(42b) Supervisory Event-Based Control of Networked Process Systems with Limited State Measurements

The design of distributed and supervisory control systems for chemical process networks is a problem of significant and growing interest in both the academic and industrial communities in process control research (e.g., [1]-[5]). Beyond handling the dynamic coupling and interactions between the constituent subsystems in controller design, the management of information flow and communication between the individual subsystems has recently emerged as another important consideration, which is receiving increased attention in light of the growing calls for moving towards smart plant operations [6]-[7]. In this direction, a quasi-decentralized model-based networked control structure that enforces closed-loop stability with minimal periodic communication was developed in [8]. Within each local control system, predictive models of the dynamics of the rest of the plant are used, together with local state measurements, to generate the local control action at times when communication between the plant subsystems is suspended, and the states of these models are updated when communication is permitted at discrete times. Using a time-triggered communication strategy with a fixed communication rate, an explicit characterization of the minimum allowable communication rate necessary for closed-loop stability was obtained. In subsequent work [9], an adaptive event-based communication strategy was used to manage the information flow in the quasi-decentralized control structure. A key idea was for each unit to monitor its local state and prompt the other units to transmit their data to update their models when the local unit is on the verge of instability. The local instability thresholds were obtained with the aid of appropriate local control Lyapunov functions. While this approach provides greater flexibility in responding to unexpected disturbances in plant operations, it could potentially increase the network load and cause delays and data losses when multiple units attempt to access the network at the same time.

An alternative event-based approach is the broadcast-based communication strategy considered in [10], where the local model estimation error is monitored continuously and the local unit transmits its data to the rest of the plant when this error breaches a certain threshold. The communication threshold is determined using a composite control Lyapunov function for the overall system. This approach avoids the need for simultaneous access to the network; however, it focuses only on stability considerations, without taking the performance of the individual subsystems into account. For example, in the event of a transient local disturbance causing the local Lyapunov function to grow for some time â?? but without causing growth in the composite Lyapunov function and therefore triggering no communication â?? the deterioration in local performance will go undetected and uncompensated for. The reduction in network load in this approach comes at the expense of sacrificing local process performance.

This limitation was addressed in [11] where a higher-level supervisor was introduced into the control structure to balance the overall plant stability requirement with the local performance needs of the component subsystems, while simultaneously optimizing the extent of information transfer between the distributed control systems. The supervisor kept track of the alarm signals reported by the local control systems in response to the local events, and decided accordingly the time and direction of information flow between the individual subsystems. The supervisory logic took into account the evolution of both the local and global control Lyapunov functions so as to meet both the stability and performance requirements. The supervisory control structure was developed for systems with full-state measurements. In practice, however, and due to problems such as installation difficulty, equipment cost, and slow sampling, only incomplete state measurements are typically available. The lack of full-state measurements poses a difficulty in the implementation of traditional event-triggered control and communication strategies which typically rely on monitoring and evaluating state-dependent thresholds. Moreover, handling the lack of full-state measurements is a more challenging problem in the context of controlling networked process systems due to the interactions between the component subsystems.

In this work, we develop a framework for supervisory event-based control of process networks with uncertain nonlinear dynamics, discrete communication between the local control systems and incomplete state measurements. Initially, a set of quasi-decentralized model-based control systems that can exchange information at discrete times over the network are designed. Each local controller relies on model-estimated states of the local and neighboring units to generate the local control action. To overcome the problem of incomplete state measurements, a suitable high-gain observer is designed and included within each local control system to generate an estimate of the local state based on the available real-time output measurements. The observer-estimated states are used to monitor and assess the stability of the local subsystems, and are also broadcast over the network to update the model estimates used by the local controllers at times when communication is triggered. The choice of a high-gain observer design is motivated by the need to decouple the local observer state estimation error from the influence of the interactions between the plant subsystems. A closed-loop stability analysis taking into account model uncertainties, model and observer estimation errors, is conducted to derive appropriate stability thresholds on both the local model estimation errors and control Lyapunov functions in terms of the local observer states. Each control system continuously monitors the discrepancy between the model-estimated and observer-estimated states, as well as the estimated evolution of the local Lyapunov function using the observer state. Alarm signals are sent to the upper-level supervisor when either threshold is breached. The supervisor collects the alarm signals, and then coordinates based on logic operations the dispatch of data transmissions between the plant subsystems. Finally, the proposed methodology is illustrated using a representative chemical process example, and compared with conventional event-triggered control approaches.

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