(172c) Resource-Constrained Stabilization of Nonlinear Process Systems Subject to Parametric Drift

The stabilization of nonlinear dynamical systems via feedback control is a fundamental problem whose practical significance spans a wide range of process control applications. Traditionally, the problem is formulated using the classical feedback control paradigm in which sensor-controller communication is assumed to take place over dedicated links, and considerations such as real-time communication resource constraints are ignored. These considerations, however, have become increasingly important in the formulation and solution of the control problem, especially with the widespread reliance on communication networks in industrial control systems, where dedicated feedback paths are replaced by resource-constrained sensor-controller communication channels.

An approach to address the resource constraints problem, which has enjoyed a wide appeal, is the use of model-based control (e.g., [1], [2], [3]). The appeal of this approach stems from the fact that it helps reduce the need for frequent sensor-controller communication over the network by relying on a process model instead. However, the extent to which the network resources are conserved is typically limited when a single model with fixed parameters is embedded in the control system. This limitation is particularly evident when the process experiences parametric drift. In chemical processes, for example, certain physical phenomena such as catalyst deactivation and heat-exchanger fouling commonly manifest themselves in the form of parameter variations that, over time, increase the mismatch between the model and plant. Mitigating the impact of this drift requires increased levels of feedback through sensor-controller communication which may not be attainable due to existing sensor-controller communication constraints.

An effort to deal with this problem was initiated in [4] where a methodology for the integration of model-based control and model identification was developed. The key idea was to re-identify the model parameters whenever needed in order to keep the plant-model mismatch, and thus the required communication rate, to a minimum. In this prior work, however, the focus was on processes where the underlying dynamics are linear. The resulting linear control, stability characterization and identification approaches are therefore not directly suited for application to processes with strong nonlinearities, especially if the process is to be operated over a wide range of operating conditions or is subject to significant process upsets.

Motivated by these considerations, we present in this work a methodology for augmenting model-based feedback control with error-triggered parameter re-identification for nonlinear processes controlled over resource-constrained sensor-controller communication channels subject to parametric variations. The goal is to maintain closed-loop stability in the presence of varying levels of plant-model mismatch during periods of parametric drift, while simultaneously keeping the sensor-controller communication rate to a minimum and maintaining acceptable levels of closed-loop performance. Initially, a stabilizing nonlinear state feedback controller is designed. The controller utilizes model-generated state estimates which are periodically updated using the available state measurements. An estimate of the maximum allowable update period is obtained and characterized in terms of the parametric uncertainty and the controller design parameters. An error monitoring scheme with a time-varying instability alarm threshold is then devised to determine on-line if and when the model parameters need to be updated. A breach of the instability threshold at some time triggers a safe-parking mode of operation in which the sensor-controller communication rate is adjusted to mitigate the destabilizing impact of increased plant-model mismatch. The measurements collected during the safe-parking mode are used to obtain new estimates of the process parameters using nonlinear grey-box parameter estimation techniques. An explicit characterization of the closed-loop stability region associated with the new model parameters is obtained to determine the appropriate post-drift sensor-controller communication rate that should be used when the model parameters are updated. The implementation of the proposed methodology is illustrated using a chemical process example.

References:

[1] Sun Y, El-Farra NH. Quasi-Decentralized Model-Based Networked Control of Process Systems. Computers & Chemical Engineering. 2008; 32(9):2016–2029.

[2] Sun Y, El-Farra NH. Resource-Aware Quasi-Decentralized Control of Networked Process Systems over Wireless Sensor Networks. Chemical Engineering Science. 2012; 69:93-106.

[3] Garcia, E, Antsaklis, PJ, and Montestruque, LA. Model-Based Control of Networked Systems, Systems &Control: Foundations & Applications. Springer International Publishing, Switzerland, 2014.

[4] Zedan A, Xue D, El-Farra NH. Integrating Model Identification and Model-Based Control of Networked Process Systems. Proceedings of 13th International Symposium on Process Systems Engineering, vol. 44 of Computer Aided Chemical Engineering, pp. 715–720. Elsevier. 2018.