(368g) Quasi-Decentralized Networked Control of Nonlinear Plants with Communication Constraints

Control of large-scale plants with geographically-distributed interconnected units is a central problem that has had a long history in process control research. Traditionally this problem has been studied within the framework of decentralized control (e.g., [3],[4]) wherein the plant is decomposed into a number of simpler subsystems (typically based on functional and/or time-scale differences between the unit operations) with interconnections, and a number of local controllers are connected to each distributed subsystem with no signal transfer taking place between the different local controllers. More recently, there has been some interest in studying plant-wide control within the distributed model predictive control framework [8]. In all these studies, however, the problem is formulated and solved within a linear control framework. Compared with the work on plant-wide control of linear systems, results on the analysis and control of nonlinear process networks have been limited. Examples include plant-wide control based on the integration of linear and nonlinear model predictive control [11], the analysis and stabilization of process networks based on passivity and concepts from thermodynamics [9], the development of agent-based control of reactor networks [6], and the analysis and control of integrated process networks using time-scale decomposition and singular perturbation techniques [1]. While the focus of these works has been mainly on the control design aspects, an important issue that has not been investigated is the management of communication constraints in the formulation and solution of the plant-wide control problem. As the need for flexibility and cost-savings in plant operations continue to drive the transition from dedicated, point-to-point connections to multi-purpose shared communication networks in the control system, there is a greater need to characterize the fundamental limitations imposed by this technology and to develop systematic methods for the integration of communication issues into the formulation and solution of the plant-wide control problem.

While the emerging paradigm of control over networks offers a natural setting to address these problems (e.g., [5], [7], [10]), most of the available results on networked control systems so far have been developed for linear systems using a centralized control architecture, and without taking complexities such as nonlinear dynamics and model uncertainty into account. A centralized control scheme implemented over a network with associated complexity and various delays is not always the best choice for the structure of the controller in a plant-wide setting. An additional drawback that arises in this context is the reduced robustness against failures in the communication medium [2]. To solve the problem where a decentralized control structure cannot provide the required stability and performance properties, and to avoid the complexity and lack of flexibility associated with traditional centralized control, a quasi-decentralized control strategy with cross communication between the plant units offers a suitable compromise. In this architecture, each unit in the plant has a local control system with its sensors and actuators connected with the local controller through a dedicated communication network. The local control systems in turn communicate with the plant supervisor (and with each other) through a plant-wide communication network. The plant supervisor is responsible for monitoring the various units and coordinating their responses in a way that minimizes the propagation of disturbances and meets the overall plant objectives.

One of the main problems to be addressed when considering the quasi-decentralized networked control system is the large amount of bandwidth required by the different subsystems sharing the communication channel. Tight control of each subsystem to minimize disturbance propagation is best achieved when there is continuous exchange of information between the different units across the plant-wide network. In traditional control architectures, the dedicated point-to-point connections make the sensor information from the neighboring units available to the control system of a given unit continuously. In networked control systems, on the other hand, the sensors from the neighboring units are connected to the control system of interest by a plant-wide network; that is, the feedback path is a network which typically has limited bandwidth and transfers information in a discrete time fashion. A tradeoff typically exists between the achievable control performance and the extent of network resource utilization. On the one hand, maximal control performance requires continuous, or frequent communication, while minimal utilization of the communication network resources (to save on communication costs) favors infrequent sharing of information. Proper characterization and management of this tradeoff is an essential first step to designing networked control and communication strategies that ensure an acceptable control performance while respecting inherent constraints on the communication medium.

One way to overcome bandwidth constraints in the plant-wide communication network is to reduce the transfer of information between the local control systems as much as possible to limit the bandwidth required from the network and free it for other tasks (e.g., other control loops using the network and/or non-control information exchange) without sacrificing stability and ultimately performance of the individual units and the overall plant. To this end, and in lieu of continuous communication of information, a dynamic model of each unit is included in the local control system of all its neighboring units to provide them with an estimate of the evolution of the states of this unit when measurements are not available from the network. The use of a model at the controller/actuator side to recreate the interactions of the local unit with one of its neighbors allows the sensors of each neighboring unit to delay sending data since the model can provide an approximation of the unit's dynamics. Feedback from one unit to another is performed by updating the states of the neighbors' models using their actual states provided by their sensors at discrete time instances. In-between consecutive transmission times, the control action for each unit relies on a collection of models that are incorporated in the controller/actuator and are running open-loop for a certain period of time.

The successful implementation of the proposed control architecture requires characterizing the maximum allowable transfer time between the sensors of each unit and the controller/actuator of the other units, which is the time between information exchanges. In general, this time depends on the degree of mismatch between the dynamics of the units and the models used to describe them. To characterize the communication frequency that minimizes network usage while preserving the desired stability and performance properties in the controlled plant, we formulate the overall closed-loop plant as a jump (switched) nonlinear system where the plant states evolve continuously in time and the estimation errors are re-set to zero at each transmission instance. The closed-loop system is analyzed using tools from hybrid system stability theory to derive an explicit characterization of the minimum transmission frequency that is necessary for closed-loop stability in terms of the model uncertainty. Comparison of the results with the case when linear control methods are applied shows that, for the same set of stabilizing initial conditions, the quasi-decentralized nonlinear control structure guarantees stability under larger update times and thus fares better under tight communication constraints. Finally, the implementation of the quasi-decentralized control structure is demonstrated through applications to representative process networks that are common in industrial systems such as plants with cascaded units and units with recycle streams.

References:

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