create a related signal, which has the same magnitude spectrum as the residual signal, but which is phase-uncorrelated with the residual signal. This latter signal is filtered by a shaping filter and attenuated to produce the desired probe signal. The characteristics of the shaping filter and the attenuator are chosen such that when the probe signal is filtered by the plant transfer function, its contribution to the magnitude spectrum of the residual signal is uniformly below the measured magnitude spectrum of the residual by a prescribed amount (for example, 6 dB) over the entire involved frequency range. The probe signal is then used to obtain a current estimate of the plant transfer function.

FIELD OF THE INVENTION 
The present invention relates to active control systems for reducing 
structural vibrations or noise. In particular, the invention relates to 
control of systems for which the dynamics of the transfer functions 
between the actuation devices and the residual sensors change with time. 
For example, if the system to be controlled is the interior noise within 
an automobile, factors such as passenger location and air temperature will 
cause these transfer functions to change with time. 
BACKGROUND OF THE INVENTION 
Active noise and vibration control systems are well known for the purpose 
of reducing structural vibrations or acoustic noise. For example, FIG. 1 
shows such a well known system with respect to acoustic noise operating 
under the traditional "filtered-x LMS algorithm" developed by Widrow et al 
(Adaptive Signal Processing, Englewood Cliffs, N.J., Prentice-Hall, Inc., 
1985). 
As shown in FIG. 1, a disturbance d which can be either sound or vibration, 
induces a response at a first measurement location on line 20, which is 
measured by the residual sensor 12. 11 is the physical transfer function H 
between the disturbance and the residual sensor 12. The disturbance d also 
induces a response at a second measurement location on line 21, which is 
measured by a reference sensor 13. 14 is the physical transfer function T 
between the disturbance and the reference sensor 13. 
The electrical signal output from the reference sensor 13 is input to 
controller 15. The purpose of controller 15 is to create a compensating 
electrical signal which, when used as an input to an actuation device 16, 
will produce a response at the residual sensor which is equal in magnitude 
but opposite in phase to the residual sensor response (20) induced by the 
disturbance d. Thus, when the residual sensor response produced by the 
controller 19 is added (see adder 18 in the FIG. 1 model) to the residual 
sensor response caused by the disturbance 20, the goal is that these two 
responses will cancel creating less vibration or acoustic noise at the 
residual sensor location. 17 is the physical transfer function P 
(hereafter referred to as "the plant") between the actuation device 16 and 
the residual sensor 12. 
The electrical signal output from reference sensor 13 is input along line 
155 to the controller 15. Controller 15 is made up of a variable control 
filter 151, whose transfer function characteristics W change based on the 
output 156 of a Least Mean Square (LMS) circuit 152. The LMS circuit 152 
receives an input 153 from the electrical signal output from residual 
sensor 12. The signal on line 155 is also input to a filter circuit P 154 
whose transfer function is an approximation of the transfer function P of 
the plant 17. The output 157 of filter 154 is fed as a second input to LMS 
circuit 152. Using inputs 157 and 153, the LMS circuit continuously adapts 
the characteristics of the variable control filter 151 in order to create 
a control signal 158 at the output of filter 151 which will drive an 
actuation device 16 to create a residual sensor response equal in 
magnitude but opposite in phase to that caused by the disturbance d 
existing on line 20. Ideally, the control filter converges to -H/PT. 
The residual sensor 12 also picks up auxiliary noise a from auxiliary noise 
sources (e.g., sensor noise and/or response to secondary disturbances). 
These are shown in FIG. 1 as inputs to model adder 18. 
This prior art system, however, assumes that the plant transfer function P 
remains nearly constant with time so that P is fixed yet provides a good 
match to P despite these changes. If however, the characteristics of the 
filter P 154 are maintained constant despite more significant changes 
which may occur in the physical transfer function P ("the plant") between 
actuation device 16 and reference sensor 12, this can lead to degraded 
performance and/or instability in the operation of the controller 15. In 
order to maximize controller performance, accurate estimates of the plant 
are required to update filter circuit P 154. 
