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

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.