Experimental Investigation of Active Noise Controller for Internal Combustion Engine Exhaust System

Jpn. J. Appl. Phys. Vol. 41 (22) pp. 6228 6235 Part 1, No. 1, October 22 #22 The Japan Society of Applied Physics Experimental Investigation of Active Noise Controller for Internal Combustion Engine Exhaust System Jian-Da WU, Chih-Keng CHEN 1, Chun-Ying LEE 1 and Tian-Hua LEE Department of Vehicle Engineering, Da-Yeh University, Chang-Hwa, Taiwan, R.O.C. 1 Department of Mechanical Engineering, Da-Yeh University, Chang-Hwa, Taiwan, R.O.C. (Received February 27, 22; accepted for publication June 26, 22) Two active noise control (ANC) algorithms for internal combustion engine exhaust systems are developed and their performances are compared in various experiments. The first controller is based on the filtered-x least mean square (FXLMS) algorithm with feedback neutralization, while the second is a fixed controller with a gain-scheduled active control technique for broadband attenuation with thermal effects. Both control algorithms are implemented on a digital signal processing (DSP) platform. Experiments are carried out to evaluate the attenuation performance of the proposed active noise control systems for an engine exhaust system. The results of the experiments indicate that both the adaptive controller and the gain-scheduled controller effectively suppress the noise of engine exhaust systems. The experimental comparison and analysis of the proposed controllers are also described. [DOI: 1.1143/JJAP.41.6228] KEYWORDS: engine exhaust system, acoustics, active noise control, digital filter 1. Introduction Noise from engine exhaust systems is known to be one of the major noise sources in internal combustion engines. It generally contains tones at the basic frequency, harmonic frequency noise and low level broadband noise. From a subjective point of view, tones are considered to be the most annoying components and thus need to be reduced. In general, previous techniques of noise control are divided into two main categories: passive noise control and active noise control. The passive noise control technique has been extensively studied and used to reduce undesired noise in the industry and the environment. The silencer component has been widely investigated and applied to automobiles. 1 3) Research interest in active noise control (ANC) was stimulated after Lueg s patent in 1936. 4) The ANC serves as a promising alternative to conventional passive control approaches; it provides advantages such as improved lowfrequency performance and low back pressure in the silencer. Its development has been rapidly advanced in the last two decades with the progress of digital signal processing (DSP) technology. Many sophisticated control algorithms and techniques have been implemented on DSP platforms for practical applications. In particular, ANC of a duct with synthesis noise has been extensively investigated both theoretically and experimentally. In control structures, ANC systems are divided into feedback control and feedforward control. The feedback control in duct ANC systems generally achieves only narrowband attenuation due to the spillover effect. 5,6) However, if a non-acoustical reference is not available but the order of the system is small, e.g., the headset problem, feedback control should be a feasible approach. 7,8) In the duct ANC configurations to date, feedforward control has become the most widely used method for reducing duct noise when a non-acoustical reference signal is available. It provides better performance in terms of suppressing noise within a moderate controller gain than feedback control. In practical implementation, the filtered-x least mean square (FXLMS) algorithm is a well-known adaptive algorithm for dealing with narrow band noise when the non-acoustical reference signal or the upstream acoustic reference signal is available. 