Intelligent adaptive active control of noise and vibration

INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

14th World Congress ofIFAC

Copyright Cl 1999 IFAC 14th Triennia! World Congress, Beijing, P.R. China

Q-9d-04-1

INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND VIBRATION

M. O. Tokhi § and S. M. Veres

:j:

§ Department ofAutomatic Control and Systems Engineering, The University of Sheffield, UK. Email: o.rokhi@j"heffield.ac.uk :f: School of Electronic and Electrical Engineering, The University of Birmingham, UK. EmaiC: [email protected]

Abstract: This paper reports on recent advances in the development of intelligent tecbniques for active control of noise and vibration. A self-tuning control mechanism is developed within a feedforward control structure. The scheme is realised with conventional recursive least squares methods, genetic algorithms and neural networks and its performance verified in the cancellation of noise in free-field and vibration suppression in a flexible beam. An iterative adaptive control scheme is then developed and realised within a feedbacklfeedforward control structnre for vibration suppression in a flexible plate. It is demonstrated that significant reduction in the level of noise/vibration is achieved with these schemes over a broad range of frequencies. Copyright © 1999IFAC Keywords: Active noise control, active vibration control, adaptive control, intelligent control, genetic algorithms, neural networks, self-tuning control.

1. INTRODUCTION

Active control of noise/vibration (disturbance) consists of artificiaHy generating cancelling source(s) to destructively interfere with the unwanted source and thus result in a reduction in the level of the disturbance at desired Iocation(s). Active noise/vibration control (active control) is not a new concept. It is based on the principles that were initially proposed by Lueg in the early 1930s for noise cancellation (Lucg, 1936). Since then a considerable amount of research work has been devoted to the development of methodologies for the design and realisation of aetive control systems in various applications. III many practical applications the problem of noise and vibration are found to be closely related. For example, a close coberence is observed in numerous situations between the two due to secondary effects. Many sources of noise, for instance, vibrate continuously while in operation and the vibration is

found to be coherent with the acoustic waves they emit. On other occasions, it is often noticed in buildings, for instance, that noise due to chattering of windows or motion of articJes is caused through ground vibrations by passing trains and/or vehicles. In these cases a control solution aimed at reducing, for example, the level of vibration will result in significant reduction in the level of noise and, to some extent, vicc versa. Moreover, the control of noise and vibration by active means is based on the same design principle. These form the basis of design by adopting a systems approach for the development of active control strategies for both noise cancellation and vibration suppression. In this manner, the devised methods can be utilised to tackle the problem of noise and vibration either in isolation or together. Active control is realised by detecting and processing the disturbance by a suitable electronic controller so that, when superimposed on the

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Copyright 1999 IF AC

ISBN: 008 0432484

INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

disturbances. cancellation occurs. Due to the broadband nature of these disturbances, it is re.quired that the control mechanism realises suitable frequency-dependent characteristics so that cancellation over a broad range of frequencies is achieved. In practice, the spectral contents of these disturbances as well as the characteristics of system components are in general subject to variation, giving rise to time-varying phenomena. This implies that the control mechanism is further required to be intelligent enough to track these variations, so that the desired level of perfonnance is achieved and maintained. Much of the work reported on active noise/vibration control has concentrated on conventional adaptive controllers (Elliott et al., 1987' Eriksson et al., 1987; Fuller et al., 1992; Snyd~r and Hansen, 1992; Tokhi and Lcitch, 1991). Recent advances, bowever, bave included active control mechanlsms :incorporating genetic algorithms (GAs) and neural networks (Hansen et al., 1996; Tokhi and Hossain, 1996; Tokhi and Wood, 1996).

14th World Congress ofIFAC

(1)

where 00 and Qr represent system models between the detection and observation points with secondary source off and on respectively. Equation (1) gives me required controller design rules which can be realised with a suitable system identification algorithm. This results in a self-tuning active control algorithm that can easily be implemented on a digital processor. Figs. 2 and 3 show the system performance thus obtained, with RLS parameter estimation algorithms, in implementing me algorithm in reduction of noise in a free-field and vibration suppression in a flexible beam environment respectively. It is noted that significant reduction in the disturbance over a broad frequency range was achieved.

