465350 Autocovariance-Based Plant-Model Mismatch Estimation for Linear MPC with Measurable Disturbances
A large portion of available MPC performance assessment techniques focus on characterizing controller performance and its degradation. These approaches include multivariate statistical process control (MSPC)  and controller performance benchmarking concepts . However, neither of these approaches is able to locate or quantify plant-model mismatch. Recently, some contributions proposed techniques to locate the input/output pair(s) where mismatch exists and quantify the magnitude of mismatch using external excitations . In our previous work, we proposed a novel autocovariance-based plant-model mismatch estimation approach for control loops under unconstrained MPC . We showed that the mismatch in model parameters (where the model was represented as a transfer function matrix) can be estimated using steady state output data. We also proposed a partition technique that extended this approach to control loops with constrained MPC .
In this work, we rely on our previous results to consider the generic case of a plant operating under setpoint changes and account for measurable disturbance in the feedback control loop. Our framework is based on a transformation that converts the raw, noisy closed-loop process output into a mean-centered variable. We then establish an explicit relation between the autocovariance matrices of the new mean-centered output and the magnitude of the mismatch. Finally, we formulate a least squares optimization problem to estimate the plant-model mismatch. The proposed approach is illustrated with a case study considering high-dimensional MIMO system featuring dynamic complexities such as higher order dynamics, time delays and inverse response.
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