Hierarchical sliding mode observers for distributed parameter systems

Abstract

In this work we suggest hierarchical sliding mode observers for complex systems which include distributed parameter systems and combinations of distributed parameter and lumped parameter systems, modeling, for example, an actuator dynamics. The main idea is based on the observer suggested previously for general nonlinear lumped parameter systems that is using the equivalent values of the discontinuous function to obtain additional information about the system state. Such observers can be written directly into system’s original variables without requiring the state transformation. In this paper, using a modal representation of the distributed system and the hierarchy of sliding modes, we develop a structure of such an observer for a wide class of systems described by partial differential equations or combinations of ordinary and partial differential equations. An example is presented which illustrates the proposed method.