2. ACTIVE CONTROL STRUCTIJRE A schematic diagram of the geometric arrangement of an active control structure, within noise/vibration

environment, is shown in Fig. 1. The (unwanted) primary disturbance is detected hy a detector (sensor), processed by a controller, of transfer characteristics C, and fed to a sccondary source. The secondary signal thus generated interferes with the primary noise/vibration so that to achieve a reduction in the level of the disturbance at and in the vicinity of an observation point In practice, the characteristics of sources of disturbance vary due to operating conditions, for instance, leading to time-varying spectra. Moreover, the characteristics of transducers, sensors and other electronic equipment used in the active control system are subject to variation due to environmental effects, ageing, etc. Under such situations the system employing a fixed controller will not perform to a desired level. Thus, an active control system is, in general, required to be capable of updating the controller cbaracteristics in accordance with the changes in the system so tllat the required level of performance is achieved and maintained. To do this an adaptive control strategy, allowing on-line design and implementation of the controller, can be utilised.

(a) Active noise control.

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Cb) Active vibration control. Fig. I. Active control structure.

3. SELF-TUNING ACTIVE CONTROL The objective in Fig. 1 is to achieve full (optimum) cancellation at the observation point. Synthesising the controller, on the basis of this objective yields (Tokhi and Leitch, 1991)

Fig. 2. Cancelled noise spectrum.

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Copyright 1999 IF AC

ISBN: 008 0432484

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INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

,

, ,,--t o

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Fig. 3. Cancelled vibration spectrum. 4. ACTNE CONTROL USING GENETIC ALGORITHMS

Genetic algorithms (GAs.) are based on the method of minimisation of the prediction error. Th.is property can be utilised at the system identification level in the self-tuning algorithm to estimate Ihe parameters of 00 and Q1 using GAs. To demonstrate this, the active control system was implemented witllin a flexible beam. Fig. 4 shows the beam response to a PRBS disturbance before and after cancellation. It is noted that the level of vibration was significantly reduced .

In this section the capabilities of neural networks at modelling and control levels are utilised to develop a neuro-active control strategy. The strategy is based on direct realisation of equation (1) using neural networks. This is shown in Fig. 5. Fig. 6 shows the system performance in reduction of noise in a freefield environment with multi-layered perceptron (MLP) and radial basis function (REP) networks accordingly. It is noted that in either case. the noise was Significantly reduced over a broad range of frequencies. As compared to Fig. 2, the perfoTIllance wilh neural networks was significantly better than that with conventional RLS-based methods. f I !

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Fig. 4 . Beam response with the GA-ba.<;ed system.

Fig. 6. Cancelled spectrum at the observation point.

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Copyright 1999 IF AC

ISBN: 0 08 043248 4

INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

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6. SUPERVISED ITERATIVE-ADAPTIVE TUNING For servo control recent iterative identification and control redesign approaches by Schrama (1992), Van den Hof et al. (1993), Parranen and Bitmead (1993) operate on the principle that closed-loop measurements are used to re-model the plant and use that to obtain a bettcr controller. It has been shown by Hjalmarson et aL (1996) that iterative identification can be better than open-loop identification plus robust control design. The windsurfer approach by Lee el a!. (1993) to iterative identification and control allows gradual increase of the closed loop bandwidths with learning. These appBcations were mainly aiming at servo control, and the applicability of these techniques in vibration and sound control is discussed in this section. In vibration and sound control applications the empba'\is is sbifted from good response to a reference (in servo control) towards good reduction of the effect of external disturbances (in sound and vibration control). In broad terms the objective is to actively modify the plant dynamics so that the transfer matrix from the disturbance to the output is dampcned in thc frequency band of the disturbance. As it was shown by Lee et al. (1993), the internal nwdel control (IMC) structure combined with closed-loop identification offen; an efficient approach in iterative control design. The corresponding control structure for a vibration control application is shown in Fig. 7, where there is no reference signal available for the use of adaptive filtering and output feedback is the only option. G is the plant transfer matrix, and H represents a

disturbance model. In an adaptive iteration the Q is a fixed gain controller and L'lG is the estimated enhancement of a nominal plant model Go. Based on the plant input and measurements y , a new L'lG and H is estimated, 00 that H is stable and nonminimum phase. Then a new controller Q is computed for the next iteration by minimising an H ~-norm 11 J(Q I G,H) IL where

with weighting function W associated with a priori knowledge on the speclrum of the disturbance source

e. In the scalar case one obtains J(QIAG,H)