Another prior art system (U.S. Pat. No. 4,677,676 Jun. 30, 1987 to 
Eriksson), as shown in FIG. 2, attempted to solve the problem of more 
significant variations of the plant. Only the components differing from 
the FIG. 1 system will be explained. Eriksson used a different controller 
25 which includes an electrical addition circuit 255 located after the 
variable control filter 251. The addition circuit 255 also receives an 
input from an externally generated probe signal n along line 256. The 
probe signal n is also input to an additional LMS circuit 258 and to a 
variable filter 257, whose characteristics are changed by the output from 
EMS circuit 258. The output of filter 257 is fed into an inverted input of 
another electrical addition circuit 259. Addition circuit 259 also 
receives an input from the residual sensor 12, and provides an output to 
LMS circuit 258. 
In Eriksson's system, the probe signal n is a low level random noise 
signal. By injecting such a probe signal into the control loop, on-line 
identification/adaptation of the plant filter 257 is approximated. The 
characteristics of filter 257 are periodically copied to variable filter 
254 (which takes the place of fixed characteristic filter 154 of FIG. 1). 
Eriksson's system allows the control filter 251 to have its transfer 
function characteristic W converge to -H/PT during closed loop operation 
in the presence of a time varying plant transfer function. The weights of 
filter 257 are adapted to approximate the plant transfer function P over 
the required bandwidth. Assuming n is uncorrelated with d and a, the 
weights of filter 257 provide an unbiased estimate of the plant transfer 
function P. 
Although time varying plants can be handled, the prior art Eriksson system 
of FIG. 2 has the following drawbacks. 
First, the magnitude of the probe signal is held constant. Therefore, as 
the magnitude of the disturbance increases relative to the probe as a 
function of frequency, the effective convergence rate for the plant filter 
will decrease. Alternatively, as the disturbance decreases relative to the 
probe as a function of frequency, the convergence rate will increase, but 
may result in causing significant noise amplification. 
Secondly, the spectral shape of the probe signal (commonly chosen as 
flat--i.e., "white noise") is independent of the spectral shape of the 
residual signal and plant transfer function. Consequently, the signal to 
noise ratio as a function of frequency for the plant estimation, the noise 
amplification as a function of frequency, and the mismatch between the 
plant transfer function P and the plant estimate P as a function of 
frequency will be non-uniform across frequency. This can result in 
temporary losses of system performance for control of slewing tonals and 
non-uniform broadband control. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to achieve an active noise and 
vibration control system which takes into account the fact that the plant 
transfer function varies with time, in which the magnitude as a function 
of frequency of the probe signal used to estimate the plant is not held 
constant over time. This will maintain the convergence rate of the control 
filter without increasing the noise amplification in the presence of 
changes in the magnitude spectrum of the disturbance. 
It is a further object of the invention to achieve an active noise and 
vibration control system which takes into account the fact that the plant 
transfer function varies with time, in which the spectral shape of the 
probe signal used to estimate the plant is dependent on the spectral shape 
of the residual signal and plant transfer function. This will minimize 
temporary losses of system performance for control of slewing tonals and 
non-uniform broadband control, which were present in the prior art as 
described above. 
The present invention attains these advantages, among others, by 
constructing an active noise and vibration control system such that the 
residual signal from the residual sensor is fed back into the controller 
and used to generate the probe signal. Measurements of the residual signal 
are used to create a related signal, which has the same magnitude spectrum 
as the residual signal, but which is phase-uncorrelated with the residual 
signal. This latter signal is filtered by a shaping filter and attenuated 
to produce the desired probe signal. The characteristics of the shaping 
filter and the attenuator are chosen such that when the probe signal is 
filtered by the plant transfer function, its contribution to the magnitude 
spectrum of the residual signal is uniformly below the measured magnitude 
spectrum of the residual by a prescribed amount (for example, 6 dB) over 
the entire involved frequency range. The probe signal is then used to 
obtain a current estimate of the plant transfer function.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The general layout of the active noise and vibration control system 
according to the present invention is shown in FIG. 3. Again, only system 
elements differing from the basic structure of FIGS. 1 and 2 will be 
explained. 
Like FIG. 2, the system of Fig. 3 injects a probe signal n into the output 
of the control filter 351 by means of an addition circuit 355. However, 
the origin of the probe signal n is quite different. The output of 
residual sensor 12 is fed back into the controller 35 and into a probe 
generation circuit 353, whose details will be explained below. The probe 
generation circuit also receives as input the weights of filter circuit 
357 which corresponds to the filter 257 of FIG. 2, so that the transfer 
function characteristics of filter 357 can be transferred to the probe 
generation circuit 353. The output of probe generation circuit 353 is 
probe signal n, which is fed to filter 357, LMS circuit 358, and addition 
circuit 355. 
