Robust adaptive feedforward control and achievable tracking for systems with time delays

Abstract

A feedback/feedforward controller architecture is developed that characterises the achievable reference tracking of real time inputs for both minimum phase and non-minimum phase systems with time delays, when there are no modelling errors or external disturbances. This characterisation is obtained by factoring the plant into its minimum phase, non-minimum phase, and time delay components, which are used to design two feedforward controllers that inject signals into two points of the feedback loop. Design constraints are provided that determine both the types of signals that may be achieved, and the feedforward controllers that will generate that output. Of course, in practice, both modelling errors and external disturbances will be present. In this case, we develop robust analysis tools that both guide the feedback controller design process, and provide rigorous robust tracking performance that guarantees for the overall resulting closed-loop system. Robust methods for designing the feedforward controllers are presented, and numerical examples are provided. The performance of this architecture depends strongly on the choice of design parameters, and the accuracy of the plant model used. Hence, the use of adaptation methods is also considered, and it is shown that they can readily be employed to improve the performance of this control methodology.