ACTIVE FEEDBACK CONTROL SYSTEM FOR TRANSIENT NARROW-BAND DISTURBANCE REJECTION OVER A WIDE SPECTRAL RANGE

Abstract: A control system provides active attenuation of excitations to a region or structure (1). A feedback sensor (14) generates a signal in response to excitations of the region (1) which is fed to a narrow-band feedback controller (5) having a frequency detector (4), a bandpass filter (6) controlled by the frequency detector (4), and a feedback control generator (8). The frequency detector (4) determines the peak frequency of the excitations. A bandpass filter (6) passes only those signals from the feedback sensor (14) in a narrow frequency band adjustably controlled by the frequency detector (4). The feedback control generator (8) receives the filtered signal from the bandpass filter (6) and produces a control output used by an actuator (13) to attenuate the excitations. Several bandpass filters (6) can be used in parallel to attenuate several frequency bands if the excitation source has a plurality of peaks. This configuration allows the bands to move across the frequency spectrum in response to the excitations.

Description: ACTIVE FEEDBACK CONTROL SYSTEM FOR TRANSIENT NARROW-BAND DISTURBANCE REJECTION OVER A HIDE SPECTRAL RANGE RELATED APPLICATION The present application is based on the Applicants' US Provisional Patent Application 60/019,166, entitled Feedback Control System For Narrow-Band And Medium-Band Active Noise And Vibration Attenuation, filed on June 5, 1996. BACKGROUND OF THE INVENTION Field of the Invention. This invention is related to systems for attenuating noise and vibration, including the nulling of primary excitations and the attenuation of narrow-band and frequency limited broad-band noise and vibrations using control signals that are applied through actuators. tatement of the Problem. Various systems have been proposed for actively reducing vibrations and noise. In general, these prior art systems can be divided into four groups. From a control view point, these can be either feedforward or feedback, and based on excitation source characteristics they are either for repetitive or random excitations. Almost all prior art systems utilize some form of computer or digital signal processing (DSP) board to implement their techniques. Therefore, regardless of the control technique or excitation source, the prior art systems are subject to cost/performance limitations due to the required processing power and sampling period. US Patents Nos. 5,245,552 and 5,233,540 concentrate on digital estimation of a feed-forward active control for single or multiple repetitive vibrations. These systems use filters, phase differentiator, and digital signal processors that are used to identify an individual peak. Its frequency and phase lag are compared to a reference signal to develop a feed-forward control action for those identified frequencies. US Patent No. 5,133,017, describes a seat with noise suppression near the occupant's ears using a direct feedforward signal and a controller that tries to estimate frequency and phase delay between the source and the detecting sensor at individual frequencies. US Patent Nos. 5,365,594 and 5,361,303, discuss an ideal adaptive control system for noise reduction based on a feedforward signal that measures excitation then uses synchronous sampling and discrete Fourier transform to adaptively estimate amplitude and phase of the outgoing control signal that would cancel the incoming noise. The proposed system did not perform in real time with the proposed processing hardware. US Patent Nos. 5,337,366, 5,278,780, and 5,408,532 describe an active control apparatus using adaptive digital filters that try to estimate, on-line, primary and secondary paths using FIR filters. Extensive digital signal processing for one-dimensional duct flow examples has been used to implement the proposed system. Thus, the upper bound of frequency range is very sensitive to the computational power of the digital processor. US Patent No. 4,654,871, 4,562,589, 5,170,433 have focused on harmonic synthesis type active noise control, using a direct feed-forward scheme that utilizes at least one reference signal containing those harmonics. On-line microprocessors are used to estimate amplitude and phase required for the control signal. US Patent NOS. 5,206,911, 5,396,561, 5,172,416, 4,677,677, and 4,677,676 demonstrate feedforward control using FIR filters to estimate primary and secondary paths dynamics, and a performance signal for adaptation of the filters' coefficients. Digital signal processors are used to implement and derive these filters on line. Controller performance is very limited by the complexity of the system and available processing power. Stability is also of concern. US Patent No. 5,117,401 discloses another feed-forward active noise canceller using adaptive digital filters that have inserted delays for a more stable closed loop system. These delays are estimated off-line to reduce on-line computations. US Patent Nos. 5,140,640 and 5,192,918 describe a feedforward adaptive noise control that utilizes a white noise pass through an adaptive filter, namely Widrow's linear combiner, to synthesize a colored noise which is equal in magnitude but out of phase with the original input noise or excitation. Digital signal processors are used to implement the adaptive filter. US Patent Nos. 5,337,365 and 5,245,664 describe an apparatus for actively reducing noise in the interior of an enclosed space using two sets of adaptive FIR digital filters and a