JSAE20014060

JSAE Review 22 (2001) 157}162

Development of an adaptive control simulation system for vehicleexhaust noise reduction

Keqiang Li�, Takeharu Tanaka��State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, People's Republic of China

�Trazc Safety and Nuisance Research Institute, Ministry of Transport, Shinkawa 6-38-1, Mitaka-shi, Tokyo 181-0004, Japan

Received 29 September 2000; received in revised form 16 October 2000

Abstract

An adaptive control strategy for vehicle exhaust noise reduction considering acceleration characteristics is presented, and itssimulation analysis system is developed in order to e$ciently examine the performance of the proposed control approach. Thesimulation system, which is implemented with the MATLAB/Simulink dynamic system analysis tools, and can be employed toevaluate the di!erent control algorithms easily, plays an important role in the control system design. After many simulation tests, suchas investigating the features of control trackability and stability under accelerated running condition, the practical application of theANC system for vehicle exhaust noise reduction is introduced. � 2001 Society of Automotive Engineers of Japan, Inc. and ElsevierScience B.V. All rights reserved.

1. Introduction

As a supplemental technique to traditional passivenoise control such as sound shielding and absorption,active noise control (ANC) has received considerableattention in recent years. The ANC method applied tovehicle exhaust noise reduction includes some advant-ages such as no increase in the exhaust back pressure andimproved performance of engine power output and fueleconomy. Furthermore, it may make the structure of theactive mu%er compact and facilitate its installation [1].Because the exhaust noise often changes with engine loador rotational speed, some preferable adaptive controlstrategy that can track these changes must be included inan ANC system. It is necessary to develop a controlsimulation system for examining the performance of theproposed control method e$ciently.In this paper, an ANCmethod for exhaust noise reduc-

tion of a medium-duty diesel truck is introduced. Toensure the successful operation of its controller ina time-varying environment, a modi"ed, variable stepsize LMS algorithm is proposed; in order to examine theperformance of the proposed control method e$ciently,an adaptive control simulation system for vehicle exhaustnoise reduction is developed. By using the simulationanalysis system, the performance of control trackabilityand stability are investigated by comparison of the

proposed method with the conventional, constant stepsize LMS method. Furthermore, the rationality andvalidity are veri"ed by employing the ANC system toexhaust noise control of a diesel engine truck subject toaccelerated running.

2. Variable step size LMS control algorithm

The vehicle exhaust noise, which is mainly caused byexhaust impulsation, is generally composed of severalharmonic components with a fundamental frequencythat varies as a function of the engine rotational speed.As the noise is periodic and is dominated by harmonicsof the basic "ring rate, the time-domain waveformsynthesis method, also called the synchronized "ltered-LMS method [2,3], in which the rotational pulse ofthe primary noise is used for the reference input, isadopted.

2.1. Time based synchronized xltered-x LMS method(SFX-TB)

The block diagram of the SFX method as applied tothe exhaust noise control problem is illustrated in Fig. 1.The concept of the method can be analyzed as if theadaptive FIR "lter is excited by an impulse train of

0389-4304/01/$20.00 � 2001 Society of Automotive Engineers of Japan, Inc. and Elsevier Science B.V. All rights reserved.PII: S 0 3 8 9 - 4 3 0 4 ( 0 0 ) 0 0 1 0 4 - 1

Fig. 1. Block diagram of SFX method as applied to exhaust noisecontrol.

period N samples:

x(n)"��

����

�(n!�N), (1)

where �( ) is the Kronecker delta function, the integerN satis"es N"¹

�/¹ where ¹ is the sampling period,

and ¹�"2�/�

�is the period of the noise with funda-

mental angular frequency ��. The "ltered reference sig-

nal r(n) is generated by passing the x(n) signal through thec(j) named secondary path:

r(n)"�������

c(j)x(n!j)"��

����

�������

c(j)�(n!j!�N)

"

��

����

c(n!�N),C(n). (2)

In Eq. (2) C(n) is said to be the aliased periodic sequence.So the coe$cients of the adaptive "lter are updated bythe well-known LMS algorithm as

w�(n#1)"w

�(n)!�e(n)r(n!i), i"0, 1,2,¸!1, (3)

where � is the step size parameter for obtaining theupdate equation. The adaptive "lter output y(n) is gener-ated as

y(n)"�������

w�(n)x(n!i)"

�������

w�(n)

����

������

�(n!�N!i)

"w����

(n), ¸"N, (4)

where j(n)"nmod¸ and ¸ is the order of the adaptive"lter. In practical application, the actual period variesfrom the normal value as a function of loading conditionsand running speed. Therefore, the time based SFX

method is adopted, i.e., the ANC system operates witha "xed sampling rate and the tap numbers of the adaptive"lter are related to the period of the fundamental fre-quency of the noise. In this way, the secondary pathestimate "lter coe$cients do not have to be changed asa function of actual engine rotation rate. Also, the track-ing capability of the SFXmethod during rapid changes ofengine rotational speed, which results in a change in thefundamental frequency of the noise, can be partly im-proved by the method.

