(309a) A State-Space Formulation for Autocovariance-Based Plant-Model Mismatch Estimation in Model Predictive Control

Model predictive control (MPC) has become the preferred strategy for handling complex, multivariate control problems in the process industries. MPC uses a model of the plant dynamics to predict response over a control horizon, and provides an optimal sequence of control moves at each time step. MPC is considered a mature technology, with thousands of implementations currently in place, benefiting from several decades of technological developments from both academic and industrial contributors [1]. In recent years, state-space model forms of MPC have gained traction. This is due to their ability to handle the full range of process dynamics, such as integrating and unstable systems, which are not in general dealt with by other model forms, such as the more traditionally used (and still predominant in applications) convolution models. State-space models also offer more flexibility in accounting for unmeasured disturbances in the state estimation step [2].

Although MPC confers benefits over, e.g., multi-loop approaches for many multivariable systems, as with any model-based method it is limited in performance by the model quality, i.e. how well the true process dynamics are represented by the model. Frequent system re-identification could in principle be implemented, but this tends to be cost prohibitive in practice; alternative methods are needed to ensure MPC performs as expected. As such, in there has recently been increasing interest in the problem of monitoring and assessing MPC controller performance. More general techniques for controller performance monitoring and assessment have been applied to MPC. Examples include data-driven methods such as Principal Component Analysis (PCA) and Partial Least Squares (PLS)-based fault detection [3], as well as benchmarking against performance indices, e.g. Linear Quadratic Gaussian (LQG) and Minimum Variance Controllers (MVC) [4],[5]. While these methods are often successful in indicating degraded control quality, they are often limited in their ability to provide useful model diagnosis. The development of techniques for quantifying MPC plant-model mismatch remains thus an area of active research.

Several approaches have been proposed, e.g., making use of partial correlation analysis [6] and frequency domain analysis with setpoint excitation [7]. In our previous work, we introduced an approach for estimating plant-model mismatch from closed loop operating data by means of an explicit output autocovariance-mismatch relation [8,9]. We demonstrated its effectiveness for MPC in with models in both convolution and transfer function form.

In this presentation, we extend our approach to the increasingly important class of MPCs which use state-space form models. We develop an autocovariance-mismatch relation, which explicitly links the mismatch in each of the state-space model parameters to the autocovariance of the process outputs. We then pose mismatch estimation as an optimization problem, wherein we seek to minimize (in the least squares sense) the discrepancy between the predicted output autocovariance and that computed from the actual data. We present a multivariable case study demonstrating the use of this approach, and we discuss some computational and statistical features of the method.

References

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