SISO approaches for linear programming based methods for tuning decentralized PID controllers. (October 2020) - Euzébio, Thiago A.M.; Yamashita, André S.; Pinto, Thomás V.B.; Barros, Péricles R.
Abstract: Two tuning techniques are proposed to design decentralized PID controllers for weakly coupled and general MIMO systems, respectively. Each SISO loop is designed separately, and the controller parameters are obtained as a solution of a linear programming optimization problem with constraints on the process stability margins. Despite the SISO approach, loop interactions are accounted for either by Gershgorin bands (non-iterative method) or an equivalent open-loop process (iterative method). The tuning results and performance from both methods are illustrated in four simulations of linear processes, and a laboratory-scale application in a Peltier process. Four applications contemplate closed-loop performance comparisons between the proposed techniques and techniques from the literature. One application illustrates the feasibility of the proposed iterative method, based on EOPs, in tuning decentralized PIDs for a 5 × 5 system. Moreover, an analysis of the effect of model uncertainty in the phase and gain margins of the closed-loop process is performed. Highlights: Two optimal design with robustness constraints PID tuning techniques are presented. The proposed techniques are assessed in simulation examples and a laboratory-scale application. One technique, utilizes constraints based on Gershgorin band to guarantee closed-loop stability. Another recasts the process into an Equivalent Open-Loop form, resulting in an iterative algorithm.