(105g) Enhancing Resource Utilization Efficiency in Networked Control of Nonlinear Distributed Processes with Parametric Drift

The stabilization of spatial profiles in spatially-distributed processes using feedback control is a fundamental problem that has a long history in process control (e.g., [1,2]). The significance of this problem spans many practical applications, ranging from control of product quality in transport-reaction processes to the reduction of frictional drag in fluid flows and the control of vibrations in structural systems. While the problem has traditionally been addressed using the classical feedback control paradigm where sensor-controller communication is assumed to take place over dedicated links, more recent efforts have focused on incorporating communication resource constraints explicitly in the distributed control system design (e.g., [3,4,5]). These efforts have been motivated by the prevalence of shared bandwidth-limited communication networks in industrial control systems and the detrimental effects that communication constraints can have on the stability and performance of the closed-loop system, if unaccounted for in the control system design.

A common theme of these studies has been to address the resource-constrained stabilization problem for distributed processes using model-based control. In this approach, sensor-controller communication is suspended for times during which an embedded reduced-order model is used to compute the control action. The model state is then updated using the available measurements whenever communication is permitted. A rigorous closed-loop analysis is performed to identify the minimum allowable sensor-controller communication rate that can be used without jeopardizing closed-loop stability. While operation at this communication rate helps reduce the utilization of network resources, the actual network resource savings that can be achieved using this approach may be limited when a single fixed-parameter model is used. Such limitations become evident when the process experiences parameter variations, which is typically the case in the operation of chemical processes. Certain physical phenomena, such as catalyst deactivation and heat-exchanger fouling, often manifest themselves in the form of parameter variations that increase the mismatch between the model and the plant over time. Mitigating the impact of parametric drift requires increased levels of feedback through sensor-controller communication to maintain closed-loop stability.

This realization has motivated recent work on the integration of model-based control with subspace identification schemes to enhance the resource utilization efficiency of the networked control system [6]. The key idea is to re-identify the model parameters when necessary 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 distributed processes where the underlying dynamics are linear. The resulting linear control, stability characterization and model identification approaches are therefore not directly suited for application to processes with strong nonliearities, especially if the process is to be operated over a wide range of operating conditions or is subject to significant process upsets. Explicit account of the nonlinear dynamics must be taken not only in the controller synthesis and subsequent closed-loop stability characterization, but also in the parameter identification component of the methodology.

Motivated by these considerations, we present in this work a framework for augmenting the model-based feedback control approach with an error-triggered parameter re-identification scheme in spatially-distributed processes modeled by nonlinear highly-dissipative PDEs subject to sensor-controller communication constraints and process parametric variations. The goal is to maintain closed-loop stability in the presence of varying levels of plant-model mismatch, while simultaneously keeping the rate of sensor-controller communication to a minimum and accounting explicitly for the presence of nonlinearities. The problem is addressed on the basis of a suitable finite-dimensional approximation that captures the dominant dynamics of the infinite-dimensional system. A residual-based monitoring scheme with a time-varying alarm threshold is developed and used to determine the conditions necessary for model parameter updates. A breach of the alarm threshold transitions process operation into a safe-parking mode in which the sensor-controller communication rate is temporarily adjusted to mitigate the impact of increased plant-model mismatch and allow the re-identification of 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 communication rate that should be used when the model parameters are updated. The implementation of the proposed methodology is illustrated using a representative diffusion-reaction process example.