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with notation G = GoAG, wbicb nicely separates the two requirements of disturbance attenuation and good modelling into the numerator and the denominator, respectively. As G is an estimate, the numerator 1- GQ can be made small in a given frequency band of the disturbance. Also, if the modelling is reasonably good in this frequency band then the denominator remains around 1, thereby not affecting attenuation noticeably. Stability and cautiousness in the ilerations is achieved by the optimisation of IIJ(Q I G,H) IL for Q. Technically, the use of dual Y oula parametrisation appears to have advantages for gradual controller enhancement as shown by Van den Hofet al. (1993).

In the case that a Signal r can be measured which is strongly correlated with e, the control scbeme can be changed to the one in Fig. 8. The dashed lines denote parameter adaptation. The idea is to tune F and G in separate iterations. In one iteratiou

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F is kept constant. Stability is ensured if G is not too distant from G , hence a good starting value of G is essential. F can be estimated by LMS adaptive filtering.

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Fig. 8. Pure feed-forward control scheme by adaptive filtering and internal modelling.

Frequently, the available signal r is weakly correlated with e, and lherefore a scbeme can be applied which combines feedback and feed-forward control a.... displayed in Fig. 9.

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Copyright 1999 IF AC

ISBN: 008 0432484

lNTELLlGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

14th World Congress ofIFAC

feedback control design. A combination of the two has been found to give the best results in a laboratory experiment of plate vibration with five parallel electromagnetic actuators as illustrated in Fig. 11.

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In each iteration two out of Q ' F and AG is kept constant while the third is tuned, A condition of stable iterations is that a stabilising initial Q is known with an associated AG . Initial stabilising Q can be found by an off-line identification experiment Optimisation of the feedback controller Q is again done by minimiSing the earlier H~­

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nonn 11 J(Q I G,H) II~. Optimisation of F can be done by adaptive LMS filtering, its effect is an addon to feedback control to enhance the overall control performance. The iterations of modelling and control design for an on-line system can be organised by segmentation of the time axis. An integer multiple of the sampling period NxT, is selected for segment size to perform one iteration (for instance in an application with 1kHz sampling rate a single iteration can be 2s long with N=2000), Input-output data sequences of length N can then be used to modify the estimated model and design the controller which will run during the next iteration period. This methodology easily lends itself to parallel processing of three functions (see Fig. 10):

Fig. 11. A laboratory example of vibration control of a plate excited with sound waves. As an illustration, Fig. 12 shows the different spectra achieved by feedback and combined feedback and feed-forward methods (pB and FB-FF). The strong extcrnal excitation prevented the feedback controller to achieve better attenuation but eliminated resonant modes. The feed-forward controlfer contributed substantially lo vibration reduction,

0) on-line control, i.e. receiving sensor signals and computing current control inputs for the actuators and also tuning of feed-forward controller.

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all plant input-output data available, (Hi) monitoting of disturbance attenuation and respecifying W for the feedback control designer

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for changing conditions of operation. Example. Active vibration control of machine enclosure plates usually allows for both the detection of signals which arc correlated with the source of excitation and for approximate modeUing of the enclosure dynamics. The fanner allows for tuning of a feed-forward controller while the latter allows for

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Pig. 12. Reduction in spectrum of vibration using feedback (FE) and combined (FB-fF) methods.

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INTELLIGENT ADAPTIVE ACTIVE CONTROL OF NOISE AND V ...