9,1) The most significant feature of the FXLMS algorithm is its adaptive property, which is important in practical applications. Unfortunately, for a broadband noise source, the pure FXLMS algorithm generally achieves poor attenuation performance. In DSP implementation, convergence speed often limits FXLMS ANC system performance when a noise source or a control plant is varied, such as in the cases of noise from normal engine slew rates or during gear shifting, because the learning process of the adaptive algorithm fails to respond fast enough to the changing operation conditions. For broadband noise control, in 1985, Roure 11) proposed a fixed controller using a spatial feedforward structure in ducts. In 1988, Munjal and Eriksson 12) derived an active controller based on an acoustic filter theory. It has also been demonstrated in Hong and Bernstein s paper 7) that a spatial feedforward structure is less affected by the spillover problem than the collocated feedback structure. Although these research works show obvious attenuation of broadband noise using the proposed ANC system, they are based on fixed controllers and can not be used in practical applications since plant uncertainty is not considered. In these structures, plant uncertainty is one of the major factors contributing to the performance as well as the stability of a system, and must be taken into account in controller design. 13) Plant uncertainty may be caused by physical conditions such as flow velocity or surrounding temperature change in engine exhaust systems. It may also be caused by errors in system modeling, measurement, and computation. Changes of physical conditions and error lead to deviations of the plant, there by affecting the robustness of control systems. In this study, an experimental comparison of the abovementioned control algorithms with modifications is applied to an engine exhaust pipe. The experiments are carried out to evaluate the thermal effects on synthetic noise and practical engine exhaust noise. The ANC systems are implemented by an adaptive filter of the FXLMS algorithm and a fixed controller with a gain-scheduled spatial feedforward structure. In the adaptive controller, the variable convergence factor filter is proposed to achieve rapid convergence and promote the stability of the controller. In the spatial structure, the sub-controllers are pre-designed off-line and 6228

Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 6229 the coefficients of these controllers are saved in a lookup table for the gain-scheduled controller. The two ANC systems are implemented on a DSP to evaluate the noise level attenuation under various temperature conditions. Furthermore, a practical engine exhaust system is investigated to verify the proposed ANC systems. The experimental results demonstrate that the adaptive filter and the gain-scheduled ANC systems effectively suppress repetitive noise of engine exhaust in a practical exhaust pipe. 2. Active Noise Control Algorithms The purpose of this work is to implement and compare the control algorithms in an experimental study to verify the two main ANC systems for synthetic noise and internal combustion engine exhaust systems. The control algorithms are based on an adaptive filter of feedforward FXLMS with a feedback neutralization algorithm and a fixed controller with gain-scheduled spatial feedforward structure, which are detailed as follows. 2.1 FXLMS with feedback neutralization filter The ANC system in a duct conventionally uses a reference microphone to measure the disturbance signal of an uncertain plant, and therefore the effect of acoustic feedback should be considered. A schematic and a block diagram of FXLMS with the feedback neutralization algorithm are shown in Fig. 1. In the block diagram [Fig. 1(b)], wðnþ expresses the primary noise source, dðnþ is the primary input signal, uðnþ is the reference input signal measured by the reference microphone, and y ðnþ is the programmable digital filter output signal considering the secondary path transfer function from the adaptive filter output to the summing junction. eðnþ is the residual signal for dðnþ and y ðnþ that is Fig. 1. Adaptive filter of feedforward FXLMS with feedback neutralization algorithm. (a) Schematic of the duct ANC system and (b) block diagram. measured by the error microphone, and is expressed as eðnþ ¼dðnÞ y ðnþ ¼dðnÞ sðnþ yðnþ ¼ dðnþ sðnþ½c T ðnþxðnþš; xðnþ ¼uðnÞ pðnþ ¼uðnÞ XL 1 f^ðlþyðn l 1Þ; where filters f^ ðnþ and sðnþ are, respectively, the estimated impulse responses of the feedback neutralization filter ^FðzÞand the secondary path filter SðzÞ at time n, which is an inherent one sample delay in the feedback through ^FðzÞ because when the reference sample uðnþ is collected, the output yðnþ has not yet been computed. cðnþ is the coefficient vector of CðzÞ at time n that is able to generate the proper control signal to attenuate the primary noise. For broadband input signals, cðnþ must represent the impulse response of transfer function CðzÞ, CðzÞ ¼PðzÞ=SðzÞ, but for narrowband input signals, cðnþ must cover a substantial fraction of the input signal period. The reference sensors for broadband and narrowband feedforward ANC