Sliding Mode State and Fault Estimation for Decentralized Systems

Abstract

The interconnection of dynamical systems gives rise to interesting challenges for control in terms of stability, robustness and the overall performance of the global interconnected systems as well as the fault tolerance of the individual subsystems. Interconnected systems can be developed either from a standpoint of centrality of control based on the construction and design of a global system that satisfies the above requirements. Alternatively, the interconnected system can be decentralized which means that the stability, performance, etc., requirements are achieved at the local (subsystem) levels. To develop a good “fault-tolerant control” strategy for decentralized systems it is necessary to take account of various faults or uncertainties that may occur throughout all local levels of the system. A powerful way to achieve this is to use robust state and fault estimation methods accounting for the model–reality mismatch that is inevitable when (a) systems are linearized and (b) when faults occur in subsystem components such as actuators, sensors, etc. The chapter develops a strategy for decentralized state and fault estimation based on the Walcott–Żak form of sliding mode observer (SMO) with linear matrix inequality (LMI) formulation. This strategy is shown to be advantageous when considering the estimation problem for a large number of interconnected subsystems. After developing the design procedure a tutorial example of two interconnected linear systems with nonlinear interconnection functions shows that the states as well as actuator and sensor faults can be robustly estimated. Finally, an application-oriented example of a three-machine power system is given which has actuator faults as well as nonlinear machine interconnections.