Comparative study of decay ratios of disturbance-rejection magnitude optimum method for PI controllers

One of the key time-domain closed-loop performance requirements is the closed-loop response decay ratio. In this paper, the decay ratios of the disturbance-rejection magnitude optimum (DRMO) tuning method [Vrančić D, Strmčnik S, Kocijan J. Improving disturbance rejection of PI controllers by means of the magnitude optimum method. ISA Trans 2004; 43: 73–84; Vrančić D, Strmčnik S. Achieving optimal disturbance rejection by using the magnitude optimum method. In: Pre-prints of the CSCC’99 conference. 1999. p. 3401–6] are analyzed and compared to decay ratios of two other modern tuning methods, i.e. the Kappa–Tau tuning method (based on time-domain step-response characteristics) [Åström KJ, Högglund T. PID controllers: Theory, design, and tuning. 2nd ed. Instrument Society of America; 1995] and the non-convex optimization tuning method (based on frequency response) [Panagopoulos H, Åström KJ, Hägglund T. Design of PI controllers based on non-convex optimization. Automatica 1998; 34: 585–601; Panagopoulos H, Åström KJ, Hägglund T. Design of PID controllers based on constrained optimisation. IEE Proc Control Theory Appl 2002; 149 (1): 32–40]. It is shown that the DRMO method results in such a closed-loop response that the decay ratio is within a relatively narrow interval when compared to the other two methods.