Arbitrary Pole Placement With Limited Number of Inputs and Outputs

In controller design problems, the quantitative description of the desired controlled system behavior is often given by specifying the closed loop poles. An output-variable, feedback control policy for a linear system of order n, with m outputs and p inputs, is described by u = −Gy. Matrix G contains p × m parameters which may be used to dictate the locations of the closed loop poles. The limiting condition for arbitrary pole placement, without some form of state estimation, is p × m = n since the p × m independent controller parameters may be used to specify the n poles. However, there is no systematic procedure for the design of controllers subject to limiting condition. In this paper, a technique based on modal system description is used to design static output-variable feedback controllers with limited number of inputs and outputs. It is shown that arbitrary closed loop pole placement is possible if p + m ⩾ n + 1 for sufficiently well coupled systems.