(555c) Analysis and Control of Networked Distributed Processes with Sensor and Actuator Errors

With the significant growth in communication and networking capabilities in recent years, process operations have become increasingly reliant on sensor and control systems that are accessed over shared communication networks rather than dedicated links. While this transition has been motivated by the economic and operational benefits of shared networks, it also introduces a number of control challenges that need to be addressed. Examples include the inherent limitations on the transmission and processing capabilities of the communication medium, in the form of network resource constraints, real-time scheduling constraints, data losses and delays, which may degrade the overall closed-loop performance and even lead to instability if not accounted for in the control system design. This realization has motivated significant research work on the analysis an design of networked control systems, and the literature on this topic is quite extensive (see, for example, [1]-[2] for some results and references in this area).

Yet, a careful examination of the available results shows that, compared with the significant attention that lumped parameter systems (modeled by ordinary differential or difference equations) have enjoyed, networked control of spatially distributed systems (modeled by partial differential equations) has received only limited attention. Efforts to address sensor-controller communication constraints in the context of spatially distributed control systems were made in a number of recent studies (see, for example, [3]-[6]) which focused mainly on highly-dissipative infinite-dimensional systems and led to a number of finite-dimensional networked control design methodologies that enforce closed-loop stability with minimal sensor-controller communication requirements.

The design methods in these studies are based on the consideration that the state measurements used for model updates are exactly known at the update time, and the assumption that the control action computed by the controller is also transmitted flawlessly and accurately to the control actuator. In many practical situations, however, these assumptions need to be re-examined in light of the possible degradation in the quality and precision of the transmitted sensor and actuator data over the network. Possible sources for the presence of measurement and actuation errors include interference with other signals in the field in the case of wireless networks, errors due to noisy sensor readings which are subject to drift over time, the use of discrete sensors (e.g., binary sensors) and discrete actuators (on/off valves) in the control system which cannot be varied continuously, the use of data fusion and aggregation techniques, and the need to conserve network bandwidth by reducing data precision. The end result in all these situations is that only inexact values of the state and/or input variables will be available, and the resulting errors may cause a significant deterioration in the closed-loop performance, if not outright instability, if not handled properly in the control system design.

Motivated by these considerations, we present in this work a methodology for the design and analysis of networked controllers for a class of spatially distributed process systems with uncertain low-order dynamics, discrete sensor-controller communication, and sensor and actuator errors. Initially, a model-based networked controller that enforces exponential closed-loop stability in the absence of sensor and actuator errors is synthesized using an approximate finite-dimensional model of the infinite-dimensional system. Lyapunov techniques are then used to analyze the implementation of the model-based controller in the presence of bounded measurement and actuation errors. Precise conditions for stability and ultimate boundedness of the closed-loop trajectories are derived and used to obtain an explicit characterization of the interdependence between the achievable ultimate bound on the one hand, and the sensor/actuator error bounds, the sensor data transmission rate, the size of process-model mismatch and the choice of sensor/actuator spatial configurations, on the other. It is shown that by judicious selection of these parameters, closed-loop stability with minimal performance degradation can be attained. Finally, the implementation of the networked controller on the infinite-dimensional system is analyzed, and the results are illustrated using a diffusion-reaction process example.

References:

[1] J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, "A survey of recent results in networked control systems,'' Proceedings of the IEEE, 95:138-162, 2007.

[2] P. D. Christofides, J. Liu, and D. Muoz de la Pena, Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications. London: Springer-Verlag, 2011.

[3] Y. Sun, S. Ghantasala, and N. H. El-Farra, "Networked control of spatially distributed processes with sensor-controller communication constraints,'' in Proceedings of American Control Conference, St. Louis, MO, 2009, pp. 2489-2494.

[4] Z. Yao and N. H. El-Farra, "On model-based networked control of nonlinear spatially distributed process systems,'' in Proceedings of 18th Mediterranean Conference on Control and Automation, Marrakech, Morocco, 2010, pp. 898-903.

[5] Z. Yao, Y. Sun, and N. H. El-Farra, "Resource-aware scheduled control of distributed process systems over wireless sensor networks,'' in Proceedings of American Control Conference, Baltimore, MD, 2010, pp. 4121-4126.

[6] Z. Yao and N. H. El-Farra, "Networked model predictive control of spatially distributed processes,'' in Proceedings of American Control Conference, Washington, DC, 2013, pp. 2062-2067.