Quasi-decentralized control refers to a distributed control strategy in which most signals used for control are collected and processed locally within each unit (typically over dedicated networks), although some signals -- the total number of which is kept to a minimum -- still need to be transferred between the plant units and their local controllers over a shared (possibly wireless) communication network to account for the interactions between the different units and minimize the propagation of disturbances and process upsets. It is a compromise solution that overcomes the stability and performance limitations of decentralized control approaches while avoiding, at the same time, the complexity and lack of flexibility associated with traditional centralized control structures. A key problem that needs to be addressed in the design of quasi-decentralized control systems is the integration of communication issues and limitations in the formulation and solution of the plant-wide control problem. This is an important problem given the increased reliance in the process industries in recent years on distributed sensor and control systems that are accessed over shared communication networks rather than hardwired. The transition from dedicated, point-to-point connections to multi-purpose shared communication networks is driven in part by the reduced installation and maintenance time and costs as well as the flexibility and enhanced reconfigurability and fault-tolerance of networked control systems [1].

The design of a quasi-decentralized control strategy that enforces the desired closed-loop objectives with minimal cross communication between the component subsystems is an appealing goal since it reduces reliance on the communication medium and helps save on communication costs. This is an important consideration particularly when the communication medium is a potentially unreliable wireless sensor network where conserving network resources is key to prolonging the service life of the network. While the emerging paradigm of control over networks (see, for example, [2], [4] for surveys of results in this area) provides a natural framework to address the issues of control and communication integration, the majority of research studies on networked control systems have focused on single-unit processes using a centralized control architecture, which is not always the best choice for the structure of the controller in a plant-wide setting. By comparison, results on networked control of multi-unit plants with tightly interconnected units have been limited.

In an effort to address this problem, we recently developed in [3] a quasi-decentralized model-based networked control framework for multi-unit plants modeled by linear systems of differential equations. In this architecture, each unit in the plant has a local control system with its sensors and actuators connected to the local controller through a dedicated communication network. The local control systems in turn communicate with one another through a shared communication network. To satisfy the desired closed-loop stability and performance properties of the overall plant with minimal cross-communication between the plant units, we embed in the local control system of each unit a set of dynamic models that provide an approximation of the interactions between the given unit and its neighbors in the plant when communication is suspended and measurements are not transmitted through the plant-wide network. The state of each model is then updated using measurements from the corresponding unit when communication is re-established. The successful implementation of this architecture requires characterizing the maximum allowable update period (equivalently, the minimum transmission frequency) between the sensor suite of each unit and the local controllers of its neighbors, which is a measure of the extent of network resource utilization. Exploiting the linear structure of the plant and the controllers, both necessary and sufficient conditions for closed-loop stability were obtained.

When this architecture is implemented on a nonlinear plant, the update period predicted by linearization-based analysis can guarantee stability for sufficiently small initial conditions where the linearization is valid. Stabilization from initial conditions that are far from the desired equilibrium point requires increasing the frequency of measurement communication (i.e., reducing the update period) 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 networked control approaches that account explicitly for the nonlinearities -- both in the control law and the communication logic designs -- and that lead to an explicit characterization of the minimum allowable cross-communication frequency that is independent of the initial condition.

Motivated by these considerations, we present in this work a nonlinear quasi-decentralized control structure for multi-unit nonlinear plants whose constituent units communicate over a shared communication network. The networked control structure accounts explicitly for the presence of nonlinearities and thus allows stabilization from large initial conditions without the unnecessary expenditure of additional network resources. To obtain an explicit characterization of the minimum stabilizing communication frequency, we consider a class of nonlinear plants where the local dynamics of each unit are nonlinear and its interactions with the other units depend linearly on the states of those units. This class arises commonly in the modeling of chemical plants in which the interconnections between different processing units are the result of material and energy stream exchanges. We synthesize for each unit a controller that consists of a nonlinear feedback component and a linear feed-forward component. The nonlinear component is designed using feedback linearization techniques and is responsible for stabilizing the unit in the absence of interconnections using the locally available measurements. The fact that these measurements are typically transmitted over a dedicated network (and can therefore be assumed to be continuously available to the local controller) allows the nonlinear controller to cancel the effects of the nonlinearities and enforce a linear closed-loop structure. In contrast to the local nonlinear controller, the linear ``feed-forward" component acts to compensate for the interconnections of the unit with its neighbors and receives measurements from those units over the shared communication network at discrete time instances only.

To reduce the frequency at which these measurements are transmitted over the shared network, we embed in each unit a set of nonlinear dynamic models that recreate the interactions of the unit with its neighbors when measurements are not available through the network. The state of each model is updated at discrete time instances when communication is re-established. By exploiting the specific structure of the plant, the properties of the hybrid linear/nonlinear controllers designed, and the rates at which the measurements are available at the local and plant-wide levels, we are finally able to formulate the overall networked closed-loop plant as a switched linear system. Both necessary and sufficient conditions for closed-loop stability are derived leading to an explicit characterization of maximum allowable update period in terms of model uncertainty and controller design parameters. Unlike linearization-based schemes, the resulting update period is independent of the initial condition and can be applied to the nonlinear plant globally without loss of stability. This feature allows expanding the operating range of the quasi-decentralized networked control structure without increasing communication requirements. The design and implementation of the proposed control structure are demonstrated through an application to a representative chemical plant.

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] Hokayem, P. F. and C. T. Abdallah, ``Inherent issues in networked control systems: A survey," Proceedings of the American Control Conference, pages 329--336, Boston, MA, 2004.

[3] Sun, Y. and N. H. El-Farra, ``Quasi-decentralized model-based control of networked process systems," Comp. & Chem. Eng., in press.

[4] Tipsuwan, Y. and M. Y. Chow, ``Control methodologies in networked control systems," Contr. Eng. Prac., 11:1099--1111, 2003.