On the exact model matching of 3-D discrete systems using feedback control

The exact model matching problem of single input-single output (SISO) systems using feedback control is considered. The closed loop transfer function of a given system is described by its 3-D transfer function, equal to a “desired” transfer function. Since the numerator of a SISO transfer function is not affected by static state feedback, series compensation is used in order to achieve the desired numerator. The problem of selecting the series compensators in the present 3-D case is generally quite involved. However, this paper notes that the model matching problem is very much simplified if the desired 3-D transfer function is factorizable and the state feed-back control is used to factorize the given transfer function. This paper provides a step-by-step example to illustrate the procedures.