Another modification of the FIG. 2 system is that the output of the 
residual sensor is fed into another electrical addition circuit 359a, 
which receives as input the output of residual sensor 12, and also 
receives, through an inverted input, the output of filter 357 along line 
356. The output of addition circuit 359a is then fed as an input to LMS 
circuit 352. 
FIG. 3 presents an approach for deriving the probe signal n from on-line 
measurements of the residual signal e. According to the invention, the 
spectral shape of the probe signal is optimized to result in nominally a 
constant signal-to-noise ratio (SNR) for the purpose of adapting the plant 
filter P 357 throughout the frequency range of concern. In addition, this 
SNR is maximized consistent with limiting noise amplification to a 
specified level. Finally, since injection of the probe signal n will 
degrade the effective convergence rate for the control filter, a procedure 
for minimizing this degradation is included. The theory embodied in 
Applicant's embodiments adapted to attain the above goals will now be 
derived. 
The power spectrum S.sub.ee of the residual signal e from FIG. 3 in the 
absence of the probe signal n (i.e., n=0) is given by: 
EQU S.sub.ee (.sup.w /.sub.o)=.linevert split.H+TWP.linevert split..sup.2 
S.sub.dd +S.sub.aa (1) 
where 
S.sub.ee ==power spectrum of the residual sensor response e 
S.sub.dd ==power spectrum of disturbance d 
S.sub.ea ==power spectrum of the auxiliary noise signal a. 
When the probe n is non-zero, the power spectrum of the residual becomes: 
EQU S.sub.ee (w)=.linevert split.H+TWP.linevert split..sup.2 S.sub.dd 
+.linevert split.P.linevert split..sup.2 S.sub.nn +S.sub.aa(2) 
Noise amplification is defined as the ratio of the power spectrum of the 
residual with the probe S.sub.ee (w) to the power spectrum of the residual 
without the probe S.sub.ee (.sup.w /.sub.o). This ratio is thus a measure 
of the impact of injecting the probe. For example, suppose that the plant 
filter were initially determined very accurately (e.g. off-line) so that a 
system noise reduction of 40 dB was obtained. If the probe circuit of FIG. 
3 with noise amplification of 2 dB were then added, the system noise 
reduction would be reduced to 38 dB. This small reduction is the price 
paid for enabling the system to maintain essentially the same noise 
reduction in spite of plant variations which might otherwise cause much 
larger noise reduction degradations, or even cause it to become unstable. 
Constraining this ratio to be less than a prescribed noise amplification 
limit throughout the controller bandwidth results in the following 
inequality: 
##EQU1## 
where NA=acceptable noise amplification level (db). 
Applicant's approach is to define the power spectrum of the probe in terms 
of the power spectrum of the residual as defined in Eq. 2. This is a 
judicious choice because it results in a probe signal strength that tracks 
changes in the disturbance level. In addition, this choice results in a 
relatively simple expression relating the spectral shape of the probe 
power spectrum to the residual. As a consequence, the probe signal power 
spectrum is defined as 
EQU S.sub.nn =.linevert split.B.linevert split..sup.2 S.sub.ee (w),(4) 
where B is a frequency-dependent shaping function to be determined. With 
this definition for S.sub.nn, the closed loop residual becomes 
##EQU2## 
The frequency dependent shaping function B is determined by substituting 
Eqs. 1 and 5 into Eq. 3 and solving for B which satisfies the equality. 
The solution for B is given in Eq. 6: 
EQU B=.beta.P.sup.-1 (6) 
where 
##EQU3## 
For this choice of B, 
##EQU4## 
From Eq. 8, the impact of the probe-signal injection is limited to 
increasing the residual uniformly across frequency by the allowed NA 
value. The SNR (of the probe signal contribution in the residual signal e) 
for estimating the plant using this choice for S.sub.nn (Eqn. 4) can be 
shown to be constant across frequency and is given by: 
##EQU5## 
As an example, for NA=2 dB, 
##EQU6## 
The effective convergence rate for the control filter 351 (W) can be 
optimized by adapting W based on an estimate of the residual signal in the 
absence of injecting the probe. This is shown in FIG. 3 by the inclusion 
of the addition circuit 359a which receives the residual e at one input 
and receives the output of filter 357 at an inverted input, and whose 
output goes to the LMS circuit 352 which acts to adapt the coefficients of 
filter 351 to thus change the transfer function thereof. 
