Abstract
When a process with actuator saturation nonlinearities is controlled with an analytical (nonmodel predictive) controller, the closed-loop performance may be of low quality due to process directionality and/or windup. This work characterizes these two phenomena and presents (a) an optimal directionality compensator and (b) nonlinear model-based control laws that optimally compensate for process directionality and windup.
Given a controller output, the process directionality compensator calculates an optimal feasible (constrained) plant input that results in a process response as close as possible to the response of the same process to the controller output. The compensator can be used for both linear and nonlinear processes, irrespective of the type of controller being used. The notion of process directionality is defined precisely, and the class of processes that do not exhibit the process directionality are characterized. The performance of the optimal directionality compensator is shown and compared with those of clipping and direction preservation, by linear and nonlinear examples.
The nonlinear model-based control laws include two distinct components: (i) an input-output linearizing controller that inherently include an optimal integral windup compensator and (ii) the optimal directionality compensator. The connections between (a) the derived control laws and (b) model state feedback control and modified internal model control are established. When one of the derived control laws is applied to time-invariant linear processes with a diagonal characteristic matrix, the resulting linear controller is exactly a reduced-order modified internal model controller.
The application and performance of one of the derived control laws are demonstrated by a chemical reactor example.
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Soroush, M. (1998). Windup and Directionality Compensation in Nonlinear Model-Based Control. In: Berber, R., Kravaris, C. (eds) Nonlinear Model Based Process Control. NATO ASI Series, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5094-1_7
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DOI: https://doi.org/10.1007/978-94-011-5094-1_7
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