On reproducing existing controllers as Model Predictive controllers

The ability to take constraints explicitly into account in the optimisation problem formulation has made Model Predictive Control (MPC) a popular control strategy. However, finding the weights in the optimisation criterion is often non-trivial and requires a fair bit of trial-and-error. Conventional controllers such as PID, on the other hand, are relatively easy to tune, and they often achieve satisfactory performance when there are no constraints. In this paper, we present three approaches for designing an MPC such that it reproduces the conventional controller when there are no constraints. The first approach is from the existing literature where a full order observer is used in the reverse engineering. The second and third approach used a reduced order observer and state augmentation respectively are proposed. The obtained controller can also serve as an initial MPC which can be further fine tuned, and constraints can later be added to evaluate any potential benefit of using MPC compared to the original controller.