The Study Of Parameterized Uncertain Nonlinear System Control

Nonlinear system control is an important topic in control theory. Because of the complexity of nonlinear properties, and uncertainties such as modeling error, disturbance, etc, many conclusions of modern control theory can not be used directly in engineering applications. Uncertain nonlinear system control is always difficult at present. The study and development of uncertain nonlinear systems are of great importance for both theory and application.In this dissertation, the tracking problem and stabilizing problem of nonlinear systems with parameterized uncertainties have been studied. The main contributions of the dissertation are summarized as follows:The feedback control is studied for a class of nonlinear systems based on the method of feedback linearization. The procedures and conditions of feedback linearization are presented.The theory and procedures of backstepping are studied, and applied in the control of both linear and nonlinear systems. Based on the systematic properties of the system, a systematic procedure is presented, which can guarantee all the states be bounded and realize global stability.The stabilization problem is investigated for a class of nonlinear systems with parameterized uncertainties. Firstly, using a parameter-independent diffeomorphism, the original model is transformed into a parametric-pure-feedback system; then, based on Lyapunov stability theory, combining both backstepping method and adaptive control method, a systematic design procedure for global continuous stabilizer is proposed.The stability problem is studied for a class of nonlinear systems with bounded matched disturbance and parameterized uncertainties. In this case, a robust adaptive control strategy is proposed, which can guarantee the global stability of the closed-loop system and the ultimate convergence of all the states in the closed-loop system. Theoretical analysis and simulation results demonstrate the efficiency of the methods.Two systematic speed tracking control strategies are proposed for PMSM nonlinear systems. Using backstepping method, the first one provides a controller which can guarantee the global stability of the closed-loop system. The second one extends the first strategy to uncertain case. By modifying the nonlinear adaptive strategy proposed by Kanellakopoulous.I, the second controller reduces the number of estimated parameters, thus reduces the dimension of the controller.