Detecting Model–Plant Mismatch of Nonlinear Multivariate Systems Using Mutual Information

For model-based control systems such as model predictive control (MPC), the model plays a key role in controller design and tuning. Performance of the controller heavily relies on the model quality so that detection of the model–plant mismatch (MPM) becomes an important task. For linear systems, many approaches have been proposed while little work has been done for MPM detection of nonlinear systems. Considering the widespread nonlinearities, mutual information (MI), as a general correlation measure, is utilized to detect MPM in this paper. The MI between dithering signals and model residuals is directly estimated to reveal process MPM. It is found that changes in the disturbance dynamics will not affect the MI, so that changes in the plant and disturbances can be easily distinguished. For large scale muliple-input–multiple-output (MIMO) systems, reidentification of the model is costly as keeping a large number of inputs in a perturbed or excited state leads to loss of normal production time. Hence it would be highly desirable to locate the subsets of mismatch so that only subsystems have to be perturbed for model updating. In this work, an MI matrix corresponding to the model error is defined to unveil mismatched submodels. This provides important information to narrow the number of potential root causes. The performance of the proposed approach is illustrated by application studies involving two simulation examples and an industrial polypropylene (PP) production process.