A great benefit of the iterative method has been the much better handling of stability than it was possible in continuously tuning feedback schemes. 7. CONCLUSION Intelligent ad.:'lptive active control schemes for broadband cancellation of noise and vibration has been presented. 1bese have been realised with conventional RLS algorithms, GAs, neural networks and iterative adaptive tuning. The pcrfonnance of the resultant systems have been veritied in the broadband cancellation of noise in frce-field and vibration suppression in a cantilever' beam and flexible plate systems. The significance of the strategy in each case has been demonstrated by impressive levels of perfonnance over broaLI range of frequencies of the disturbance. It has been shown that global cancellation of the disturbance to a significant level can be achieved by devising such approaches. 8. REFERENCES Elliott, S.J. an dB. Rafaely (1997). Frequencydomain adaptation of feed-forward and feedback controllers. Proc. A CT1VE'97, Budapest, 21-23 August, 1997, pp. 771-788. Elliott, S. J., Stothers, I. M. and Nelson, P. A. (1987). A multiple error LMS algorithm and its application to the active control of sound and vibration. IEEE Transactions on Acoustics Speech, and Signal Processing, 35, (10), PP'. 1423-1434. Eriksson, L. 1., AlIie, M. C. and Greiner, R. A. (1987). The selection and application of an HR adaptive filler for use in active sound attenuation. IEEE Transactions on Acoustics, Speech, and Signal Processing, 35, (4), pp. 433437. Fuller, C. R., Rogers, C. A. and RoberlShaw, H. H. (1992). Control of sound radiation with active/adaptive structures. JOltrnal Of Sound and Vibration, 157, (1), pp. 19-39. Hansen, C. H., Simp1Son, M. T. and Wangler, C. T. (1996). Application of genetic algorithms to active noise and vibration control, In Crocker, M. J. and Ivanov, N. 1. (eds.), Proceedings of the fourth International Congress on Sound and Vibration, St Petersburg, 24-27 June 1996, International Scientific Publications, Aubum, 1, pp. 371-388. HjaImarson, M. Gevers and F. DeBruyne (1996). For model based control design closed loop identi11cation gives better performance. Automatica, 32, (12), pp. 1659-1673.

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Kosut, R (1996) Iterative adaptive robust control via uncertainty model unfalsification. 13 th IFAC Triennial World Congress, San Francisco, pp.91-96. Lee, A.G., B.D.D. Anderson, R.L. Kosutand LM.Y. Mareels (1993). On robust perfonnance improvement tlIrough tlIe wind-surfer approach to adaptive robust control. Proc. 32"d CDC, San Antonio, Texas, Dec. 1993, pp. 2821-2827. Lueg, P. (1936). Process of silencing sound oscillations. US Patent 2043416. Partanen, A.G. and RR Bitmead (1993). Two-stage iterative identification/controller design and direct experimental control1er refinement. Proc. 32 nd CDC, San Antonio, Texas, Dec. 1993, pp. 2833-2837. Schrama, E.I.P (1992). Accurate identification for control: the necessity of an iterative scheme. Selected Topics in Identification, Modelling and Control, Vol. 4, 1992, Delft Univ. Press, pp. 1116. Snyder, S. D. and Hansen, C. H. (1992). Design considerations for active noise control systems implementing the multiple input, multiple output LMS algorithm. Journal of Sound and Vibration, 159, (1), pp. 157-174. Tokhi, M. O. and Hossain, M. A. (1996). Active vibration control of flexible beam structures using genetic algorithms, In Cracker, M. J. and Ivanov, N. I. (eds.), Proceedings of the fourth International Congress on Sound and Vibration, St Pctcrsburg, 24-27 June 1996, International Scientific Publications, Auburn, 1, pp. 423-430. Tokhi, M. O. and Leitch, R. R. (1991). Design and implementation of self-tuning active noise control systems. lEE Proceedings-D: Control Theory and Applications, 138, (5), pp. 421-430. Tolffii, M. O. and Wood, R (1996). Neuro-adaptive active control, In Crocker, M. 1. and Ivanov, N. 1. (eds.), Proceedings of the fourth International Congress 011 Sound and Vibration, St Petersburg, 24-27 June 1996, International Scientific Publications, Auburn, 1, pp. 399-406. Van den Hof, P.M.J. , R.J.P. Schrama, O.H. Bosgra and R.A, de Callafon (1993). Identification of normalized coprime plant factors for iterative model and controller enhancement. Proc. Of 32 nd CDC, San Antonio, Texas, Dec. 1993, pp. 2839-2843. Veres, S.M. (1998) Iterative identification and control redesign via un-falsified sets of models. International Jar/malo/Control. (To appear). Veres, S.M. and V.F. Sokolov (1998). Adaptive robust control under unknown model orders. AUlOflU/.tica, 34. (5). pp.

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