microprocessor. The objective of this feedforward controller is to use a reference signal and FIR filters for estimation of primary and secondary paths to synthesize the control signal. US Patent No. 5,388,160 and 5,416,845 combine ideas of Eriksson and others who have used adaptive FIR filters and adds a secondary performance signal to update the filter coefficients. A combined Hubert circuit, coherence signal, and LMS algorithms are used for filter coefficients adaptations. US Patent Nos. 5,384,853 and 4,878,188 add a residual noise detector to the FIR adaptive filter approach to provide an active noise control system that incorporates background level detection. US Patent No. 5,332,061 extends the concept of feedforward repetitive noise control, using an adaptive digital filter, to the problem of active vibration attenuation generated by engine excitation in a vehicle. US Patent Nos. 5,146,505 and 5,222,148 use the adaptive filter and reference signal for harmonic noise control induced by an engine. US Patent Nos. 5,293,578 and 5,319,715 introduce devices that operate on a pure feedforward control based on an adaptive wave synthesis concept. Band pass filters are used to identify individual frequencies. Adaptive delays and gain adjustments are added to the reference signal to calculate an appropriate output signal. These adaptations take place using a digital signal processor. US Patent Nos. 5,416,844 and 5,111,507 use a reference signal with the same frequency as the excitation signal and an adaptive digital filter to estimate primary and secondary paths. In case of the vehicle noise control, signals from the crank angle and fuel injection valve are used. The overall scheme is a feedforward control approach. US Patent No. 5,377,276 utilizes two sets of adaptive digital filters for its feedforward control. One set concentrates on the periodic component of the noise and the other set handles the random component. Adaptive filters are implemented by means of digital signal processing boards. US Patent No. 5,091,953 utilizes a plurality of sensors to detect individual frequencies of a repetitive excitation source, then utilizes feedforward adaptive digital filters to synthesis the control signal. Solution to the Problem As is clear from the references cited above, the prior art has concentrated on adaptive feedforward using digital signal processing (DSP) components and has utilized one or more performance sensors for adaptation of discrete transfer functions describing the primary and secondary noise/vibration propagation paths. Some prior art has also focused on feedback control in both fixed/robust or adaptive forms. Feedforward and feedback controllers differ in a few significant ways. Feedforward controllers require a feedforward sensor to provide future information to the controller about what is going to occur in the disturbance spectrum. This sensor typically needs to be information rich, an accurate estimate of the disturbance, and must sufficiently lead the disturbance to allow for the digital signal processing. In the case of the feedforward control algorithm of harmonic synthesis, the feedforward sensor is a tachometer and, so, is less costly. A tachometer sensor only provides frequency information and not magnitude information, requiring costly digital signal processing components to adapt the magnitude of the control effort. In contrast, feedback control does not use a feedforward sensor, thus reducing cost. Without the benefit of this ^advanced information, a feedback controller must be designed to be robust, or reject disturbances across the entire spectral range of the disturbance. Stability criterion dictates that the performance at each point along the spectrum of the disturbance must be decreased with a widening spectral rejection range. The present invention addresses the shortcomings and introduces a true feedback controller with concentrated feedback action and consequently, high performance, for a finite number of transient attenuation regions across a near-infinitely wide disturbance range. SUMMARY OF THE INVENTION This invention provides a system for single or multiple narrow-band vibration or noise disturbance rejection for bands transient across a wide spectral range by applying feedback control to the region via actuators and continuously tracking the dominant frequencies and adapting to the excitation frequencies. The narrow-band excitation vibration or noise are sensed by one or more sensors. For the narrow-band feedback control, a plurality of parallel bandpass filters are used for isolating peak frequencies. The center frequencies of these bandpass filters are directly controlled, by analog or digital means, allowing the bands to move across the frequency spectrum in response to the sensed input noise or vibration excitations. The isolated bands are separately delayed in a fixed or scheduled fashion to assure that disturbances within each narrow band will be 180 degrees out-of-phase when the signal (electrical, acoustic, or vibratory) completes the feedback path. Sensors are located in the region to provide information about the residual noise or vibration in the form of feedback signals to the control unit. Considering a variety of noise and vibration situations, if excitation is caused by a rotating machinery as shown in FIG. 3, the resulting noise spectrum is dominated by certain peaks which are in a fixed multiplicative relation to each other according to the dynamics of the rotating machinery. As the fundamental frequency of the disturbance varies (through a change in the revolutions-per-minute of the machinery) , all of the peaks shift in frequency to reflect the change. Robust feedback control achieves attenuation across the whole disturbance spectral range by formulating a generic fixed controller which provides control effort across the entire range and at every frequency, whether there is disturbance energy at that frequency or not. In contrast, the present invention provides discrete bands of feedback attenuation which can provide increased attenuation due to the relatively narrow width of the band. These bands then track the disturbances in frequency using a disturbance tracking system or sensor, resulting in significantly more attenuation at the location of the disturbance peaks over what can be achieved by the prior art including robust control and harmonic synthesis controllers and mechanisms. A key feature of this control system is the ability to implement it using computer hardware or inexpensive analog and pseudo-analog components. The control methodology results in a significant reduction in computational intensity, allowing the computer hardware to be lower cost. The analog and pseudo-analog implementation provide identical performance with a significant reduction in cost. This form of implementation also eliminates the constraints of throughput which are present with digital processing. Signal conditioning of the feedback signal is very dependent upon the domain of the plant (acoustic, electrical, mechanical, structural) being controlled and dynamic characteristics of the plant (minimum phase or non- minimum phase) . The difficulty is in the accounting of the relative delay and gain associated with each frequency component within the disturbance signal. Feedback controllers accounting for these broadband characteristics must generally be custom designed for each plant. In contrast, the present system is capable of tracking periodic disturbances and adjusting the feedback cancellation band to envelope the frequency of the disturbances to be attenuated. Due to the narrow-band characteristics, it is applicable to a much wider array of applications and does not require the exhaustive design of conventional feedforward or feedback control systems. Seven separate aspects are included in the specification of this invention. There are three aspects of this system related to the tracking sensor which is used and two more aspects of this system relating to whether the required feedback delays are fixed or also adaptive. There are also two aspects of the invention related to whether the feedback loop gain is fixed or adaptive. In one aspect of the invention, the tracking signal is provided to the feedback cancellation system from a direct sensor signal, e.g. tachometer, mounted on the machinery generating the undesired disturbance. The varying tachometer signal causes the center frequencies of the feedback attenuation bands to overlay the correspondingly varying disturbance frequencies. In another aspect of the invention, an indirect tachometer type signal is generated from a separate disturbance sensor capable of measuring a primary disturbance periodic frequency which can be used to determine and track the frequencies of this and other undesirable disturbance signals. A third aspect of the invention uses a separate disturbance sensor and a spectrum analysis device to estimate the frequencies of the undesirable periodic components of the disturbance. This information is then used to program programmable feedback bandpass filters to center the disturbance attenuation bands about the primary disturbance frequencies. The fourth aspect of the invention uses a fixed phase- delay mechanism, such as an analog, digital, or pseudo- analog allpass filter or tapped delay line to cause the 180 degree phase inversion. This aspect is applicable to cases where the phase roll-off of the feedback path is sufficiently slow and/or the disturbance peaks are sufficiently immobile to guarantee that the feedback phase error will not be significant enough to cause instability. A fifth aspect of this invention uses the information provided from whichever tracking sensor or frequency estimation mechanism to control an adjustable phase-delay mechanism, such as an analog, digital, or pseudo-analog allpass filter or programmable tapped delay line to cause the 180 degree phase inversion. The sixth aspect of the invention uses a fixed gain to provide sufficient feedback control effort to cause disturbance rejection without instability. This aspect is applicable to cases where the gain of the feedback loop is sufficiently flat throughout the range of the disturbance peaks. A seventh aspect of this invention uses the information provided from whichever tracking sensor or frequency estimation mechanism to control an adjustable gain mechanism, such as an analog variable gain amplifier or mixed-signal multiplying digital-to-analog controller, to cause sufficient feedback control effort for disturbance rejection without instability in the presence of a varying feedback loop gain. The present invention offers significant advantages over similar existing harmonic feedforward and feedback systems. The present invention utilizes a tracking sensor which has considerably less information constraints or requirements when compared to those required for existing feedforward and/or harmonic synthesis methods. This invention also offers advantages over feedforward methods due to the fact that feedback control can respond nearly instantaneously to gain variations. Pure