2.2. Variable step size SFX-TB method

According to the theory of adaptive "lters, it is veryimportant but di$cult to determine the optimal step sizeparameter �, which strongly a!ects the performance ofthe control system. Improper selection of � might eithermake the convergence speed unnecessarily slow or intro-duce a large misadjustment [2,4,5]. To control theexhaust noise of a truck in actual running conditions,especially during acceleration, an adaptive controlalgorithm that can both achieve rapid convergence andminimize misadjustment is demanded. In this paper,a variable step size SFX-TBmethod is proposed to devisean adaptive algorithm which is more e$cient than theconventional "ltered-x LMS algorithm. The updatingof adaptive "lter coe$cients with the method can beimplemented in the following notation:

w�(n#1)"�

w�(n)!�e(n)r(n!i), �'�

�,

w�(n)!�

�e(n)r(n!i), others,

(5)

in which

�"��A

�/A

�,

A�"max��e(0)�, �e(1)�,2, �e(n)��,

A�"max��e(M#0)�, �e(M#1)�,2, �e(M#N

�!1)��,

M"N�#N

�#2#N

���,

whereA�is the absolute value of the measuredmaximum

residual error e(n) until the time index n, A�is the abso-

lute value of the measured maximum residual error e(n)in the kth period of noise with fundamental frequency,��is the minimum value of the step size �, �

�is the

maximum value of the step size � and N�is the sampling

point of the ith period. � is allowed to vary between thevalues �

�and �

�. The selection of �

�is based on

the condition of stability, whereas ��is chosen to balance

the convergence speed and the desired misadjustment.High values of � are "rst chosen to achieve rapid conver-gence. After convergence, low values are adopted to min-imize misadjustment, and � can be changed only with theresidual error signal.

158 K. Li, T. Tanaka / JSAE Review 22 (2001) 157}162

Fig. 2. Block diagram of simulation system.

3. Design of the hybrid simulation system

The simulation analysis is necessary for shorteningthe period of control system development. In order toevaluate the performance of the proposed method e$-ciently, the control simulation supporting system is de-veloped and many related simulation tests are conductedusing the simulation system.

3.1. Design of the hybrid simulation system

When an adaptive control simulation system for ve-hicle exhaust noise reduction is applied in practice, somefactors such as system modeling and running condition(e.g. constant running and accelerated running), whichin#uence the simulation results, should be consideredappropriately. In this research, the system model is de-signed with the MATLAB/Simulink dynamic systemanalysis tool [6], and the method of hybrid simulation isadopted for improving the reliability of the simulationprocess. Although the transfer function of the secondarypath between the second sound source and error micro-phone is di$cult to obtain directly, it can be expressed byits experimental model, while the other parts of the sys-tem are modeled with the MATLAB/Simulink blockfunction. The adaptive control simulation system de-signed for vehicle exhaust noise reduction is shown asa block diagram in Fig. 2.The simulation system contains the basic block func-

tions of MATLAB/Simulink and the subsystems whichare made of the basic block functions or experimentalmodels. The upper part of Fig. 2 expresses the exhaustnoise before control, in which the situation of enginerotation is described with the `Chirpa block. That meanswhen the fundamental frequency and its harmonic com-ponents, the sweeping start frequency and its end fre-

quency are set, the varying conditions of engine rotationcan be simulated. Furthermore, if the sweeping timeinterval is assumed to be a value close to in"nity, theconstant engine speed condition can also be approxi-mated. The `Matrix Gaina block represents the ampli-tudes of harmonic components of the exhaust noise, andthe `Transport Delaya block is used to express the phasedi!erences between engine outlet and the exhaust muf-#er. The `Zero-Order Holda block is used for convertingthe continuous system into a discrete one and the`Noisea block is for considering the system disturbednoise.Fig. 3 shows the block diagram of the `pulse producera

subsystem which is used to produce the impulse of thereference signal in the SFX-TB method.The block `Chirp 1a shown in Fig. 2 is a sine-wave

simulating the fundamental component of the enginerotation. Let the signal `In 1a pass through the sub-system `pulse producera, as shown in Fig. 3. Afterprocessing with block functions such as `Switcha and`Relational Operatora, the impulse trains of the referencesignal can be obtained.Fig. 4 is the block diagram for the adaptive "lter of the

SFX-TB LMS method.In making the error path model between the secondary

loudspeaker and the error microphone shown in Fig. 4,the traditional method is to ignore the model or describeit with a simpli"ed one because of some technologicaldi$culties in representing the model mathematically. Inthis research the hybrid simulation system containing anexperimental model is adopted to resolve this problem.In order to get the updating coe$cients of the adaptive"lter, the `LMS Coe$cient Updatea subsystem is de-signed with the SFX-TB method including the variablestep-size algorithm proposed above. The subsystem fea-tures make it easy to replace di!erent control algorithms,

K. Li, T. Tanaka / JSAE Review 22 (2001) 157}162 159

Fig. 3. Block diagram of subsystem `pulse producera.

