Prediction Error Based Performance Monitoring, Degradation Diagnosis and Remedies in Offset‐Free MPC: Theory and Applications

We present in this paper a control performance monitoring method for linear offset-free model predictive control (MPC) algorithms, in which the prediction error sequence is used to detect whether the internal model and the observer are correct or not. When the prediction error is a white noise signal, revealed by the Ljung-Box test, optimal performance is detected. Otherwise, we use a closed-loop subspace identification approach to reveal the order of a minimal realization of the system from the deterministic input to the prediction error. When such order is zero, we prove that the model is correct and the source of suboptimal performance is an incorrect observer. In such cases, we suggest an optimization method to recalculate the correct augmented state estimator. If, instead, such order is greater than zero we prove that the model is incorrect, and re-identification is suggested. A variant for (large-scale) block-structured systems is presented, in which diagnosis and corrections are performed separately in each block. Two examples of different complexity are presented to highlight effectiveness and scalability of the method.