systems are always different. In fact, the former uses an acoustic sensor and the latter uses a non-acoustic sensor. In application, the acoustic feedback will not be considered when the reference sensor uses a nonacoustic sensor (i.e., fiber-optic sensor). The objective of the adaptive filter is to minimize the mean square error (MSE), ^ ¼ e 2 ðnþ, and the updating formula for the FXLMS algorithm is expressed as cðn þ 1Þ ¼cðnÞþx ðnþeðnþ: ð3þ In the updating formula, is a convergence factor that affects the stability and convergence rate when an ANC system is in operation. However, filters FðzÞ and SðzÞ are unknowns and must be estimated by additional filters. Therefore, the filtered reference signal is generated by passing the reference signal through the estimated secondary path filter, and the compensated feedback signal is generated by passing the output signal of the adaptive filter through the estimated feedback neutralization filter. Hence, x ðnþ ¼^sðnÞ xðnþ ¼^sðnÞ ½uðnÞ pðnþš ð4þ pðnþ ¼f^ðnÞ yðn 1Þ; ð5þ where ^sðnþ and f^ ðnþ are the estimated impulse responses of the secondary path filter ^SðzÞ and the feedback neutralization filter ^FðzÞ, which are estimated simultaneously using the offline modeling technique. In practical applications, it is difficult to estimate the optimal value of convergence factor in the LMS algorithm. The convergence factor not only controls the convergence rate but also determines the excess MSE; furthermore, is inversely proportional to convergence time. In general, a large guarantees the tracking capability of the algorithm; however, this capability is reduced when MSE is exceedingly large. By contrast, a small will affect the tracking capability and the convergence speed. Therefore, the selection of the optimal convergence factor in an adaptive filter is important. In this study, the variable convergence factor is proposed for the FXLMS algorithm and the adjustment rules are adopted on the residual signal eðnþ, and then, the updating formula is altered as l¼ ð1þ ð2þ

62 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 8 cðn þ 1Þ ¼cðnÞþ max x ðnþeðnþ >< cðn þ 1Þ ¼cðnÞþUx ðnþeðnþ; ð6þ >: cðn þ 1Þ ¼cðnÞþ min x ðnþeðnþ where U is variable convergence factor and expressed by e max U ¼ max ð7þ e mean where max is the maximum convergence factor and the selection is based on the stability conditions, min is the minimum convergence factor and the selection is chosen to balance the tracking ability and the desired extent of MSE after the adaptive filter has converged, e max is the maximum residual signal, and the e mean is the mean residual signal. For prime control, a large value of max is chosen to achieve rapid convergence when ANC starts operation, and after convergence, the convergence factor is continuously changed depending on eqs. (6) and (7) at any time. 2.2 Gain-scheduled broadband ANC controller Many linear time-varying systems have no general solutions for the dynamic equations except for some special cases. It is often difficult to design a time-varying controller in an analytical way. Some approaches such as robust control and gain-scheduled control have been applied for linear time-varying systems. Robust control has the advantage of guaranteeing stability and performance. However, it is constructed in a complicated manner and is therefore not suitable for dynamic performance. The gainschedule technique is a control technique for systems with widely varying dynamics. Linear parameter varying systems are linear time-varying plants whose state-space matrices are composed of fixed functions of some vectors with various parameters. In this study, the sub-models of a gain-scheduled control system are based on the spatial feedforward ANC control structure of a duct. In this ANC structure, an upstream input microphone is installed near the noise source but far away from the noise control source, as shown in Fig. 2. For the spatial feedforward structure, a fixed control system, originally developed by Roure in 1985, 11) is used. The structure is often employed in applications where a nonacoustical reference is not available and broadband attenuation is desired. In the control theory, the structure is not actually feedforward and it shares the same design constraints on the performance, stability and robustness as the other feedback systems. If the system contains no damping, the poles of the controller will lie on the imaginary axis and the controller will be unstable. These unstable poles are introduced as a consequence of acoustic feedback. 