(284b) Autocovariance-Based Model Mismatch Diagnosis for MPC with State Estimation

Model predictive control (MPC) is widely used in the process industries for complex, multivariate control problems [1],[2]. MPC offers significant advantages over conventional multi-loop PID control schemes; however, as a model-based method, its performance depends greatly on the quality of the process model. If the model used in the MPC does not provide an accurate representation of the plant, control performance will suffer. Recognizing this, practitioners invest significant time and resources in the model building phase of an MPC implementation, performing, e.g., extensive open loop step testing to the plant dynamics.

Nevertheless, chemical process systems are subject to a variety of physical phenomena (corrosion, fouling, catalyst deactivation) and other changes (to equipment, process operation, etc.) that cause the plant dynamics to drift in time, such that the response at a given time after the system identification effort will be different from the model used in the MPC. Since frequent model updating iscostly, re-identification efforts are generally only pursued once controller performance has degraded severely.

A method for detecting plant-model mismatch before this stage would thus be highly desirable, and MPC controller performance monitoring (CPM) has become an area of vigorous research activity in recent years. Many proposed approaches are extensions of previously established CPM methods to MPC systems. Notably, data-driven methods like Principal Component Analysis and Partial Least Squares regression have been proposed [3],[4]. More recently, approaches based on input-output partial correlation analysis [5] and statistical analysis of higher moments of the output and error distribution [6] have been introduced to improve specificity; they attempt to trace the source of the mismatch to a subset of variables. In our previous work, we provided further specificity, proposing an output autocovariance-based method for both locating and quantifying plant-model mismatch from routine operation data, i.e. without requiring disruption to the process [7],[8],[9].

In this work, we extend the autocovariance-based approach to the important class of systems consisting of state-space MPC controllers employing Kalman filtering for state estimation. Since, in contrast to previous frameworks, these systems incorporate both state and output noise models, we represent the closed loop outputs as Vector Moving Average processes from which the theoretical autocovariance function can be derived [10]. Then, the sample estimator for the autocovariance of process outputs obtained from routine operating data is used to formulate a minimization problem, whose result is an asymptotically consistent estimator of the true plant-model mismatch. We present case studies demonstrating the application of our approach for MPC systems with state estimation.

References

 

[1] S. J. Qin, “Statistical process monitoring: Basics and beyond,” Journal of Chemometrics, 17:480–502, 2003.

[2] M. L. Darby and M. Nikolaou, “MPC: Current practice and challenges,” Control Engineering Practice, 20(4):328–342, 2012.

[3] J. Yu and S. J. Qin, “Statistical MIMO controller performance monitoring. Part I: Data-driven covariance benchmark,” Journal of Process Control, 18:277–296, 2008.

[4] A. AlGhazzawi and B. Lennox, “Monitoring a complex refining process using multivariate statistics,” Control Engineering Practice, 16:294–307, 2008.

[5] Abhijit S. Badwe, Ravindra D. Gudi, Rohit S. Patwardhan, Sirish L. Shah, and Sachin C. Patwardhan, “Detection of model-plant mismatch in MPC applications,” Journal of Process Control, 19(8):1305–1313, 2009.

[6] V. Botelho, J.O. Trierweiler, M. Farenzena, R. Duraiski, “Perspectives and challenges in performance assessment of model predictive control,” Canadian Journal of Chemical Engineering, 94: 1225–1241, 2016.

[7] S. Wang, J. M. Simkoff, M. Baldea, I. Castillo, D. Stanley, L. Chiang, and R. Bindlish, “Autocovariance- based plant-model mismatch estimation for linear model predictive control,” Systems and Control Letters, vol. DOI:10.1016/j.sysconle.2017.03.002, 2017.

[8] S. Wang, J. M. Simkoff, M. Baldea, I. Castillo, D. Stanley, L. Chiang, and R. Bindlish, “Autocovariance- based MPC model mismatch estimation for systems with measurable disturbances,” Journal of Process Control, vol. DOI:10.1016/j.jprocont.2017.03.002, 2017.

[9] J. M. Simkoff, S. Wang, M. Baldea, I. Castillo, D. Stanley, L. Chiang, and R. Bindlish, “Plant-model mismatch diagnosis and estimation from closed-loop data for state-space MPC,” AIChE Journal, 2017 (submitted).

[10] G. Box, G. Jenkings, and G. Reinsel, Time Series Analysis: forecasting and control, Prentice-Hall, Inc., 3rd edition, 1994.