An Optmization-Based MIMO PID Controller Tuning Method for Linear Systems Under Constraints
PID Controller, Actuator Saturation, Systems under Constraints, Invariant Sets, MIMO Systems, Optimization.
In this work we propose a methodbased on optimization for tuning PID controllers, for linear Multiple-Input Multiple-Output (MIMO) discrete-time systems subject to constraints on the output variables and saturation of the actuators. From a polytopic modeling of saturation, conditions are presented for a polyhedron contained in the set of constraints to be positively invariant with respect to a closed-loop system with a MIMO PID controller. Such conditions are used in the formulation of a nonlinear optimization problem, whose solution provides the controller parameters that satisfy the constraints, guarantee local stability and optimize the performance of the closed loop system. Both a centralized and a decentralized controller are analyzed. The efficiency of the proposed method is evaluated from numerical simulation results.