Research And Application Of Output Regulation For Uncertain Nonlinear Systems

Output regulation is one of the core problems in the field of automatic control,which includes the stabilization of the system,the suppression of external disturbances and the tracking of reference signals.Its research goal is to design a feedback controller so that the system can suppress external interference and track the reference input,and the signals of the closed-loop system are ultimately uniformly bounded.However,in most of the literature,most of the system control directions are known,obviously only a few systems can meet this condition,which limits its application in practical problems.In this paper,the problem of adaptive output regulation for uncertain nonlinear systems with unknown control direction is studied firstly,and then the problem of output regulation for output feedback systems with unknown high frequency gain symbols is further studied,and the results are applied to Chua's circuit problem.The specific research contents are as follows:1.The problem of adaptive output regulation for a class of uncertain nonlinear systems with unknown control direction is studied.The control direction is unknown,and the system itself and the external system contain unknown parameters,which increases the difficulty of dynamic feedback controller design.In order to solve this problem,first of all,suppose the regulator equation is solvable,then design the linear internal model by using the internal model principle,transform the coordinate of the system,and calculate the new state equation;then,transform the robust output regulation problem into the robust stabilization problem,and use the adaptive control method and Nussbaum dynamic gain technology to propose a new dynamic output Feedback control method.The simulation results show that the proposed control algorithm is effective.2.The output regulation problem of a class of output feedback systems with unknown high frequency gain symbols is studied.Because the high frequency gain sign is unknown and has nonlinear external system,it brings a challenge to the design of the controller.In order to solve this problem,an appropriate immersion system is used to design the nonlinear internal model,and then the coordinate transformation of the output feedback system is carried out to obtain the state equation of the augmented system.Then,a new control law is derived by combining Nussbaum dynamic gain technology and recursive backstepping method,and then the dynamic feedback controller is obtained.The proposed control algorithm is applied to a specific example and Chua's circuit.Through MATLAB simulation experiments,the results show that the designed dynamic feedback controller ensures the tracking error to approach zero asymptotically,and realizes the tracking control of output voltage and current in Chua's circuit.The simulation results show that the proposed control algorithm is effective.