A Geometric View on Inversion-based Detection Filter Design in Nonlinear Systems
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A GEOMETRIC VIEW ON INVERSION-BASED DETECTION FILTER DESIGN IN NONLINEAR SYSTEMS * A. Edelmayer, J. Bokor and Z. Szabd Systems and Control Laboratory, Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Kende u. 13-17, H- 1111, Hungary e-mail: edelmayerOsztak±, hu Abstract. In this paper the idea of input reconstruction by means of system inversion is discussed. In view of the latest results of geometrical system theory the properties of the inverse is characterized. It is shown how the dynamic inversion approach can be used to construct residual generators to fault detection and isolation. Linear and nonlinear systems with vector relative degree are considered. Copyright (~ 2003 IFA C. Key words. Fault detection and isolation, Input observability, Input reconstruc- tion, Inverse system, Nonlinear systems, Vector relative degree. 1. INTRODUCTION Consider the general state space model of the dynamical system subject to multiple, possible simultaneous failures m he(t)- f(x, u) + ~-~gi(x, u)vi i m v(t) = + e (x, i (1 ) where f, g, h, g are analytic functions of time with X(t) e X C ~n, u(t) e ]~m, y(t) e ]~m, the vector valued state, input and output variables of the system, respectively, u(t) is the fault signal (ul,...,um) T whose elements ui : [0,+c~) -+ are arbitrary functions of time. Note that the fault signals u/ can represent both actuator and sensor faults, in general. The goal is to detect the occurrence of the components u/ independently from each other and identify the fault component * This work has been supported by the Hungarian Na- tional Science Foundation (OTKA, Grant No: T 032408) which is gratefully acknowledged by the authors. which specifically occurred. Usually, the detection and isolation of faults is established by a decision process which is based on the residual. The residual generator, by utilizing the usual pro- cess signals assumed to be available for measure- ments (outputs and control inputs), reproduces the fault signal at its output that is zero in normal operation of the system, while it differs from zero if a particular fault occurred. There are various ways that can be used in con- structing residual generators. Traditional meth- ods are based on the error dynamics of a state observer, see e.g., the geometric design approach initiated by Massoumnia (1986) for LTI systems. The same geometric interpretation was followed by Edelmayer et al. (1997) for LTV, moreover, Hamm ouri et al. (1999) for bilinear and De Persis and Isidori (2001) for nonlinear systems, just to mention a few. These approaches were used in a number of situations differing in the assumptions on noise, disturbances, robustness properties and in the specific design methods. For comparison, see some representations in the literature like
A Geometric View on Inversion-based Detection Filter Design in Nonlinear Systems
