Enhancing PID Tuning with Routh Stability and Empirical Correlations: Performance Comparison and Applications

Abstract

This paper presents a new rule-based method called the Routh Stability with Empirical Correlation (RSEC) for tuning a PID controller under model/process mismatch. The RSEC method employs a two-stage calibration procedure to accommodate the FOPDT modeling error in the PID tuning. The RSEC calibration utilizes the deadtime to time constant ratio to adjust the dimensionless tuning parameters subject to specified gain and phase margins. It results in empirical correlations relating the dimensionless tuning parameters to the deadtime to time constant ratio. The second calibration establishes correcting factor correlations for the modeling error. Servo and regulatory simulations demonstrated that RSEC produces the smallest ITAE of 0.396 and 0.151 when tested in a cascade process, outperforming the other control tuning methods, including Skogestad IMC (SIMC). Further application of the developed RSEC method to several examples of SISO and MIMO processes shows the efficacy of the new tuning method compared to the well-established Robust Response Time, AMIGO, and SIMC.