harmonic approaches, such as harmonic synthesis, also assume pure tones within the disturbance spectra. Rotating machinery periodic disturbances are typically accompanied by lesser magnitude secondary sideband components which are offset slightly in frequency from the primary disturbance due to system non-linearity and, often, variances in frequency about the dominant frequency. These additional or locally transient components, which would lie within the feedback attenuation bands, would be naturally attenuated. Prior art in the harmonic synthesis approach only attenuates individual frequency peaks and not the sidebands. BRIEF DESCRIPTION OF THE DRAWINGS The present invention can be more readily understood in conjunction with the accompanying drawings, in which: FIG. 1 shows a schematic block diagram of the present noise and vibration control system. FIG. 2 is a schematic block diagram of the proposed control system. FIG. 3 is a graph showing the in-cabin power spectrum of noise from a propeller-driven aircraft, indicating that narrow-band frequencies dominate the overall noise level. FIG. 4 is a block diagram of a virtual center frequency generator. FIG. 5 is a block diagram of one example of a commercially available externally controlled center-frequency bandpass filter. FIG. 6 is a block diagram of one example of a commercially available externally controlled allpass filter for fixed or tracking phase compensation. FIG. 7 is a block diagram of a microprocessor controlled gain block for scheduled gain adjustment of feedback loop gain based on disturbance frequencies. FIG. 8 shows the disturbance spectrum for a small prop aircraft with the present invention off and on. DETAILED DESCRIPTION OF THE PREFERED EMBODIMENT FIG. 1 shows an overall schematic diagram of the present system. A region 1 (e.g., a structure or an enclosed region of space) is excited with a vibration or noise source 2 (e.g., vehicle engine vibration, aircraft jet engine noise, propeller air-rush noise, generator noise, vibration of a compressor in an appliance, or noise from an electric transformer) . The vibration source 2 can generate narrow-band or broadband excitations, including noise, vibrations, or acoustic energy. As shown in FIG. 1, the present invention can be combined, if necessary, with other control algorithms 9, e.g. pseudo-feedforward control, through an adder 15. The resulting control signal is sent to the actuators 13. As shown in FIG. 1, the narrow band feedback controller includes a virtual center frequency generator 4 , as shown in greater detail in FIG. 4. The vibration source 2 also excites a pseudo-excitation sensor 3 (e.g. , a microphone or an accelerometer at or near the vibration source 2) that receives an acoustic or vibratory signal and outputs an analog electrical signal to a bandpass filter 10 which isolates the frequency of the fundamental excitation, as depicted in FIG. 4. Alternatively, a frequency sensor, or wave measuring sensor could be substituted. The resulting output signal from the bandpass filter 10 is sent through a zero-crossing detector 11 which converts the analog signal into a digital pulse train. These pulse trains are sent to a phase-locked loop 12 for frequency amplification to match the required center frequency of the filter. The resulting frequency-amplified pulse trains are sent to the bandpass filter 6 which operates based on a switched capacitor filter, as shown in FIG. 5. For example, the bandpass filter 6 can be a CMOS active filter driven by the clock pulses generated by the phase-locked loop 12 and controlled by a combination of resistors. This universal monolithic filter has three output pins that allow configuration of all-pass, high-pass, low-pass, and bandpass filters. The center frequency of these filters can be adapted to a desired frequency by means of the input clock frequency. The bandpass filter 6 shown in FIG. 5 is made of switched-capacitor networks which are configured to operate as an analog filter approximation with a center frequency equal to l/50th or 1/lOOth the frequency of the pulse train at the clock input pin. Thus, the clock allows digital control and center frequency adaptation. Returning to FIG. 2, the all-pass filters 7 have full- spectrum unity gain and a frequency-dependent phase characteristics. Switch-capacitor all-pass filters have programmable filter quality (Q) , which determines the steepness of the phase curve and a controlling clock input as described for the bandpass switched capacitor filter. If the phase curve roll off and/or input clock frequency and clock ratio are chosen appropriately, then the delay of the passband will be appropriate to cause a net 180 degree phase shift at the center of the narrow passband being excited by the vibration source 2. Resulting signals from the all-pass filters 7 are sent to gain control mechanisms and summed for output. In the non-fixed phase or non-fixed gain cases, the bandpassed feedback signals are passed through digitally controlled allpass filters and/or digitally controlled gain blocks prior to feedback summation. In the fixed phase case, a fixed frequency allpass filter can be used for phase compensation. In the non-fixed phase case, the disturbance frequency detection sensor signal is used to determine the disturbance frequency or frequencies present and that information is used to set the digitally controlled allpass filter or tapped delay line to the phase shift appropriate for that disturbance filtering. If scheduled phase compensation is used, the phase schedule is determined