Analytical approach to tuning of model predictive control for first-order plus dead time models

Model predictive control (MPC) is an effective control strategy in the presence of system constraints. The successful implementation of MPC in practical applications requires appropriate tuning of the controller parameters. An analytical tuning strategy for MPC of first-order plus dead time (FOPDT) systems is presented when the constraints are inactive. The available tuning methods are generally based on the user´s experience and experimental results. Some tuning methods lead to a complex optimisation problem that provides numerical results for the controller parameters. On the other hand, many industrial plants can be effectively described by FOPDT models, and this model is therefore used to derive analytical results for the MPC tuning in a pole placement framework. Then, the issues of closed-loop stability and possible achievable performance are addressed. In the case of no active constraints, it is shown that for the FOPDT models, control horizons subsequent to two do not improve the achievable performance and control horizon of two provides the maximum achievable performance. Then, MPC tuning for higher order plants approximated by FOPDT models is considered. Finally, simulation results are employed to show the effectiveness of the proposed tuning formulas.