IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 6, NO. 1, JANUARY 1998 33 Application of Model-Matching Techniques to Feedforward Active Noise Controller Design Jwu-Sheng Hu, Shiang-Hwua Yu, and Cheng-Shiang Hsieh Abstract— In this paper, three digital model-matching tech- niques in 2 , , and 1 performance measures are applied to design digital feedforward controllers for active noise cancellation in ducts. Different measures account for different optimization objectives in terms of physical signals. The distributed nature and high-bandwidth requirements of the control system result in a large set of parameters in plant description and these design techniques proved to be useful in solving the controllers numerically. Experiments were conducted using a floating-point digital signal processor that produced broad-band noise reduc- tion. Design variations and noise reduction effects in terms of human perception are also discussed. It is experimentally proved that using model-matching designs, the causality principle originally raised by Paul Lueg does not have to be satisfied in order to actively reduce the noise level. Index Terms—Acoustic noise, active noise cancellation, digital filters, digital signal processors, -infinity optimization, model matching methods. I. INTRODUCTION M ODEL-MATCHING techniques are fundamental to a wide variety of linear control systems design problems [6], [17], [33]. While many feedback control problems can ultimately be formulated as model-matching problems, the most straightforward application is to design feedforward controllers [11], [18], [28]–[30], [35]. Generally speaking, a feedforward controller has to invert the plant in a certain way, i.e., making the signal path from reference input to output as close to identity as possible. To characterize the word “close,” several mathematical indexes such as the - norm (maximum amplitude of a transfer function) or 2 - norm (energy of the impulse response) fit naturally into the picture. As a result, model-matching techniques based on these measures have become very useful in designing feedforward controllers [31]. Basically, optimization of various error measures is the key to these techniques. However, there are two different approaches to deal with the design problem. When reference or disturbance signal types are known, e.g., step or sinusoidal functions, it is necessary to include the signal in the error measure. Usually this is accomplished by directly optimizing the error signal in different time-domain measures [15]. For unknown signal types (e.g., random or nonstationary), the Manuscript received March 19, 1996; revised June 2, 1997. Recommended by Asociate Editor, E. G. Collins, Jr. This work was supported by the National Science Council of Taiwan under Grant NSC84-2732-E009-009. The authors are with the Department of Control Engineering, National Chao-Tung University, Hsinchu, Taiwan, R.O.C. Publisher Item Identifier S 1063-6536(98)00578-8. optimal solutions are obtained by considering worst case scenarios. Consequently, instead of minimizing error signals, deviation of signal paths from identity is optimized. This paper describes the application of model-matching techniques to designing digital feedforward active noise con- trollers. As an effective way of reducing low-frequency noise, active noise control methods have drawn much attention in recent years [12], [23]. Perhaps the most popular controller- design approach is based on the least mean square (LMS) algorithm originally developed by Widrow [36]. Although many modifications of this algorithm have been developed [7], [8], the basic controller structure applied to active noise cancellation is as shown in Fig. 1. The dotted line in Fig. 1 represents the controller’s tuning path. Several modifications are done when ’s measure- ment contains the influence of acoustic feedback from the control speaker. From this figure, it is quite clear that for persistently-excited noise inputs, LMS actually tries to solve the model-matching problem on-line with respect to the least- mean-square measure. The ideal controller (a perfect match) must fulfill (1) or (2) In most cases (2) cannot be satisfied due to nonminimum phase zeros and delay steps (which correspond to zeros at infinity). Attempts have been made to approximate the inverse by curve- fitting the spectrum of using an FIR filter [27]. In that case, only the and spectra are required. From the discussion in the preceding paragraph, it is clear that selecting (Fig. 1) off-line can be cast as a model- matching problem. Further, from the design standpoint, this is almost identical to a tracking design problem. Recent progress in tracking control shows the value of using preview steps in designing feedforward controllers [1], [13], [22], [25], [31], [32]. Preview steps are necessary to minimize the effect of nonminimum phase zeros which are common in sample-data systems when both sampling rates and relative degrees are high [2]. In order to use preview steps, future information on reference or disturbance signals is required. For active noise control systems, the hardware configuration is usually arranged such that the noise transmission path is longer than the control sound transmission path (see Fig. 1). In other words, has more delay steps than in the sense that a signal is injected simultaneously into both paths. The difference in delay steps 1063–6536/98$10.00  1998 IEEE