PID algorithm based on GPC for second-order models with input and output constraints⁎

This paper presents a novel constrained PID algorithm that performs almost the same as a constrained GPC tuned with a unit control horizon and an output soft constraint. The proposed approach computes the PID tuning parameters using the unconstrained GPC solution for first or second-order process models and uses a geometric approach, which avoids the use of an optimiser, to compute the final control action combining the PID tuning with a constraint-mapping law. Simulation results are used to illustrate the simplicity and good performance that can be obtained with the proposed approach, which is an interesting solution for PID applications in which output constraints are considered and low computation time of the control law is required.