Equation 8 shows also that this feedback probe-generation approach is 
potentially unstable in a power sense, that is, the noise amplification is 
related to .beta..sup.2. This is expected since the probe signal n is 
based on the power spectrum of the residual e, which carries no phase 
information. The potential instability of this path is not a problem, 
however, since .beta. is a design parameter chosen in accordance with Eq. 
7, thereby limiting noise amplification to a prescribed level. 
Thus, the strength of the probe signals and the spectral shape thereof are 
chosen such that the impact of injecting the probe signals into the loop 
is limited to increasing the power spectrum of the residual sensor by a 
prescribed amount throughout the frequency range over which the plant is 
to be estimated, in the presence of variations in the plant, or changes in 
the disturbance level. 
Next, a procedure is presented for generating a probe signal that satisfies 
the desired relationship between the power spectra of the probe and that 
of the residual signal, such a probe signal being uncorrelated with the 
disturbance and auxiliary noise signals. 
From the development presented above, the power spectrum of the probe 
signal to be generated is given by Eq. 11. 
##EQU7## 
One procedure for generating a probe signal n that satisfies Eq. 11 and is 
uncorrelated with the disturbance d and noise a is shown in the block 
diagram of FIG. 4. 
FIG. 4 shows a preferred frequency-domain embodiment of the probe 
generation circuit 353 of FIG. 3. As shown in FIG. 4, the residual signal 
e output from the residual sensor 12 of FIG. 3 is input to a DFT circuit 
401 which takes the Discrete Fourier Transform of the time domain residual 
signal e thus translating it into the frequency domain. 
Once in the frequency domain, the phase component of the residual is 
randomized by phase spectrum randomizer circuit 402. For example, the 
output of a random number generator is used to replace the phase values of 
the residual. In so-randomizing the phase, it is ensured, however, that 
the DC and Nyquist indexes (bins) of the DFT result are purely real. Also, 
it is ensured that the phase values above Nyquist are opposite in sign to 
their mirror images below Nyquist. Therefore, the resulting magnitude and 
phase spectrums are conjugate symmetric. 
Then, the randomizer circuit output is shaped in the frequency domain using 
inverse filter 403. The inverse filter corresponds to the inverse of the 
plant transfer function as shown in the expression for the shaping 
function given in Equation 6. That is, the spectrum of the residual (once 
decorrelated with the disturbance and auxiliary noise via the phase 
scrambling of phase spectrum randomizer circuit 402) is filtered in the 
frequency domain by an estimate of the inverse of the plant. 
An estimate of the frequency response of the plant is obtained by copying 
the weights of the plant filter estimate from plant filter P 357 into the 
probe generation circuit 353, where they appear on line 409 of FIG. 4. The 
copied weights are then transformed into the frequency domain by taking 
the DFT of the weights using DFT circuit 408. The size of the DFT's in 
circuits 408 and 401 must be the same. The frequency transformed weights, 
which correspond to an estimate of the frequency response of the plant, 
are then input to inverse filter 403, where the inverse of the frequency 
response of the plant is taken, frequency-by-frequency, at those 
frequencies resulting from DFT circuit 408. The output of phase spectrum 
randomizing circuit 402 is filtered in the frequency domain using inverse 
filter 403 by multiplying the complex spectrum output from 402 by the 
frequency response of the inverse filter 403 at each frequency resulting 
from DFT circuits 401 and 408. 
The output of inverse filter 403 is fed into Inverse Discrete Fourier 
Transform (IDFT) circuit 405, where the signal is transformed back into a 
real-valued time domain signal. Next, windowing and overlapping functions 
take place by means of windowing and overlapping circuit 406 in order to 
remove possible discontinuities between successive time records of the 
time domain transformed signal. Such windowing and overlapping operations 
operate under the same principle as those which are known for use in 
signal processing for Discrete Fourier Transform analysis of a time 
series. For example, a Hanning window with 50% overlapping may be used for 
this purpose. 
The time series data are then scaled by the gain term .beta. discussed 
above in Eq. 6, by means of the scale by .beta. circuit 407. The resultant 
probe signal n is then injected into the control loop of FIG. 3 from the 
output of probe generation circuit 353. 
