Performance degradation diagnosis and remedies in offset-free MPC

Linear offset-free MPC algorithms augment the internal model with integrating “disturbances”, which are estimated from output measurements along with the model states. We develop in this paper a performance monitoring strategy for general offset-free MPC algorithms, in which we use the prediction error sequence to detect whether the internal model is correct and/or the augmented state estimator is appropriate. 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. We prove that, if such order is zero, the model is correct and the source of suboptimal performance is an incorrect estimator. In such cases, we propose 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. Two illustrative examples are presented.