TOWARDS STABLE ADAPTIVE CONTROL FOR NONLINEAR SYSTEMS

The problem of robustness of adaptive controllers in the presence of nonlinear and/or unmodeled dynamics is addressed. The performance and robustness of the recently introduced Model Dependent Control (MDC) are examined for the non-adaptive case. Adaptive MDC is presented and the stability for application to linear systems is investigated. Finally, a novel adaptive controller is presented for application to activated sludge processes.The non-adaptive MDC method is revisited so as to handle independently set-point tracking and disturbance rejection. Only two parameters need to be tuned and these influence directly control quality and robustness. It is proved that given uncertainty bounds a robust MDC controller can be designed even for open-loop unstable systems.Two adaptive controllers based on the MDC methodology are presented. For the first, the MDC tuning parameters are constant, whereas for the second they are tuned on-line depending on the estimated model error. Stability is established for both controllers for application to linear time invariant systems. The adaptive MDC is applicable to open-loop unstable and/or minimum phase systems.An adaptive optimal bang-bang control algorithm is developed that compensates for diurnal feed variations in the activated sludge process for wastewater treatment. Also, the Cautious Self-Tuning Controller is employed for regulation of the dissolved oxygen concentration. Simulations with an activated sludge model are carried out and the performance of both controllers is studied.The stabilizing and the Cautious Self-Tuning Controller are introduced. These controllers are able to perform effectively in the presence of nonlinearities and model uncertainty typical of industrial processes. They incorporate a dead-beat adaptive controller and a robust one independent of the estimated model. The robust controller becomes dominant in case of a large plant/model mismatch, switching to the adaptive controller as the estimated model improves. Both controllers are applicable to open-loop stable and minimum phase systems. Simulations with highly nonlinear models demonstrate their effectiveness, even when other adaptive controllers give unsatisfactory performance.