Tracking Control Of Induction Motors

Induction motors are a class of nonlinear multivariable uncertain strong-coupling hybrid systems subject to disturbances, which constitutes a benchmark example for nonlinear control. They are described by a fifth order nonlinear differential equation with two inputs and only two state variables available for measurement. The control task is further complicated by the fact that induction motors are subject to unknown load disturbances and the parameters are highly uncertain. So the researches on analysis and regulation of the machines are receiving more and more attentions. Based on the analysis of the mathematical model of induction motor, this paper addresses the problem of tracking control of stator flux and torque.Tracking control is to design a controller such that the regulated outputs are driven to the desired references. Generally, there are two kinds of methods to solve the control problem: one is the global method, that is using the mathematical model and control objects to get the control law; the other is piecewise method, that is employing sampling, comparing and switching logic to choose the corresponding control signals according to outputs errors of different control time periods.The main contributions of this paper are as follows:First, piecewise-based tracking technology-direct torque control (DTC) is discussed, the principle of DTC , the heuristic algorithm and its approximate ratio are introduced, then a new decoupling property between stator flux and torque is revealed, which amends the existing results. Based on this, the stability analysis of DTC is presented. The stator flux and torque regulators are given by state feedback.Second, a global method based on Lyapunov stability is used to perform asymptotic tracking control. As the mathematic basis of the flux regulation model, the general conclusion for asymptotic tracking of non-homogeneous linear time-invariant systems and convergency of time-varying ones are discussed. Then the sufficient condition of stator flux asymptotic tracking is presented. The tracking errors and converging speed of non-feedback and linear feedback controller are compared while the resistances of stator and rotor are varying. In the case of therotor speed being measurable or unmeasurable, the sufficient conditions for torque regulation are proposed respectively. The control refrences is divided into 2 areas, and 3 type state feedback controllers are presented, while the torque asymptotic tracking control is implemented.All the results of this paper are verified by simulation experiment. Simulation results show the efficiency of presented methods.