(140c) Resource-Aware Scheduled Control of Distributed Process Systems Over Wireless Sensor Networks

Augmenting existing process control systems with wireless sensor networks is an important step towards realizing the vision of a smart reconfigurable plant which utilizes advanced cyber-infrastructure and communication technologies to tightly integrate process control and operations with real-time process information [1]. However, the integration of wireless sensor networks within existing control systems challenges many of the assumptions in traditional process control methods which are based on the study of dynamical systems linked through ideal channels with flawless synchronous communication between the control system components. Unlike wired networks, wireless networks may occasionally be unreliable and are also resource-constrained due to limited processing and computational capabilities or due to limited power when the wireless sensors are deployed in harsh environments where a continuous power supply is not feasible and the wireless devices have to rely on battery power instead.

Realizing the potential of wireless sensor networks in process control therefore requires the development of systematic methods to effectively handle these issues from a control point of view. Despite the substantial and growing body of research work on networked process control (e.g., see [2] for some recent results and references), the overwhelming majority of research studies in this area have focused on lumped parameter systems modeled by ordinary differential or difference equations. Many important engineering applications, however, are characterized by 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 and implementation of networked control systems for spatially distributed processes remain open problems that need to be investigated and addressed.

This contribution presents an integrated model-based networked control and scheduling framework for a class of spatially distributed process systems modeled by highly-dissipative PDEs controlled over a resource-constrained wireless sensor network. The framework aims to enforce closed-loop stability while simultaneously minimizing the rate at which each node in the network must collect and transmit measurements to the controller so as to conserve the limited resources of the wireless devices and extend the lifetime of the network as much as possible. To this end, the exchange of information between the sensors and the controller is initially reduced by embedding within the controller a finite-dimensional model that captures the dominant dynamics of the distributed parameter system and provides the controller with an estimate of the evolution of the dominant modes when measurements are not transmitted through the network. The state of the model is then updated using the actual measurements provided by the sensors when communication is re-established at discrete time instances. To further reduce WSN utilization, only a subset of the deployed sensors are allowed to transmit their data at any given time to provide updates to the model, while the rest are kept dormant. In this manner, closed-loop stability of the plant becomes dependent not only on the controller design but also on the selection of the sensor transmission scheduling strategy. By formulating the networked closed-loop system as a switched infinite-dimensional system, a combination of hybrid system and singular perturbation techniques are used to obtain an explicit characterization of the maximum allowable update period (or, the minimum allowable communication frequency) between the sensors and the controller needed to enforce exponential stability in the infinite-dimensional closed-loop system. This characterization is obtained in terms of the sensor transmission schedule, the sensor transmission times, the degree of mismatch between the process dynamics and the model embedded in the controller as well as the degree of separation between the slow and fast eigenvalues of the differential operator. We show that by judicious selection of the transmission schedule and the model, it is possible to enhance the savings in WSN resource utilization over what is possible with transmission configurations that do not employ scheduling. Finally, the proposed methodology is illustrated through an application to a transport-reaction process example.

References:

[1] Christofides, P. D., J. F. Davis, N. H. El-Farra, K. Harris, and J. N. Gibson, ``Smart plant operations: Vision, progress and challenges," AIChE J., 53:2734-2741, 2007.

[2] Sun, Y. and N. H. El-Farra, ``Quasi-decentralized Model-based Networked Control of Process Systems", Comp. & Chem. Eng., 32: 2016-2029, 2008.