Zero Dynamics of Physical Systems From Bond Graph Models—Part I: SISO Systems

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 the zero dynamics is usually complicated, especially if a form which is closely related to the physical system and suitable for design is required. In this paper, a method is proposed to derive the zero dynamics of physical systems from bond graph models. This method incorporates the definition of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of the zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. In addition, if isolated subsystems which exhibit the zero dynamics exist, they can be found. Thus, the design of physical systems including the consideration of the zero dynamics become straightforward. This approach is generalized for MIMO systems in the Part II paper.