Nonlinear PI Control Of Nonlinear Uncertain Systems And Its Application

The study of uncertain dynamics is one of the hottest areas in the controlcommunity. Nonlinear PI control emerged as a new approach in stabilizing uncertainsystems, which differs from the classical adaptive control consisting an identifier anda parameterized feedback law. In fact, in this method the controller can be obtainedonly provided that the boundaries of the uncertain term are known. In this paper wefirst consider the nonlinear PI speed control of permanent magnet synchronous motor(PMSM). The PMSM model was established considering various uncertainties. Dueto the complex uncertainties of the model, it is difficult to apply adaptive control.Therefore, according to nonlinear PI control method, we design the nonlinear PIcontroller based on the information of the uncertain terms' boundaries and simulationresults show the good dynamical response and disturbance tolerance of the controlsystem.In industrial areas, many practical systems are often characterized by the copresence of dynamical phenomena occurring in multiple time-scales, which can bemodeled by a class of systems with singular perturbation parameters. This leads to thegreat significance of the study of controlling singularly perturbed systems. In thispaper, motivated by the work in [2], we give an alternative way to overcome the effectof unmodeled dynamics and external disturbances of a class of nonlinear singularlyperturbed systems by using nonlinear PI control method. Two nonlinear PI controllaws are applied to each subsystem to deal with the unknown uncertainties and thecomposite controller is proved to be effective in stabilizing the original system. Onthe other hand, the control of chaotic system has significant use in many applications,especially in biologic system. Chua's circuit is a typical chaotic system, which willdemonstrate the chaotic behavior if the parameters are deliberately designed.Simulation studies on Chua's chaotic system illustrated the nonlinear PI controllerdesign procedure and showed the effectiveness of the control scheme.