Multivariable Nonadaptive Controller Design

Although proportional-integral-derivative control remains one of the most common control schemes used in industry, its tuning still remains inadequately understood in many applications. This task becomes much more challenging when applied to multi-input multi-output (MIMO) systems. This article presents the design of a discrete-time robust multivariable (nonadaptive) tracking controller that comes with a simple structure, requires very limited information on the plant model, and is relatively easy to tune. In addition to being easy to tune and implement, an objective of this controller is to deal with a class of large-scale systems with complex dynamics. We analytically demonstrate the robustness and convergence of the closed-loop system for a class of MIMO linear time-varying systems. The overall superiority of the proposed controller is experimentally validated on a Barrett robot arm in a laboratory environment. The article also provides a stochastic framework of the general setting of the controller. Within this framework, two minimum mean square error optimal solutions of the controller are provided; one is designed for the case where the number of inputs is not greater than the number of outputs, and the other is for the antithesis.