(586b) Networked Control of Nonlinear Spatially Distributed Process Systems

With the significant growth in computing and networking abilities in recent times, as well as the rapid advances in actuator and sensor technologies, there has been an increased reliance in the process industry on sensor and control systems that are accessed over communication networks rather than dedicated links. Networked control systems have many advantages, such as reduced installation and maintenance time and costs, enhanced flexibility and ease of diagnosis and reconfiguration; yet, they also pose a number of fundamental issues that need to be resolved before process operation can take full advantage of their potential. These issues, which stem from intrinsic limitations on the information transmission and processing capabilities of the communication medium, challenge many of the assumptions in traditional process control theory dealing with the study of dynamical systems linked through ideal channels, and have emerged as topics of significant research interest to the control community. Despite the substantial and growing body of work in this area, the overwhelming majority of research studies have focused on lumped parameter systems modeled by ordinary differential or difference equations. Many chemical processes, however, are characterized by strong spatial variations, owing to the underlying physical phenomena such as diffusion, convection, and phase-dispersion, and are naturally modeled by partial differential equations (PDEs). At this stage, the design of networked control systems for spatially distributed processes remains an open problem that needs to be investigated and addressed.

In a recent work [1], we developed a methodology for the design of model-based networked control systems for spatially distributed processes described by linear parabolic PDEs. A key idea was to enforce closed-loop stability with minimal sensor-controller communication over the network. This was realized via (1) the inclusion of a finite-dimensional model that captures the dominant process dynamic modes within the control system in order to provide the controller with state estimates when measurements are not transmitted through the network, and (2) updating the model state using the actual measurements provided by the sensors at discrete time instances. By exploiting the linear structure of the PDE and the controller, necessary and sufficient conditions for stability of the infinite-dimensional networked closed-loop system were obtained leading to an exact characterization of the minimum allowable communication rate under both full-state and output feedback control. When this architecture is implemented on a nonlinear process, however, the update period predicted by the liberalization-based analysis is expected to guarantee stability only for sufficiently small initial conditions. Stabilization from large initial conditions (if at all feasible) requires increasing the frequency of sensor-controller communication substantially which leads to additional network utilization. Since many chemical processes are characterized by strong nonlinear dynamics and need to operated over wide regions of the operating space for economic reasons, it is important to develop distributed networked control approaches that account explicitly for the nonlinearities both in the control law and in the communication logic designs.

In this contribution, we present a model-based networked control architecture for spatially-distributed processes modeled by highly-dissipative nonlinear PDEs with measurement sensors that transmit their data to the controller/actuators over a resource-constrained communication network. Our objective is to design a resource-aware networked control structure that minimizes network resource utilization without jeopardizing closed-loop stability. Both state and output feedback control problems are considered. Model reduction techniques are initially used to derive an approximate finite-dimensional system that captures the dominant dynamics of the PDE. The finite-dimensional model is used to design a nonlinear feedback controller that enforces closed-loop stability in the absence of communication suspensions. To reduce the transfer of information over the network, sensor-controller communication is suspended for time intervals during which the controller relies on the predictions of the model, and is re-established at discrete time instance at which the state of the model is re-set using the available state measurement. When complete state measurements are unavailable, a nonlinear finite-dimensional state observer is included in the sensor to generate an estimate of the slow states from the available measurements. This estimate is then broadcast at network transmission times to update the state of the model in the controller. By analyzing the hybrid dynamics of the networked closed-loop system, and exploiting the stability properties of the controller and observer designs, we obtain an explicit characterization of the interplays between the range of allowable update periods, the size of process-model mismatch, and the controller and observer design parameters. The analysis also reveals how these interplays are influenced by the choice of the spatial locations of the control actuators and measurement sensors. Using singular perturbation techniques, precise conditions for stability of the infinite-dimensional networked closed-loop system are derived. Finally, the results are illustrated through an application of the developed methods to the problem of stabilizing the zero solution of the Kuramoto-Sivashinsky equation.

References:

[1] Sun, Y., S. Ghantasala and N. H. El-Farra, ``Networked Control of Spatially Distributed Processes with Sensor-Controller Communication Constraints," Proceedings of American Control Conference, pp. 2489-2494, St. Louis, MO, 2009.