Online Detection of Model-Plant Mismatch in Closed-Loop Systems With Gaussian Processes

In model-based strategies, such as real-time optimization (RTO) and model predictive control (MPC), the process model plays an important role. However, model-plant mismatch is inevitable because of various uncertainties in the real application. Therefore, it is highly desirable to detect the mismatch online with measurements of the closed-loop system. This article proposes a mismatch detection approach based on a Gaussian process (GP) model, which is integrated with RTO and MPC to improve economic performance. The GP model is obtained by training a dataset, including parameters and measurements. An ideal system with no model-plant mismatch is designed to compare to the real control system having mismatch. The outputs error of the two systems is used to build a feedback mechanism to adjust the estimation. The re-estimated parameters are used to update the model RTO and MPC. The proposed approach is nonintrusive and can be used in multiinput–multioutput nonlinear systems. Based on the benchmark model of a continuous-stirred tank reactor, a detailed 4-in-4-out nonlinear model of the Fischer esterification reaction is provided to demonstrate the performance of the proposed approach. The result shows that the relative biases of estimates decrease from 5 to 1%, and the economic profit increase by 1.5%