13) This controller is capable of achieving global noise cancellation downstream from the control source in a finite-length duct: H ð j!þ G Roure ð j!þ ¼ ð8þ ½H 1 ð j!þh ð j!þ H 2 ð j!þš; where H ðj!þ is the transfer function between the error microphone and the upstream reference microphone, H 1 ðj!þis the frequency response function between the reference microphone and the noise control speaker, and Fig. 2. Fixed controller of spatial feedforward structure. (a) Schematic of the duct ANC system and (b) Roure s controller. H 2 ðj!þ is the frequency response function between the error microphone and the control speaker. It is noted at this point that all functions of eq. (8) are measurable. In 1988, Munjal and Eriksson 12) derived an ideal duct noise controller capable of achieving global noise cancellation downstream of the control source in a finite-length duct: C ideal ¼ Z sa e jkuy Y 1 e 2jk uy ; ð9þ where Z sa is the acoustic impedance of the noise control source, Y ¼ c=s is the characteristic impedance of the duct, c is the sound speed, S is the cross-sectional area of the duct, k is the wave number, and uy is the distance between the reference microphone and the noise control source. It has also been demonstrated in Hong and Bernstein s 7) paper that a spatial feedforward structure suffers less from the spillover problem than the collocated feedback structure. Referring to Fig. 2(a), w, u, e and y are exogenous noise, measurement, performance variable and control output, respectively; the transfer functions are self-explanatory from the subscripts: G ew ð j!þ C ZSP ð j!þ ¼ G ew ð j!þg uy ð j!þ G ey ð j!þg uw ð j!þ : ð1þ This controller requires knowledge of the disturbancerelated transfer functions, G ew and G uw,which are generally unavailable in practice. To solve the problem, a more practical but equivalent controller proposed by Roure in eq. (8) is used. This can prove the equivalence between the zero spillover controller and the ideal controller. Dividing the numerator and the denominator of eq. (1) byg uw ðj!þ: C ZSP ð j!þ ¼ G ewð j!þ G uw ð j!þ G ey ð j!þ G uy ð j!þ G ewð j!þ G uw ð j!þ

Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 6231 H ð j!þ ¼ H 2 ð j!þ H 1 ð j!þh ð j!þ ¼ C Roure ð j!þ: ð11þ From the above discussion, depending on the nature of the system configuration and the measurement of transfer functions, Roure s ANC controller will be used for the sub-system controller, and implemented by using FIR filters in various thermal conditions; details of the experimental investigation are as follows. 3. Experimental Investigation The proposed ANC system is applied to attenuate undesirable noise in an exhaust pipe. The complete experimental arrangement of the exhaust pipe ANC system for synthetic noise with thermal conditions is shown in Fig. 3. The exhaust pipe exhibits noise attenuation by active and passive noise control techniques: passive control components are combined with the silencing designs of reactive and dissipative silencers for large attenuation over a broad frequency range specific to high-frequency noise, where as the active control components are consist of a control loudspeaker and microphones for low-frequency noise. The locations of the microphones and the loudspeaker are indicated in the figure. In order to mitigate the adverse effect of acoustic feedback, a backward-facing control loudspeaker and unidirectional microphones are used in hardware design, and the compensation of feedback neutralization is considered in control algorithms. In this study, primary noise sources include synthetic random noise and practical internal combustion engine exhaust noise. The proposed ANC systems are implemented on a MHz floating-point TMS32C32 DSP equipped with two 16 bit analog I/O channels by using the adaptive filter of feedforward FXLMS with the feedback neutralization algorithm and the fixed controller with gain-scheduled spatial feedforward structure that are implemented by the FIR structure. The sampling frequency is chosen to be 2 khz, and considering the cutoff frequency of the exhaust pipe and the poor low-frequency response of the loudspeaker, we chose a control band width of 1 Hz. In the proposed ANC system, the adaptive filter takes into account variable convergence factor that is different from the conventional FXLMS algorithm with the constant convergence factor. The variable convergence factor is applied using eqs. (6) and (7) to achieve rapid convergence and superior control stability. The fixed controller is implemented by employing eq. (11) of Roure s algorithm and the gain-scheduled technique is utilized for various thermal conditions. Every estimated filter is obtained by the off-line technique. The implemental significations of synthetic noise and practical engine exhaust noise are described as follows. 