This procedure for probe signal generation results in a closed loop 
feedback path. It is potentially unstable in a power sense, as shown in 
Eq. 8. As a consequence, the scaling factor .beta. must be limited to 
avoid excessive noise amplification. Because this closed-loop path is 
potentially unstable only in a power sense, however, filtering performed 
in this path need not be causal. That is, filters can be applied directly 
to the magnitude response of the residual power spectrum. For example, 
median smoothers in frequency can be used to advantage in order to remove 
tonal components in the residual. As a specific example, a median smoother 
can be placed in parallel with the phase spectrum randomizer circuit 402 
of FIG. 4. 
The use of instantaneous DFTs to characterize the power spectrum of the 
residual is beneficial because it allows the probe signal strength to 
adjust for relatively rapid changes in the magnitude spectrum of the 
disturbance as a function of time. The magnitude spectrum of the probe 
signal is determined from the magnitude response during the previous time 
record for the DFT. Since these time records are typically on the order of 
a few seconds (to resolve the spectral features of the plant transfer 
function), the time delay between changes in disturbance level and a 
change in probe strength is kept small. 
Further, the use of DFT processing to generate the probe signal results in 
a difference equation relating the power spectra of the residual with and 
without the probe. 
EQU S.sub.ee(w) (k)=S.sub.ee(w/o) (k)+.beta..sup.2 S.sub.ee(w) (k-1),(12) 
where k is the index of the current DFT time record. 
Therefore, an equivalent expression for Eq. 8 becomes 
##EQU8## 
In this expression, the term .beta..sup.2i can be viewed as a "forgetting 
factor." To the extent that the residual power spectrum is "nominally" 
stationary (i.e., is nearly constant over time records for which 
.beta..sup.2i is significant), the summation in Eq. 13 approaches 
##EQU9## 
which agrees with Eq. 8. 
Further, if it is known in advance that the disturbance, d, is bandlimited 
within a specific bandwidth, e.g., if d is a steady tone, then the plant 
need only be estimated over a limited frequency range. Therefore, a band 
limiting filter can be inserted after the phase spectrum randomizer 
circuit 402. This reduces computation requirements in certain 
applications. 
Derivation for MIMO Control: 
The derivation of the probe-generation approach for 
multiple-input-multiple-output (MIMO) control systems follows from the 
single-input-single-output (SISO) approach detailed above. In general, 
extending SISO concepts to analogous MIMO concepts is well known. See 
Elliott et al., "A Multiple Error LMS Algorithm and its Application to the 
Active Control of Sound and Vibration", IEEE Transactions on Acoustics, 
Speech, and Signal Processing, Vol. ASSP-35, No. 10, p. 1423-1434, October 
1987; and Elliot et al., "Active Noise Control", IEEE Signal Processing 
Magazine, October 1993, p. 12-35. In particular, the vectors of residual 
power spectra in the absence of the probe signal and with the probe signal 
are defined in Equations 14 and 15, respectively. 
EQU S.sub.ee (.sup.w /.sub.o)=.linevert split.H+TWP.linevert split..sup.2 
S.sub.dd +S.sub.aa (15) 
EQU S.sub.ee (w)=I-.linevert split.PB.linevert split..sup.2 !.sup.-1 
{.linevert split.H+TWP.linevert split..sup.2 S.sub.dd +S.sub.aa }(15) 
where 
S.sub.ee ==power spectrum of the residual sensor vector e 
S.sub.dd ==power spectrum of disturbance vector d 
S.sub.aa ==power spectrum of the auxiliary noise vector a, 
and 
I==S.times.S identity matrix 
S==number of residual sensors 
.linevert split.x.linevert split..sup.2 ==matrix whose elements are the 
squared magnitudes of the elements of matrix X. 
The expressions in Equations 14 and 15 have assumed that the elements of 
the disturbance vector and the auxiliary noise vector are statistically 
independent. An equivalent expression could be written for the case where 
the elements of each of these vectors are not statistically independent. 
In addition, the result of Equation 15 is obtained by defining the vector 
of probe signal power spectra in terms of the vector of residual signal 
power spectra in a similar manner as for the SISO case described above. 
The equivalent expression to Equation 4 for the MIMO case is given in 
Equation 16. 
