(199b) Data Driven Plant Model Mismatch Estimation for Dmc with Unknown Noise Variance

The recent decades have seen the fast development and wide application of model predictive control (MPC). A survey on a large number of industries [1] reported thousands of working MPC implementations, and this number has grown significantly. MPC techniques are favored in practice due to their ability to account for complex process dynamics, as well as for input, state and output constraints. However, MPC implementations remain vulnerable to plant-model mismatch. Such mismatches are inevitable in practical process plants due to such as corrosion, catalyst deactivation, fouling, etc. As a consequence, a drift in operating conditions and a gradual increase in the discrepancy between model predictions and plant states/outputs will inevitably occur.

The quality of predictions directly determines the performance of the MPC controller. System re-identification is the natural choice for MPC internal model updating. This, however, involves lengthy experimental campaigns that are themselves costly, and can lead to production disruptions and lost profit. Motivated by this, we develop an autocovariance-based approach to optimally quantify the plant-model mismatch from existing closed-loop data sets.

When considering the mismatch estimation problem, two challenges arise: 1) capturing model mismatch in the cost function of the optimization problem; 2) obtaining correct statistical information on output noise.

Our previous work [2] produced an explicit relation between model mismatch and output autocovariance matrices within the context of unconstrained model predictive control framework and initially addressed the mismatch estimation issue by assuming noise model to be known. In this work, we address two practical issues. First, we extend these ideas to the industry-accepted dynamic matrix control (DMC) framework [3]. Then, we relax the assumption concerning knowledge of the output noise, and derive the means to compute noise signal parameters from the data. Several case studies are presented, demonstrating, i) improvement in model predictions and, ii) the ensuing improvements in closed loop performance.

[1] Qin, S.J., et al, A survey of industrial model predictive control technology, Control Engineering Practice, 11, pp. 733-764, 2003

[2] Wang, Siyun, et al. Autocovariance-based plant-model mismatch estimation for linear model predictive control. Systems & Control Letters 104, pp. 5-14, 2017

[3] Roffel, B., et all. Advanced practical process control. Heidelberg: Springer, 2004.