Sensitivity-based dynamic performance assessment for model predictive control with Gaussian noise

TL;DR

This paper introduces a sensitivity-based method to evaluate and compare the dynamic performance of economic and tracking model predictive control strategies under Gaussian noise, aiding in controller selection and design.

Contribution

A novel sensitivity-based approach for pre-assessing the dynamic economic and tracking performance of MPC strategies in noisy environments is proposed.

Findings

The method accurately predicts performance differences between control strategies.

It enables pre-configuration of boundary and target movements for stability.

Simulations demonstrate effective guidance for controller design.

Abstract

Economic model predictive control and tracking model predictive control are two popular advanced process control strategies used in various of fields. Nevertheless, which one should be chosen to achieve better performance in the presence of noise is uncertain when designing a control system. To this end, a sensitivity-based performance assessment approach is proposed to pre-evaluate the dynamic economic and tracking performance of them in this work. First, their controller gains around the optimal steady state are evaluated by calculating the sensitivities of corresponding constrained dynamic programming problems. Second, the controller gains are substituted into control loops to derive the propagation of process and measurement noise. Subsequently, the Taylor expansion is introduced to simplify the calculation of variance and mean of each variable. Finally, the tracking and economic performance surfaces are plotted and the performance indices are precisely calculated through integrating the objective functions and the probability density functions. Moreover, boundary moving (i.e., back off) and target moving can be pre-configured to guarantee the stability of controlled processes using the proposed approach. Extensive simulations under different cases illustrate the proposed approach can provide useful guidance on performance assessment and controller design.