EQU S.sub.nn =.linevert split.B.linevert split..sup.2 S.sub.e'e' (w),(16) 
where 
EQU S.sub.e'e' (w)=S.sub.ee (w). (17) 
For the MIMO case, however, a new signal vector e' has been explicitly 
defined which is related to the residual vector e. Specifically, the 
individual elements of the signal vector e', while satisfying the power 
spectrum relationship of Equation 17, are chosen to be statistically 
independent of each other and uncorrelated with the elements of the 
residual signal vector e. That is, the elements of the vector of power 
spectra S.sub.e'e' (w) are equal to the power spectra of the corresponding 
elements in S.sub.ee (w) (see Equation 17), but the elements of the signal 
vector e' are chosen to be statistically independent and uncorrelated with 
the disturbance and auxiliary noise vectors. This latter requirement, 
which can be achieved via a phase spectrum randomizer circuit similar to 
the circuit 402 shown in FIG. 4, ensures an unbiased estimate of the plant 
transfer function matrix. 
The equivalent constraint of Equation 3 (using the equality) for MIMO 
control is given in Equation 18. 
EQU S.sub.ee (w)=10.sup.(NA/10) S.sub.ee (.sup.w /.sub.o) (18) 
It follows from Equations 14, 15 and 18 that for MIMO applications, the 
solution for the shaping matrix B becomes, 
EQU B=.beta.P.sup.+, (19) 
where .beta. is a constant defined previously in Equation 7, and where 
P.sup.+ is the matrix inverse of the transfer function matrix (taken 
frequency by frequency) between the actuation devices and the residual 
sensors if P is a square matrix. For non-square plant matrices, P.sup.+ 
is the pseudo inverse of this transfer function matrix taken frequency by 
frequency. For a discussion of the pseudo inverse, see Lawson et al, 
Solving Least Squares Problems, Prentice-Hall, Inc., 1974, p. 36-40. 
Extension of Approach to Feedback Control: 
Applicant's approach presented above for feedforward control systems is 
applicable for feedback control systems as well. For example, for MIMO, 
the shaping function matrix B is again equal to a constant .beta. times 
the inverse (or pseudo-inverse for non-square plants) of the transfer 
function matrix between input signals to the actuation devices and the 
responses of the residual sensors, which is the closed-loop plant transfer 
function matrix. For the feedforward systems of FIGS. 1-3, this transfer 
function matrix is the plant matrix P. For feedback systems, the inverse 
to be taken is of the transfer function matrix between the inputs to the 
actuation devices and the responses of the residual sensors during 
closed-loop operation. As an example, for a controller whose transfer 
function characteristics are described by matrix C, the expression for the 
shaping function matrix B becomes, 
EQU B=.beta.{I+PC!.sup.-1 PC}.sup.+ (20) 
Equation 20 assumes that the probe signal vector is injected at the input 
of the control filter matrix C. Equivalent expressions can be written for 
the case where the probe is injected at the output of the control filters, 
or for the case where other filters are included in the feedback loop. 
FIG. 8 shows a block diagram of a feedback embodiment of the invention 
using SISO (single-input-single-output), as an example of the general 
feedback principles discussed above. Here, the shaping function B is again 
equal to a constant .beta. times the inverse of the transfer function 
between the input to the actuation devices and the response of the 
residual sensors during closed-loop operation. For example, for a 
controller whose transfer function characteristics are described by the 
transfer function C, the expression for the shaping function B becomes, 
EQU B=.beta.(PC/1+PC).sup.-1 (21) 
In FIG. 8, the disturbance d is input to adder 801 as a first input and the 
output of the plant 802 is input as a second input to adder 801. The 
output of adder 801 is the residual signal e on line 803, which is 
measured by residual sensor 826. 
The residual 803 is input through an inverted input to a second adder 804 
which also receives an input from the probe signal n. The output of adder 
804 is sent as an input to control filter C 805 whose output c is sent to 
an actuation device 825. 
The residual 803 is also provided as an input to probe generation circuit 
806, which can have the structure shown in FIG. 4, for example. The probe 
signal n is generated at the output of probe generation circuit 806. The 
probe signal n is also sent to a DFT circuit 807 whose output is provided 
to a conjugate circuit 808a and another conjugate circuit 808b. 
The output of DFT circuit 807 is provided as an input to first multiplier 
809. The output of conjugate circuit 808a is also provided as a second 
input to first multiplier 809. The output of conjugate circuit 808a is 
also provided as a first input to a second multiplier 810. 
The residual signal e is provided as an input to DFT circuit 807a, whose 
output is provided as a second input to second multiplier 810. A divider 
811 receives a divisor input from the output of first multiplier 809 and a 
dividend input from the output of second multiplier 810. The output of 
divider 811 is an estimate of the quantity (PC)/(1+PC). As shown by line 
830 at the output of divider 811, the estimated frequency response is 
transferred into the probe generation circuit 806, equivalent to line 404 
of FIG. 4. 
