An Analytical Tuning of MPC Control Horizon Using the Hessian Condition Number

Marwa Turki , Nicolas Langlois (1) , Adnan Yassine (2)

1 Pôle Automatique et Systèmes
2 IMAG - Institut d'Informatique et de Mathématiques Appliquées de Grenoble

Model Predictive Control (MPC) is based on the concept of receding horizon, the future output prediction, and the minimization of a cost function to provide the optimal control sequence. MPC controller contains three parameters: a control horizon Nc, a prediction horizon Np and a weighting factor λ. A successeful implementation of MPC requires an appropriate setting of these parameters. In this paper, an analytical approach for tuning the control horizon is presented while taking into account constraints. The idea of our novel approach consists on computing the value of the optimal control horizon in such a way it ensures the numerical stability. The interest of our approach is to be applicable to a wide set of linear controllable Single-Input Single-Output (SISO) processes whatever their orders. The issues of numerical condition and closed-loop stability are addressed in this paper. The proposed approach is tested via a simulated pH neutralization process. Results are compared to emphasize the effectiveness of the proposed approach.

Mots clés: effective rank; condition number; stability guarantee; SISO system; Predictive control; control horizon tuning; analytical approach

Domaines: Automatique / Robotique

Marwa Turki, Nicolas Langlois, Adnan Yassine. An Analytical Tuning of MPC Control Horizon Using the Hessian Condition Number. 14th International Workshop on Advanced Control and Diagnosis, Nov 2017, Bucharest, Romania. ⟨hal-02282128⟩