State space modeling in multichannel active control systems

Reference:
G. Nijsse, M. Verhaegen, B. De Schutter, D. Westwick, and N. Doelman, "State space modeling in multichannel active control systems," Proceedings of the 1999 International Symposium on Active Control of Sound and Vibration (ACTIVE 99) (S. Douglas, ed.), Fort Lauderdale, Florida, pp. 909-920, Dec. 1999.

Abstract:
In recent years, Active Control (AC) research and applications have gained much attention, e.g. Active Noise Control, Active Vibration Control and Active Acoustic Structural Control. Due to the complexity of the acoustics, large scale applications, such as actively canceling broad-band noise in a wide area, still pose serious computational problems when using hardware which is not too complex and expensive. For that reason we are looking for ways to reduce the computational burden in AC systems for reducing the price and the complexity of the hardware.
One of the methods we recently successfully investigated and which we deal with in this paper, is the use of state space models instead of finite impulse response models (FIR models) in AC systems. While FIR models are commonly used in AC, they can require a large number of coefficients, deteriorating the computational complexity, especially in poorly damped plants and/or broad-band noise control applications. On the other hand, one of the advantages of state space models is that they reduce the number of coefficients and the number of computations dramatically due to their minimal parameterization.
In this paper we show how state space models can be used in AC systems and we discuss their advantages compared to FIR models. We also illustrate our approach for a vibrating plate structure.