Development and performance evaluation of an infinite horizon LQ optimal tracker

Abstract

The paper presents an infinite horizon LQ optimal tracking control solution (LQ tracker) for discrete time linear time invariant systems. The reference preview need is reduced to only two steps irrespective of the type of reference signal making real-time implementation an achievable goal. A rigorous proof of optimality is provided for a set of infinite horizon reference commands which includes the linear combination of constant and exponentially bounded signals. Dissipativity, finite gain and l1 performance of the controlled system are also evaluated. The behaviour of the proposed LQ tracker and its previously published sub-optimal version with one-step preview is demonstrated in conjunction with an application example. Their performances are compared to those of alternative solutions including set point control and model predictive control considering aspects of practical application. Finally, it is concluded that the proposed rigorous solution of the infinite horizon tracking problem and its sub-optimal version are real-time realizable and perform advantageously in some aspects compared to other solutions.