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

Economic model predictive control and tracking model predictive control are two popular advanced process control strategies used in various of fields. Nevertheless, for a given process, which controller should be chosen to achieve better performance is uncertain when noise exists. To this end, a sensitivity-based performance assessment approach is proposed to pre-evaluate the dynamic economic and tracking performance of them and guide the controller selection in this work. First, their controller gains around the optimal steady state are evaluated using the sensitivities of corresponding constrained dynamic programming problems. Second, the controller gains are substituted into the control loop 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 based on the proposed approach. Extensive simulations under different cases prove that the proposed approach can provide useful guidance on performance assessment and controller design.