(687c) Networked Control of Spatially Distributed Processes with Sensor-Controller Communication Constraints

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. The development of a control strategy that enforces the desired closed-loop objectives with minimal communication requirements between the control system components is an appealing goal since it reduces reliance on the communication medium and helps reduce network resource utilization. This is an important consideration particularly when the communication medium is a potentially unreliable wireless sensor network where conserving network resources (e.g., battery power) is key to prolonging the service life of the network. Beyond saving on communication costs, the study of this problem provides an assessment of the robustness of a given control system and allows the designers to identify the fundamental limits on the tolerance of a given networked control system to communication suspension. This can be a major consideration in deciding a priori whether the desired control objectives can be met with a certain kind of network.

Despite the substantial and growing body of research work on control over communication networks, 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). Typical examples of these systems include transport-reaction processes and fluid flow systems. Unlike spatially homogeneous processes, the control problem arising in the context of spatially-distributed processes often involves the regulation of spatially distributed variables (such as temperature and concentration spatial profiles) using spatially-distributed control actuators and measurement sensors. While the study of distributed parameter systems in process control has been an active area of research, the design and implementation of networked control systems for spatially distributed processes remain open problems that need to be investigated and addressed.

In this contribution, we present a methodology for the design of networked control systems for spatially distributed processes described by linear parabolic partial differential equations (PDEs) with measurement sensors that transmit their data to the controller/actuators over a bandwidth-limited communication network. The central design objective is to reduce the transfer of information from the sensors to the controller as much as possible without sacrificing closed-loop stability. This is achieved by (1) applying modal decomposition techniques to derive a finite-dimensional system that captures the PDE's dominant dynamics, (2) including a model of this system in the controller to provide it with an estimate of the dominant modes when sensor-controller communication is suspended, (3) updating the state of the model using the actual measurements when communication is re-established, and (4) explicitly characterizing the maximum allowable update period in terms of the model accuracy and the sensor and actuator spatial locations. We show that this characterization is exactly preserved when the networked control structure is implemented on the infinite-dimensional system under full state feedback. In the case of output feedback, an observer is included to generate estimates of the dominant modes from the available measurements which are then used to reset the model state. A singular perturbation formulation is then used to link the maximum stabilizing update period for the infinite-dimensional system with the separation between the slow and fast eigenvalues of the differential operator. We show that the stability criteria can be used to determine the optimal sensor and actuator configurations that maximize the networked closed-loop system's robustness to communication suspensions. Finally, the proposed methodology is illustrated using a simulation example.