On Relative Degrees and Zero Dynamics from System Configuration

Relative degrees and zero dynamics are intrinsic system properties associated with a given input-output pair. In the design of output tracking controllers, the relative degree and the stability of the zero dynamics of the control plant are usually assumed to be known in advance, and are determined by analyzing the system dynamic equations. With the help of bond graphs and through physical reasoning, a set of rules are proposed in this paper to determine the relative degree and the stability of the zero dynamics for a class of systems independent of the system dynamic equations. The rules establish a connection between these system properties and the physical structures, and are useful guidelines on the adjustment of relative degrees and zero dynamics for the purpose of control design.