Optimal tracking control for linear stable tall plants

Control design for plants having more outputs than inputs (tall plants) must deal with a fundamental constraint. This constraint arises given that, in general, zero stationary error cannot be achieved in all channels for arbitrary references and disturbances. In mathematical terms, this is due to the fact that the plant transfer function is not right-invertible. In this paper a real p×m (with p > m) transfer matrix G[z] is considered. The focus is on an optimal control which minimizes a quadratic norm, under some constraints on stationary errors for step references. In particular we consider when the references are steps with arbitrary directions, and we want to achieve zero stationary error in m channels, meanwhile in the others (p-m) we only aim to obtain a good transient behaviour. We also propose an heuristic criteria to choose which channels will exhibit zero steady state errors; that criteria relies on a gramian based interaction measure.