Alternative Approach to Use RLS Algorithm in Multivariable Online Adaptive PID Controllers for MIMO Systems

Abstract

ABSTRACTThe proportional-integral-derivative (PID) is widely used in industrial control systems due to its simplicity. For multi-input multi-output (MIMO) systems, choosing the PID gain values is a difficult task especially that in most applications system parameter variations and changes in operating conditions occur. Thus, there is necessity to find parameters adjustment method in which PID gains should be adapted to handle such changes. This paper is concerned with the design of a multivariable adaptive PID (APID) controller in which recursive least square (RLS) algorithm is used as an adaptation mechanism. The RLS algorithm, on the contrary of its usual application as an identification method, is used in the proposed controller to update the PID gains online forcing the system to behave like a desired reference model. Unlike other techniques, the proposed multivariable APID controller has the advantage that it does not impose restrictions on the system structure such as being stable, square, minimum phase, nor almost restrict positive real. Since stability is a vital issue in the evaluation of control systems, therefore stability analysis of the proposed approach is developed using Lyapunov stability theory. Comparative simulation results demonstrate the superiority of the proposed multivariable APID controller over another two different controllers when applied to MIMO systems especially for unstable systems when the controlled systems suffer from parameter variations or uncertainties.