Fig. 4. Block diagram of SFX-TB LMS adaptive "lter.

check the temporary data and compare the results ofsimulations.To summarize the adaptive control simulation system

developed for vehicle exhaust noise reduction, we can"nd:

(1) Based on adopting the hybrid simulation scheme, theerror path between the secondary loudspeaker anderror microphone can be modeled easily, and alsothe simulation results can be achieved precisely.

(2) Both acceleration and constant engine rotation con-ditions can be simulated on the same system bysetting the sweeping time interval appropriately.

(3) Because subsystems can be rebuilt according to dif-ferent aims, the categories of simulation, such as therevising of control algorithms, the evaluation of in-terim processes and the display and saving of real

time control results can be chosen freely, so that it ispossible to get better operability and e$cient simula-tion in practical applications.

3.2. Results of simulation analysis

Using the developed simulation system, and analysis ofsimulation parameters such as sampling frequency, tapnumbers of the adaptive "lter and value of step size wasconducted. Furthermore, the system performance of con-trol trackability and stability are investigated consider-ing the acceleration condition of engine rotation.Fig. 5 illustrates the simulation results of the variable

step size algorithms in comparison with the conventionalalgorithm whose step size in constant. Fig. 5(a) shows theresponses of the residual error signal with the two kindsof methods, assuming the engine is rotating at a constant

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Fig. 5. Simulation results with two methods: (a) at a constant speed of n"1200 rpm; (b) during speed change from n"1200 to 2400 rpm.

Fig. 6. Truck exhaust noise control test set up. Fig. 8. Tracking analysis results of the exhaust noise.

Fig. 7. Time history of the exhaust noise.

speed of n"1200 rpm. Fig. 5(b) shows the responses ofthe residual error signal with the two methods duringengine acceleration from n"1200 to 2400 rpm.From the results shown in Fig. 5, we can observe that

the proposed variable step size SFX-TB algorithm canprovide faster convergence and less misadjustment thanthe conventional constant step size algorithm in the ap-plication of active noise control.

4. Experimental analysis

Experiments of exhaust noise control of a truck duringacceleration are conducted using the ANC system involv-ing di!erent control algorithms. Fig. 6 is the test set up,and Figs. 7 and 8 are the experimental results. Fig. 7shows the time history of the measured exhaust noisein the case of three conditions: ANC system turnedo!, ANC system turned on with constant step sizealgorithm and the variable step size algorithm. Thestep size �"0.4 is the best selection for noise control ofthe truck, as determined by trial and error with theconventional constant step size algorithm. Fig. 8 showsthe tracking analysis results of the noise in the samecases.

It has been pointed out that it is necessary for the ANCsystem of vehicle exhaust noise control to be capable oftracking changes in engine load and rotational speed.Since the step size parameter is appropriately chosen asa function of measured residual error signal in the pro-posed method, it has the capability of better trackabilityand stability during the control process. It is veri"edby these experimental results that the e!ect of tracking

K. Li, T. Tanaka / JSAE Review 22 (2001) 157}162 161

control is particularly evident at the beginning of arotational speed change.

5. Conclusions

In this paper we studied the adaptive control approachfor vehicle exhaust noise reduction with a modi"ed vari-able step size LMS algorithm which uses a relativelyappropriate and simple method for step size changesduring the control process. An adaptive control simula-tion analysis system was developed for evaluating thefeatures of the control system. The following conclusionswere obtained:

(1) As it is necessary for an ANC system to deal withaccelerating engine conditions in the application ofvehicle exhaust noise reduction, the variable step sizeSFX-TB method, in which only the residual errorsignal is needed for calculating the step size para-meter �, is recommended.

(2) The developed adaptive control simulation systemfor vehicle exhaust noise reduction is capable of

testing the performance of the proposed controlstrategy e$ciently.

(3) The simulated and experimental results show thatthe developed simulation system plays an importantrole in practical applications. The proposed controlalgorithm can make the ANC system for vehicleexhaust noise reduction yield better controllabilityand stability than the conventional method.

References

[1] Tanaka, T., Li, K., Study on the active exhaust mu%er for mediumsize engine truck, Proc. JSAE Conf. No. 9939712 (1999).

[2] Kou, S.M., Morgan, D.R., Active Noise Control System, Wiley,New York (1996).

[3] Hamada, H., Ito, K., Uto, S., Miura, T., Synchronized "ltered-xalgorithm and its application to active control of sound and vibra-tion, Proc. Acoust. Soc. Jpn. (1992).

[4] Widrow, B., Stearns, S.D., Adaptive Signal Processing, Prentice-Hall, Englewood Cli!s, NJ, 1985.

[5] Elliott, S.J., Nelson, P.A., Active noise control, IEEE Signal Pro-cess. Mag., pp. 12}35 (October 1993).

[6] The MathWorks, Inc. MATLAB/Simulink Handbook, Ver. 5(1999).

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