In FIG. 8, standard signal processing techniques are also used, but not 
illustrated to preserve clarity. That is, standard windowing and 
overlapping occurs before the inputs to the DFT's and ensemble averaging 
of the multiplier outputs takes place before the multiplier outputs are 
sent to the dividers. 
The output of DFT circuit 807 is provided to conjugate circuit 808b, whose 
output is then provided as a first input to third multiplier circuit 812. 
Third multiplier circuit 812 receives a second input from the output of 
DFT circuit 807b which receives an input from the output of control filter 
805. The output of third multiplier circuit 812 is provided as a divisor 
input to second divider circuit 813, which receives a dividend input from 
the output of second multiplier circuit 810. 
The output of second divider circuit 813 is an estimate of the frequency 
response of the plant P. This estimate is provided to circuit 814 which 
generates the weights for control filter 805 therefrom. Techniques for 
this conversion are well known to those of ordinary skill in the art. See 
Athans et al., Optimal Control--An Introduction to the Theory and Its 
Applications, McGraw-ESG Hill, Book Company, 1966; Maciejowski, Multi 
Variable Feedback Design, Addison-Wesley Publishing Company, 1989; 
.ANG.strom et al., Adaptive Control, Addison-Wesley Publishing Company, 
1989. 
The above feedback SISO system has been described with respect to a 
frequency domain implementation. It can be appreciated that the feedback 
technique can also be implemented in the time domain, using LMS 
algorithms, to achieve the same results according to the general 
principles described above. 
A purely time domain embodiment of the probe generation circuit 353 of FIG. 
3 will now be described, in association with FIG. 6. 
In this embodiment, the residual e is passed through a bulk time delay 
circuit 601 which delays a portion of the residual for a predetermined 
short time delay. The purpose of this bulk delay is to delay the input by 
a sufficient amount so that the output signal is uncorrelated with the 
input signal. The size of the time delay is chosen so as to be longer than 
estimates of the impulse response of the plant. Since the delay of the 
delay circuit 601 is short, the amplitude at the output is substantially 
the same. That is, the residual has not had enough time to change 
substantially during the short time delay, yet sufficient time has elapsed 
(relative to the impulse response of the plant), to decorrelate the output 
of delay 601 with its inputs at all but tonal disturbance frequencies. 
Therefore, in the absence of tonals in the disturbance, the resultant 
output signal is phase-uncorrelated with the residual e. 
As further shown in FIG. 6, the output of the delay circuit 601 is an 
inverted input to adder 602. The residual e is also input to an adaptive 
filter 603 whose output is presented as another input to the adder 602. 
The adaptive filter 603 has its weights adapted by means of an LMS circuit 
604, which receives inputs from both the residual e and from the output of 
the adder 602. By providing such additional circuitry, tonal contributions 
in the residual e can be removed. 
The output of adder 602 is then input to a Scale by .beta. circuit 607 
which scales the adder 602 output by the value .beta.. The circuit 607's 
output is then input to adaptive filter 609, delay circuit 610 and plant 
estimate copy (P copy) filter 608. Filter 608 periodically receives copied 
weights from filter 357 of FIG. 3. The output of filter 608 is input to 
LMS circuit 611. 
The output of delay 610 is fed to an inverted input of adder 612 while the 
residual signal, e, is applied to a non-inverting input to adder 612. The 
output of adder 612 is applied as a second input to LMS circuit 611. The 
LMS circuit controls the transfer function characteristics of the adaptive 
filter 609 so as to generate the probe signal, n, at output line 613. 
The function of delay 610 is to delay the output of the scale by .beta. 
circuit 607 for a time approximately equal to the time it takes for this 
output to pass through the various adaptive filters, so as to account for 
the transit time through such filters, as is generally well known in the 
art. See Widrow et al cited above. Such a delay period is typically much 
shorter than that of bulk delay 601. 
Accordingly, the circuits 607-612 perform the shaping function of Eqn. 6 by 
multiplying the output of adder 602 by scale factor .beta. and filtering 
the resultant signal by an estimate of the inverse of the plant. 
Two variations on the probe generation circuit embodiments of FIGS. 4 and 6 
will now be given with reference to third and fourth embodiments of FIGS. 
5 and 7. The embodiments in FIGS. 5 and 7 provide alternate approaches to 
perform the functionality of circuit elements 401 and 402 in FIG. 4, or to 
perform the functionality of circuit element 601 in FIG. 6. 
