Control of non-minimum phase systems with dead time: a fractional system viewpoint

Abstract

In this paper, a unified theory is proposed for the fractional control of the non-minimum phase plus dead time systems via the introduction of the fractional filter-PID control and stability inequality. More precisely, three Theorems from a fractional system-theoretic viewpoint are developed. The first Theorem deals with the controller design through the notion of generalised internal model control. That embeds the fractional filter-PID controller coupled with the unified form of the Smith predictor and the inverse compensator. The second Theorem designs a bound on the fractional filter parameter that leads to a stable feedback system. The third Theorem deals with the stability of a fractional quasi-characteristic polynomial of the commensurate order arising from the control of non-minimum phase systems with dead time. Two illustrative second-order plus dead time non-minimum phase systems are presented to test the efficacy of the resulting fractional filter-PID controller that obeys the stability bound. Controller and sensitivity performance indices for the nominal as well as mismatch cases reveal the effectiveness and robustness of the proposed method for enhanced closed-loop performance. Thus, the generalised inverse compensator, the fractional filter-PID controller and the stability inequality in corroboration with numerical simulations demonstrate the better control of non-minimum phase systems with dead time.