Autocovariance-Based Plant-Model Mismatch Estimation for Linear MPC with Measurable Disturbances

Model predictive control (MPC) has become the standard approach for multivariable, constrained control in the chemical process industries [4]. MPC is capable of handling large-scale, non-square and highly interacting plants, while accounting for constraints on inputs, outputs and state variables. However, the performance of MPC controllers is highly dependent on the quality and accuracy of the process model. Phenomena such as corrosion, catalyst deactivation and fouling will cause the operation of a chemical process to drift away from the point where the model was identified. Compensating for such plant-model mismatch via (frequent) model update experiments is costly and inefficient, and it is highly desirable to develop an approach for quantifying plant-model mismatch using readily available closed-loop operating data.

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) [1] and controller performance benchmarking concepts [3]. 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 [2]. In our previous work, we proposed a novel autocovariance-based plant-model mismatch estimation approach for control loops under unconstrained MPC [6]. 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 [5].

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.

References

 [1] A. AlGhazzawi and B. Lennox. Model predictive control monitoring using multivariate statis- tics. J. Proc. Contr., 19:314–327, 2009.

[2] Abhijit S. Badwe, Ravindra D. Gudi, Rohit S. Patwardhan, Sirish L. Shah, and Sachin C. Patwardhan. Detection of model-plant mismatch in MPC applications. Journal of Process Control, 19(8):1305–1313, 2009.

[3] T. J. Harris. Assessment of closed loop performance. Can. J. Chem. Eng., 67:856–861, 1989.

[4] S. J. Qin and T. A. Badgwell. A survey of industrial model predictive control technology. Control Engineering Practice, 11:733–764, 2003.

[5] S. Wang, J. Simkoff, M. Baldea, L. Chiang, I. Castillo, R. Bindlish, and D. Stanley. Data- driven plant-model mismatch quantification in input-constrained linear mpc. In Proceedings of The 11th IFAC Symposium on Dynamics and Control of Process Systems, Trondheim, Norway, 2016.

[6] S. Wang, J.M. Simkoff, M. Baldea, L. Chiang, I. Castillo, R. Bindlish, and D. Stanley. Autocovariance-based plant-model mismatch estimation for unconstrained linear MPC. Sys. & Contr. Lett., page submitted, 2016.