Zero Assignment for Robust $H_{2}/H_{\infty}$ Fault Detection Filter Design

In practical engineering, it is inevitable that a system is perturbed by noise signals. Unfortunately, $H_{\infty} /H_{\infty}$ filtering may fail to detect some faults when the noise distribution matrix are the same as the fault distribution matrix. In this paper, it is shown that the dynamic feedback gain of a dynamic filter introduces additional zeros to the filter, and both the filter poles and the additional zeros can be assigned arbitrarily. In order to attenuate band-limited noises, the zero assignment technique is used, and an optimal dynamic fault detection filtering approach is proposed by locating the zeros to the noise frequencies and optimizing the poles. Compared to other dynamic filter design approaches, the zero assignment technique gives a better tradeoff between more design freedom and computation costs. As shown in the simulation, a better noise attenuation and fault detection performance have been obtained. The zero assignment in multivariable fault detection filter design would be the main contribution of this paper.