from the feedback loop transfer function estimate. Otherwise, on-line phase adaptation is used. Digitally controlled phase compensation can be accomplished by either controlling the clock input frequency to a fixed clock ration switched capacitor filter or by controlling the clock ratio and Q on a microprocessor-programmable allpass filter. For the non-fixed gain case, the output of the allpass filter is fed into a microprocessor-controlled gain block. The block diagram of such a device comprised of a multiplying digital-to-analog converter is shown in FIG. 7 although other functionally equivalent implementations are possible. The objective is to perform multiples of narrow-band frequency excitations (e.g. for excitation sources having a series of narrow peaks as illustrated in FIG. 3) , so the control output from the narrow band controller 5 should be sent to the actuators 13 for input to the excited region 1. As shown in FIG. 4, a main component of the virtual center frequency generator is a phase-locked loop. Phase- locked loops have a variety of configurations and usage including extracting periodic signals, digital or analog frequency multiplication (known as frequency synthesis) , and tone generation. The phase-locked loop 12 in this invention is used as a frequency synthesizer to multiply the frequency of the disturbance by a value corresponding to the clock ratio of the filters to create a mechanism by which the disturbance directly controls the center frequency of the disturbance isolation filters. The narrowband feedback controller operates as a direct analog to a feedforward notch filter. By summing a broadband signal with a negated bandpass filter output of that same signal, the resulting transfer function of the operation is: 1 - H(s) where H(s) is the transfer function of the bandpass filter. This is the classical form of a notch filter, which also is the sensitivity function defined in the control literature for disturbance rejection systems. By simple transfer function manipulations, we can reformulate the feedforward notch filter describe above as a feedback disturbance rejection system. Assuming that detector and actuator dynamics are part of the plant transfer function, we wish to find a feedback controller which will have a sensitivity function looking like our above mentioned notch filter. The controller, H'(s), is determined from the equation: 1 = ! _ H(s) 1 + H' (s) where H' (s) is a controller in the feedback loop of the resulting closed-loop system. Solving for H' (s) yields the ideal feedback controller for disturbance rejection to be: H(s) H « (s) = 1 - H(s) which, parenthetically, is a bandpass filter with an additional positive feedback loop around it in the feedback path of our controller configuration. This result suffers from two distinct disadvantages: 1) positive feedback in the feedback path will cause stability issues and 2) the transfer function H'(s) is not easily implemented in inexpensive components. Still, in order to get narrow bands of attenuation, we must use a high quality (Q) value for our bandpass filters. This offers us an advantage which is seen when substituting the classical second order form of the bandpass filter. If (Wo/Q)s H( S )= s"2 + (Wo/Q)ε + Wo~2 then H(s) (Wo/Q)s H'(Ξ) = = 1 - H(s) s 2 + Wo~2 and, since Q is high (>>0) and consequently, Wo"2>>Wo/Q, we make the assumption that H' (s) is approximated by H(s) except a very low gain. This assumption is verified by simply looking at the location of the roots of the two corresponding characteristic equations. The result allows us to create a feedback controller with a sensitivity plot resembling a notch filter while using an unconditionally stable and easily i plementable feedback control element. The addition of phase compensation is required when the acoustic or vibration sensor and actuator dynamics are significant and decoupled from the plant. Still, because the control effort is isolated to a few distinct frequencies across the disturbance range at any one instance in time, the phase compensation is only necessary for those few frequencies. This results in the simple addition of a phase compensation device such as an tuned allpass filter or a tapped delay line with an appropriate sample frequency and buffer length. To summarize, this invention presents an active noise and vibration control system that: 1. Employs a narrowband controller 5 to simultaneously attenuate both dominant peaks and their closely aligned sidebands that are commonly found in rotating machinery. 2. Can handle frequency mismatch between the pseudo- excitation signal sensed by the sensor 3 and the excitation source 2. 3. Adapts to and tracks variations in the excitation f equency. 4. Can be implemented in all analog components and thus significantly reduces controller cost, especially in comparison with prior art systems that need microprocessors or digital signal processors. The above disclosure sets forth a number of embodiments of the present invention. Other arrangements or embodiments, not precisely set forth, could be practiced under the teachings of the present invention and as set forth in the following claims. While the methods herein described, and the forms of apparatus for carrying these methods into effect, constitute preferred embodiments of this invention, it is to be understood that the invention is not limited to these precise methods and forms of apparatus, and that changes may be made in either without departing from the scope of the invention, which is defined in the appended claims.

