Zero Dynamics of Physical Systems From Bond Graph Models—Part II: MIMO 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. In the Part I paper, a method is proposed to derive the zero dynamics of SISO systems from bond graph models. Using this approach, the design of physical systems, including the consideration of zero dynamics, can be performed in a systematic way. In this paper, the extension of the proposed method for MIMO systems is presented. It is shown that for MIMO systems, the input-output configurations determine the existence of vector relative degrees. If a system has a vector relative degree, it’s zero dynamics can be identified by a straightforward extension of the proposed method. If a system does not have a vector relative degree, a dynamic extension procedure may be used to fix the structure. By doing so, the zero dynamics can still be identified in a similar manner. It is also shown that if the input-output configurations are ill-designed, not only the relative degrees do not exist, but also the zero dynamics can not be reasonably defined. In that case, independent tracking controls for all the outputs are impossible. Therefore, the results in this paper provide a guideline for the design of the input-output configurations as well as the zero dynamics of MIMO systems.