3.1 Experiments of synthetic noise source under various temperature conditions 3.1.1 FXLMS with feedback neutralization filter The experimental setup is shown in Fig. 3. A synthetic random noise signal is generated by a dynamic signal analyzer (HP-35665A) and output to the imitation loudspeaker. The exhaust pipe with a heater wound around it is used for validating the experimental ANC controllers. The experimental result of the proposed ANC system is shown in Fig. 4. The experimental result shows that the total band noise attenuation achieved is 4.2 db, and because the variable convergence factor is used, the adaptive filter can rapidly converge and have the more robust stability. The total band noise attenuation is defined by Z f2 Z f2 ATT(dB) ¼ 1 log 1 E off df E on df ; ð12þ f 1 where E off is the noise level when the controller is switched off, and E on is the noise level when the controller is switched on. Furthermore, various temperatures ranging from 2 Cto 1 C are applied to demonstrate the proposed ANC system s performance. Experiments demonstrate that the adaptive filter is robust to various temperature conditions and can achieve the total band noise attenuation by 4 5 db. The attenuation performance is almost the same as that in Fig. 4. f 1 PSL (db) 2 1 1 2 Frequency (Hz) Fig. 3. Experimental arrangement of the proposed ANC system for synthetic noise under various temperature conditions. Fig. 4. Experimental results of the adaptive filter for reducing synthetic noise source. Solid line depict control off; dashed line depicts control on.

6232 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 2 2 1 1 1 2 1 2 Freqency(Hz) (a) (b) 2 2 1 1 1 2 (c) 1 2 (d) 2 1 1 2 (e) Fig. 5. Experimental results of the fixed controller with gain-scheduled technique in different temperature conditions using different controllers for synthetic noise source. Solid lines depict control off, dashed lines depict control on. (a) 2 C, (b) C, (c) C, (d) 8 C and (e) 1 C. 3.1.2 Gain-scheduled ANC controller To verify the gain-scheduled control algorithms for an ANC system, a preliminary experiment is conducted using Roure s controller under different temperature conditions and using different control designs. The transfer functions H ðj!þ; H 1 ðj!þ and H 2 ðj!þ are measured before the experimental implementation in various temperature conditions ranging from 2 C to 1 C. The controllers (C 2 ; C ;...; C 1 ) are independently designed by using eq. (8) with different, H ðj!þ; H 1 ðj!þ and H 2 ðj!þ. The controllers are experimentally implemented under different temperature conditions. The experimental results of proposed controllers under different temperature conditions are shown in Figs. 5(a) 5(e). It is found that the proposed ANC system is

Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 6233 2 2 1 1 1 2 1 2 (a) (b) 2 2 1 1 1 2 1 2 (c) (d) Fig. 6. Experimental results of the fixed controller under different temperature conditions using the controller. Solid lines depict control off, dashed lines depict control on. (a) C, (b) C, (c) 8 C and (d) 1 C. effective for broadband noise attenuation in the frequency range of 1 to Hz. In order to understand the thermal effects on the spatial feedforward ANC system, the proposed ANC system is implemented under different temperature conditions ranging from C to 1 C by using the same controller (C 2 ) which was designed for use at 2 C. The experimental results are shown in Figs. 6(a) 6(d). Significant performance degradation is observed at temperatures ranging from C to 1 C, where system properties have been perturbed from the nominal one for which the control plant is designed. In order to suppress the degradation of attenuation performance, a gain-scheduled active control system for broadband attenuation of noise in ducts using the spatial feedforward structure with thermal effects is proposed. The transfer functions H ðj!þ; H 1 ðj!þ and H 2 ðj!þ are measured off-line at various temperatures. The controllers are predesigned to be C 2 ; C ;...; C 1, based on a lookup table of the DSP program. The DSP program is designed with an auto-switch function that is dependent on the different temperature inputs from a thermocouple. The sub-controller of proposed system is determined from 8 C 2 ; 11 C T < C; >< C ; C T < C; C Roure ð j!þ ¼ C ; C T < 7 C; C 8 ; 7 C T < 9 C; >: C 1 ; 9 C T < 11 C; ð13þ The experimental results indicate that the proposed design is effective for reducing the duct broadband noise under various temperature conditions. The total band attenuation is also summarized in Table I. The table shows that the Table I. Total band attenuation of fixed controller with gain schedule for synthetic noise in various temperature conditions. Test condition controller 2 C C C 8 C 1 C C 2 5.5 db 4.1 db 2.21 db.2 db 1:2 db C 3.1 db 5.6 db 3.5 db.1 db :2 db C 1.6 db 2.4 db 5.3 db 2.6 db.7db C 8.4 db 1.5 db 3.85 db 5.5 db 2.8 db C 1 1:6 db.1 db 1.9 db 3.9 db 5.2 db