Claims: What is claimed is: 1. A control system for active attenuation of excitations to a region, said control system comprising: a feedback sensor for generating a signal in response to excitations of the region; an actuator for attenuating excitations of the region; and a narrow band feedback controller controlling said actuator having: (a) a frequency detector for determining a peak frequency of the excitations; (b) a bandpass filter receiving said feedback sensor signal as input, and passing only filtered signals in a frequency band adjustably controlled by said frequency detector; and (c) a gain mechanism receiving said filtered signals from said allpass filter and producing a control output for said actuator to attenuate excitations of the region. 2. The control system of claim 1 further comprising a plurality of bandpass filters in parallel receiving said feedback sensor signal as input, with each bandpass filter having a frequency band adjustably controlled by said frequency detector. 3. The control system of claim 1 further comprising: an adder for combining said control signals from said narrow band feedback controller feedback path or paths. 4. The control system of claim 1 wherein said narrow band feedback controller further comprises an all-pass filter having frequency-dependent phase characteristics for shifting the phase of said control signal for said actuator to attenuate said excitations. 5. The control system of claim 1 wherein said feedback bandpass filter comprises a digital bandpass filter having a center frequency adjustably controlled by the frequency of said pulses. 6. A control system for active attenuation of excitations to a region, said control system comprising: a feedback sensor for generating a signal in response to excitations of the region; an actuator for attenuating excitations of the region; and a narrow band feedback controller controlling said actuator having: (a) at least one frequency detector for determining a peak frequency of the excitations; (b) a plurality of bandpass filters in parallel receiving said feedback sensor signal as input, and outputting signals in a frequency band having a center frequency adjustably controlled by said frequency detector; and (c) a feedback control generator combining said output signals from said bandpass filters and producing a control output for said actuator to attenuate excitations of the region. 7. The control system of claim 6 wherein said narrow band feedback controller further comprises an all-pass filter having frequency-dependent phase characteristics for shifting the phase of said control signal for said actuator to attenuate said excitations. 8. The control system of claim 6 wherein said feedback bandpass filter comprises a digital bandpass filter having a center frequency adjustably controlled by the frequency of said pulses. 9. A control system for active attenuation of excitations to a region, said control system comprising: a feedback sensor for generating a signal in response to excitations of the region; an actuator for attenuating excitations of the region; a narrow band feedback controller controlling said actuator having: (a) at least one frequency detector for determining a peak frequency of the excitations; 80 (b) a plurality of bandpass filters in parallel receiving said feedback sensor signal as input, and outputting signals in a frequency band having a center frequency adjustably controlled by said frequency detector; and 85 (c) a gain control mechanism scaling said output signals from said bandpass filters and producing a control output for said actuator to attenuate excitations of the region; and an adder for combining said control signals from said 90 narrow band feedback controller. 10. The control system of claim 9 wherein said narrow band feedback controller further comprises an all-pass filter having frequency-dependent phase characteristics for shifting 95 the phase of said control signal for said actuator to attenuate said excitations. 11. The control system of claim 9 wherein said frequency detector further comprises a phase-locked loop for producing 100 a series of pulses having a frequency determined by said peak frequency, said pulses controlling said frequency band of said bandpass filter. 12. The control system of claim 11 wherein said feedback 105 bandpass filter comprises a digital bandpass filter having a center frequency adjustably controlled by the frequency of said pulses. 13. The control system of claim 11 wherein an analog, pseudo- 110 analog, or digital forms of the control system comprising a fixed frequency and/or fixed phase and/or fixed gain are used for the cases where the disturbance and/or control loop are sufficiently time-invariant to allow non-tracking control.

Inventors: MAGUIRE DANIEL J, SHOURESHI RAHMAT A, MAGUIRE, DANIEL, J., SHOURESHI, RAHMAT, A.
Applicants: COOPER TIRE & RUBBER CO, MAGUIRE DANIEL J, SHOURESHI RAHMAT A, COOPER TIRE & RUBBER COMPANY, MAGUIRE, DANIEL, J., SHOURESHI, RAHMAT, A.
Application year: 1997
Main classification: A61F2
IPC codes: G10K11