Two-degree-of-freedom multi-input multi-output proportional�integral�derivative control design: Application to quadruple-tank system

Abstract

This article is concerned with designing a 2-degree-of-freedom multi-input multi-output proportional�integral�derivative controller to ensure linear quadratic regulator performance and H ? performance using a non-iterative linear matrix inequality�based method. To design the controller, first, a relation between the state feedback gain and proportional�integral�derivative gain is obtained. As the gains of proportional�integral�derivative controller cannot, in general, be found out from this relation for arbitrary stabilizing state feedback gain, a suitable form of the matrices involved in linear matrix inequality�based state feedback design is then chosen to obtain the proportional�integral�derivative gains directly. The special structure of the above matrices allows one to design proportional�integral�derivative controller in non-iterative manner. As a result, multi-objective performances, such as linear quadratic regulator and H ? , can be achieved simultaneously without increasing the computational burden much. To enhance the reference-input-to-output characteristics, a feedforward gain is also introduced and designed to minimize certain closed-loop H ? performance. The proposed control design method is applied for multi-input multi-output proportional�integral compensation of a laboratory-based quadruple-tank process. The performance of the compensation is studied through extensive simulations and experiments. � IMechE 2018.