6234 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. proposed ANC system achieves 5 6 db total band attenuation by using an exact controller. The performance is extremely poor in other unsuitable controllers since the control plant is changed. 3.2 Application of practical engine exhaust noise 3.2.1 FXLMS with feedback neutralization filter To explore the practicality of the proposed ANC system, the noise source is replaced by a four-cylinder, four-stroke, 2.8-liter internal combustion engine exhaust system. The experimental arrangement for a practical engine exhaust system is shown in Fig. 7. The engine exhaust noise generally contains tones at the fundamental frequency and its harmonics. Furthermore, the tones fluctuate with the engine speed. The fiber-optic sensor is utilized to detect the feedforward signal that is related to engine exhaust noise. In this experimental implementation, the related reference signal of the engine can be measured by the ignition system or the flywheel signal. However, the ignition system may have substantial interference that will affect the controllability, and therefore the reference signal is picked up near the engine flywheel by using a fiber-optic sensor. Furthermore, a frequency multiplier circuit is utilized to revise the reference signal error due to the engine flywheel signal whose frequency is half the frequency of the engine speed. The experimental results of the proposed controller that uses a reference microphone and a fiber optical sensor are shown in Figs. 8(a) and 8(b), where the engine speed is 1 rpm. The results demonstrate that tonal noise attenuation is realized at the fundamental frequency (52 Hz) and its harmonics. In order to verify if the adaptive filter can effectively attenuate engine exhaust noise under different conditions, the engine speed is varied in the range from 8 to 2 rpm. The experimental results demonstrate that the proposed ANC system is useful in suppressing engine exhaust noise by 3 4 db for total band attenuation, and the experimental results are listed in Table II. A/D Low-pass filter Pre. Amp. Error microphone Dynamic Signal Analyzer HP35665A DSP TMS32C32 D/A Low-pass filter Power Amp. Control loudspeaker A/D Low-pass filter Pre. Amp. Reference microphone Cooling system A/D Frequency multiplier circuit Pre. Amp. Fiber-optic sensor Fig. 7. Experimental arrangement of the proposed ANC system for practical engine exhaust systems. PSL (db) PSL (db) 9 8 7 3.3 db 3.1 db 3.6 db 1 1 2 2 3 9 8 7 4.6 db Frequency (Hz) (a) 4.2 db 4.3 db 1 1 2 2 3 Frequency (Hz) (b) Fig. 8. Experiment results of the adaptive filter for reducing engine exhaust noise at 1 rpm. Solid lines depict control off, dashed lines depict control on. (a) Reference microphone and (b) fiber-optic sensor. Table II. Total band attenuation of practical engine exhaust system. Engine speed (rpm) 8 12 1 2 2 Adaptive controller with reference 3.5 db 3.4 db 3.2 db 3. db 2.7dB microphone Adaptive controller with fiber-optic 4.1 db 3.8 db 4. db 3.7dB 3.4 db sensor Fixed controller with gain schedule 4.2 db 3.9 db 4.1 db 3.8 db 3.9 db 3.2.2 Gain-scheduled ANC controller The proposed gain-scheduled ANC controller is obtained from a sub-controller with a control design that differs from that of the preceding experiments. The experimental result of the proposed controller is shown in Fig. 9, where the engine speed is 1 rpm. The result shows that the proposed controller fails to reduce tonal noise since the reference signal is not a tonal frequency, but is useful to suppress broadband noise in a fixed broadband spectrum. The engine is operated under different conditions to explore the proposed controller. The experiment demonstrates that the proposed ANC system effectively suppresses engine noise by 3 4 db for the total band attenuation, and the results of the experiment are listed in Table II.

Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 1 J.-D. WU et al. 6235 PSL (db) 9 8 7 1 1 2 2 3 Frequency (Hz) Fig. 9. Experiment results of the fixed controller with gain-scheduled technique for reducing engine exhaust noise at 1 rpm. Solid lines depict control off, dashed lines depict control on. 4. Conclusions We compared two control algorithms of the ANC technique for reducing undesirable noise in a practical exhaust pipe. The experimental results reveal that the control performance of the adaptive filter of feedforward FXLMS with the feedback neutralization algorithm and that of the fixed controller with gain-scheduled spatial feedforward structure are different. The comparison of the two systems is summarized in Table III. Some conclusions for practical implementation are also noted. The convergence rate is a Table III. Control performance of adaptive filter and fixed controller. Controller performance Adaptive filter Fixed controller Convergence time Moderate Short Stability Moderate High Adaptability Yes No Environment effect Low Moderate Spectral capability Broadband and narrow band Broadband Microphone space Limit Limit Filter order Low High Computation Less Much critical factor affecting the real-time control performance and the stability of adaptive filters. The experimental results demonstrate that the performance of an adaptive filter is poor as a gain-scheduled controller although the variable convergence factor is taken into account in the adaptive filter. This is because the adaptive filter must asymptotically adjust the weight coefficient and the fixed controller is based on the total plant characteristics of the control system. From another point of view, the adaptive filter possesses the ability to adapt to different control conditions, for instance, temperature and pressure, and therefore the adaptive filter is less affected by the environment than the fixed controller. This disadvantage of the fixed controller can be compensated by using the gain-scheduled technique. Some characteristics of the two ANC systems such as adaptability, environment effects, filter order and computation are also presented. Various active control algorithms are expected to be used in different control structures, and future research should focus on the development of robust adaptive controllers to accommodate perturbations as well as uncertainties in the control system. Acknowledgement This work was supported by the National Science Council in Taiwan, Republic of China, under project number NSC- 89-2745-212-3. 1) M. L. Munjal: Acoustics of Ducts and Mufflers with Application to Exhaust and Ventilation System Design (John Wiley & Sons, New York, 1986) p. 1. 2) L. Huang: J. Sound & Vib. 238 (2) 575. 3) A. Selamet and Z. L. Ji: J. Sound & Vib. 231 (2) 1159. 4) P. Lueg: U.S. Patent 243416 (1936). 5) M. R. Bai and D. J. Lee: J. Acoust. Soc. Am. 12 (1997) 2184. 6) R. L. Clark and D. S. Bernstein: J. Sound & Vib. 214 (1996) 784. 7) J. Hong and D. S. Bernstein: IEEE Control Syst. Tech. 6 (1998) 111. 8) D. G. MacMartin and S. R. Hall: J. Sound & Vib. 148 (1991) 223. 9) P. A. Nelson and S. J. Elliot: Active Control of Sound (Academic Press, London, 1992) p. 171. 1) S. M. Kuo and D. R. Morgan: Active Noise Control Systems: Algorithms and DSP Implementations (John Wiley & Sons, New York, 1995) p.54. 11) A. Roure: J. Sound & Vib. 11 (1985) 429. 12) M. L. Munjal and L. J. Eriksson: J. Acoust. Soc. Am. 84 (1988) 186. 13) J. D. Wu and M. R. Bai: Jpn. J. Appl. Phys. (21) 6634.