PID gain scheduling by parametric model predictive control

This paper considers the problem of augmenting the PID structure with the MPC functionality of constraint handling and optimization. Firstly, we review the MPC framework which can be built from a model and a linear feedback gain. This linear gain can be any preexisting multi-loop PID design in the unconstrained case, or based on the two stabilizing PI/PID design for multivariable systems we introduce here. The resulting controller is a feedforward PID mapping, a straightforward form without the need of tuning PID to fit an optimal input. Secondly, the parametric solution of MPC further suggests a PID network implementation by utilizing gain scheduling schemes available in industry.