Zero Dynamics of Nonlinear MIMO Systems from System Configurations - A Bond Graph Approach

Abstract

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems, Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics, However, the calculation of zero dynamics is usually complicated, especially in a form which is suitable for design. In th is paper, a method of deriving the zero dynamics from bond graph models is proposed. This method incorporates the definit ion of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. Isolated subsystems which exhibit the zero dynamics can be found if they exist. Thus, the design of physical systems including the consideration of zero dynamics becomes straightforward. This approach is generalized for non linear MIMO systems.