(148d) Supervisory Event-Triggered Control of Networked Process Systems
With the increased emphasis on smart plant operations in recent years, there has been an emerging shift towards the integration of wireless sensor networks in process monitoring and control systems. This shit brings significant economic and operational benefits but also introduces fundamental challenges due to the intrinsic limitations on the computational and communication resources of wireless devices. These limitations favor keeping the information exchange over the network to a minimum so as to conserve network resources, while maximizing process performance favors increased communication levels. An effort to address this conflict in the context of large-scale distributed process systems was initiated in  where a quasi-decentralized model-based networked control structure was developed with the aim of enforcing closed-loop stability with minimal communication requirements. A key idea was to embed, within each local control system, a set of predictive models that generate estimates of the states of the neighboring units when communication is suspended, and to update the models when communication is restored. Under the assumption of a fixed communication rate, an explicit characterization of the minimum allowable communication rate was obtained. In a subsequent study , a quasi-decentralized control strcture using a state-dependent communication logic was developed for nonlinear systems. The key idea there was to have each unit monitor the evolution of the local state and prompt the other units to send their measurements to update their models only when the unit is on the verge of instability. The local instability threshold for each unit was obtained based on a suitable local control Lyapunov function. Compared with the fixed communication rate approach, this approach allows the plant to adapt to changes in operating conditions by varying the communication rate; however, it can also lead to increased network utilization and the possibility of delays when all plant units attempt to access the network at the same time.
An alternative approach was proposed in  where a decentralized event-triggered communication strategy was presented. In this approach, each unit includes an additional model of its own dynamics and uses it to monitor the evolution of the model estimation error in the other plant units. When the error exceeds a certain threshold, the unit transmits its measurement updates to the other units in order to maintain closed-loop stability. The transmission thresholds in this case are determined based on a composite control Lyapunov function for the overall system. While this approach avoids the need for the different units to access the network at the same time, it focuses only on the overall plant stability without taking the performance of the individual subsystems into account. This can result in significant performance deterioration in situations where, for example, a transient local disturbance causes the local Lyapunov function to grow for some time but does not cause similar growth in the composite Lyapunov function (and thus does not trigger model updates). The lack of communication in this case will cause the local performance deterioration to go undetected and uncompensated for. The reduction in network utilization in this approach essentially comes at the expense of sacrificing local process performance.
To address the limitations of previous methods, we present in this work a supervisory event-triggered control framework for multi-unit dstributed plants subject to discrete communication between the local control systems. The objective is to balance the overall plant stability requirement with the local performance needs of the individual subsystems, while simultaneously optimizing the extent of information transfer between the distributed control systems. The proposed control structure is hierarchical in nature. It includes at the lower level a set of quasi-decentralized networked control systems that exchange state measurements at discrete times. Each control system relies on a model of the local subsystem as well as a set of models of the interconnected units, which are used to estimate the states of those units when communication is suspended. By monitoring both the local model estimation error and the evolution of the local control Lyapunov function, the local controller sends alarms to the higher-level supervisor in the event that either one breaches its specified threshold. The supervisor keeps track of the alarm signals reported by the various units and decides accordingly which models need to be updated (i.e., which subsystems should communicate with one another) at any given time. The supervisory logic takes into account the behavior of the local control Lyapunov functions as well as that of the composite control Lyapunov function for the overall plant in order to meet both the stability and performance requirements. The theoretical results are applied to a reactor-separator plant example, and the simulation results show the supervisory control strategy to be more effective than previous approaches using either an adaptive or a fully decentralized control strategy. The supervisory control approach achieves similar performance with less frequent model updates, and also takes the performance of the individual subsystems into explicitly into account.
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