(723a) Robust Hybrid Control of Nonlinear Process Systems Subject to Control and Communication Constraints

Many chemical processes are characterized by strong nonlinearities, uncertain dynamics and input constraints. Not surprisingly, these problems have been the subject of significant research work within process control over the past two decades, and led to the development of systematic methods for robust nonlinear and constrained control (see, for example, [1] for some results and references in this area). A close examination of the available results, however, shows that the control problem is typically formulated and addressed within the traditional feedback control setting where the sensors are assumed to transmit the collected measurements continuously and directly to the controller. With the increasing complexity of the process/controller interface in modern control systems, there is a fundamental need to re-examine the classical feedback control paradigm in ways that take into account the additional information-processing devices involved. Emerging issues such as resource constraints, processing and communication delays, data sampling and losses, measurement quantization and real-time scheduling constraints, challenge many of the assumptions in traditional process control methods and need to be integrated explicitly in the control system design.

In this contribution, we consider the problem of robust stabilization of nonlinear process systems subject to control and communication constraints, where the control constraints are due to the physical limitations on the capacity of the control actuators, and the communication constraints are the result of inherent limitations on the measurement sensor sampling rate. To compensate for the unavailability of measurements between sampling instants, an inter-sample model predictor of the closed-loop system is used to provide estimates of the process state that the controller can use to calculate the control action. However, the co-presence of control and sampling rate constraints creates a conflict in the control design objectives in that the set of initial conditions starting from which stability can be achieved (i.e., the stability region) is limited by the control constraints, while the invariant region that the process state can eventually be steered to (i.e., the terminal set) is largely determined by the model uncertainty (the discrepancy between the dynamics of the actual process and that of the inter-sample model predictor), and it is usually the case that the control configuration that has the largest stability region does not have the smallest terminal set. As a result, steering the process state to a small neighborhood of the nominal steady-state of the system starting from a large initial condition cannot, in general, be achieved using a single control configuration. To address this problem, we propose a hybrid control strategy that switches between different control configurations. Specifically, a Lyapunov-based nonlinear controller that enforces practical closed-loop stability is initially synthesized for each control configuration, and the corresponding stability region and terminal set are then characterized in terms of the control constraints, the sampling period and the model uncertainty. To resolve the conflict mentioned earlier, a switching strategy that orchestrates a finite number of transitions between the different control configurations is devised based on the location of the closed-loop state with respect to the stability regions and terminal sets at any given time. In addition, the minimum number of transitions needed for the state to evolve from a given initial condition to a given terminal set is also characterized. Finally, the implementation of the developed hybrid control method is demonstrated using a chemical process example.

References

[1] P. D. Christofides and N. H. El-Farra, Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays. Berlin/Heidelberg: Springer-Verlag, 2005.