Finite Time Convergence Of The Nonlinear System Controller Design And Applications

Recently, the nonlinear system has been a priority and hotspot of the research of control theory. The thesis gives a summary introduction to finite-time convergence of nonlinear control systems, including engineering background, theory significant, research status, being problem, definition and designing steps, etc. A concise summary is given for current control approaches and results of the motor model. The tracking control problem of motor systems consist the main theme of the thesis. The research results obtained by the author can be divided into two parts:Part1. Finite-time tracking controller design for synchronous motor modelThe most controllers for synchronous motor focus on Feedback linearization, Passivity-based control, Backstepping etc. In this paper we proposed a new kind of finite time switching controller based on variable structure control theory. The tracking controller for a class of permanent-magnet synchronous motor is designed. During the control process, the first phase is to induce the system state into a prescribed state (or region) under the current control law by using the relay switching control, and the second phase is to switch to a terminal sliding mode control such that system state reaches to the equilibrium point in a finite time. The boundedness of all the signals in the closed loop system and the global stability of equilibrium point are guaranteed and the system states accurately track the states of the reference signal in a finite time. The simulation validates the efficiency of the control scheme. Most importantly, this controller can be applied to more complicated synchronous motor models.Part2. Finite-time tracking controller design for induction motorThe most controllers for induction motor focus on linear optimal controller, linear model reference adaptive controller, non-adaptive input-output decoupling controller etc. In this section a new recursive controller is given by using variable structure theory to the global tracking problem. The boundedness of all the signals in the closed loop system is guaranteed and the system states accurately track the states of the reference signal in afinite time. When the tracking error reaches to zero, the control signal also becomes zero in the same finite time. The simulation validates the efficiency of the control schemes.