In embodiment three of FIG. 5, the residual signal e is input to a finite 
impulse response (FIR) filter coefficient determination circuit 502, which 
functions to select successive time records of the residual signal e for 
use as FIR filter coefficients by residual filter circuit 503. The output 
of FIR filter determination circuit 502 is provided as a control input to 
residual filter circuit 503. The length of the time records by circuit 502 
should be chosen long enough to resolve the spectral features of the 
plant. This time record length, together with the sample rate of the 
controller, dictate the number of coefficients to be used in residual 
filter 503. 
The output of a random number generator 504 is provided as a data input to 
residual filter 503. The amplitude of the random noise from the random 
number generator 504 is chosen so that the average power spectral density 
is 0 dB throughout the frequency range of concern. The output of residual 
filter 503, on line 505, is the output of the random number generator 504 
filtered in the time domain by residual filter 503. 
Since the magnitude spectrum of the random noise is chosen to be flat, when 
such noise is passed through residual filter 503, the magnitude spectrum 
of the output will approximate the magnitude spectrum of the residual. The 
output of the residual filter 503 will be uncorrelated with the residual e 
by virtue of using the random number generator 504 as input to residual 
filter 503. 
The output of residual filter 503 on line 505 can be used directly as an 
input to scale by .beta. circuit 607 in FIG. 6. Alternatively, the output 
of residual filter 505 can be passed through DFT circuit 501; then, as in 
FIG. 4, the frequency domain result on line 506 is passed to inverse 
filter 403, IDFT circuit 405, windowing and overlapping circuit 406, and 
scale by .beta. circuit 407. 
FIG. 7 shows a fourth embodiment which is related to that presented in FIG. 
5. In FIG. 7, however, the roles of the residual signal and random number 
generator are, in effect, reversed as compared to FIG. 5. In FIG. 7, the 
residual signal e is provided as a data input to scrambling filter 703, 
whose weights are updated periodically through a control input from FIR 
filter coefficient determination circuit 702, whose function is to select 
successive time records of the output of random number generator circuit 
704. The length of the time records selected by circuit 702 and the 
amplitude of the random number generator 704 are the same as those 
described for circuits 502 and 504 of FIG. 5. The output of scrambling 
filter 703 is the residual signal e filtered in the time domain by 
scrambling filter 703. 
The output of the scrambling filter 703 will be uncorrelated in phase but 
have substantially the same magnitude (power) spectrum as the residual 
signal e. 
The output of the scrambling filter on line 705 can be used directly as an 
input to the scale by .beta. circuit 607 of FIG. 6. Alternatively, the 
output of the scrambling filter can be passed through DFT circuit 701, and 
as in FIG. 4, the frequency domain result on line 706 is passed directly 
to inverse filter 403, IDFT circuit 405, window and overlapping circuit 
406, and scale by .beta. circuit 407. 
Other techniques for decorrelating the phase spectrum of the residual yet 
maintaining the amplitude spectrum thereof, when generating the probe, 
could be derived by those of ordinary skill in the art. Such techniques 
are considered within the scope of coverage of the appended claims. 
For the feedforward case of FIG. 3, it is known (see Eriksson) to allow for 
the possibility of a feedback transfer function between the output of the 
actuator 16 and the response of the reference sensor 13. This transfer 
function is not shown in FIGS. 2 or 3 to preserve clarity. The probe 
generation procedures disclosed herein can be easily extended to and apply 
equally well to those systems where such a feedback transfer function is 
significant. 
An algorithm for generating an "optimal" probe signal for the purpose of 
on-line plant identification within the context of feedforward and 
feedback algorithms applied to systems with time-varying plants has been 
disclosed. This algorithm differs from the more traditional techniques in 
that it is implemented as a closed-loop feedback path, and the spectral 
shape and overall gain of the probe signal are derived from measurements 
of the residual error sensor. The resulting probe signal maximizes the 
strength of the probe signal as a function of frequency, providing uniform 
SNR of the probe relative to the residual for estimating the plant 
transfer function. This SNR level is related to acceptable noise 
amplification through a simple expression. 
As a consequence of increasing the SNR for plant estimation relative to 
that achieved by using "white" noise probe signals for "non-white" 
residuals and plants, this new probe generation algorithm offers the 
possibility for more uniform broadband reduction and better system 
performance in the presence of slewing tonals in the disturbance.