| The permanent magnet synchronous motor (PMSM) is the sole motor which has been proved can display chaos by model. The mathematical model of the PMSM is similar to that of the famous chaotic Lorenz system under certain conditions, which provides us with specific orientation for studying the secure and stable operation of PMSM. The recent investigations have indicated that with systemic parameters falling into a certain area the PMSM can exhibit chaotic behaviours, which threaten the secure and stable operation of motor drive system. Thus, it is indispensable to study mechanism behind the action of chaos and the methods of controlling or suppressing chaos in PMSM. In this thesis, some proper and applicable methods are researched to control chaos in PMSM. The research work of this dissertation may help to maintain the industrial drive system’s security operation. The main research work of this dissertation has seven parts as follows:First, we investigate how chaos dynamics of PMSM depends on current time-delayed feedback in which the delay time is both fixed and varying in time. We choose model parameters for which the PMSM displays, in the absence of feedback, chaotic oscillations. The stable operation islands of PMSM are first investigated in the parameter space of feedback gain and delay time. It is found that dynamic delay time feedback can obtain stabilization of unstable steady states over a much larger domain of parameters in comparison to the static delay time feedback. The mechanism behind the action of current time-delayed feedback is also addressed.Second, the nonlinear dynamics of PMSM with v/f control is investigated intensively. First, the equilibria and steady-state characteristics of the system are formulated by analytical methods. Then, some of its basic dynamical properties, such as characteristic eigenvalues, Lyapunov exponents and phase trajectories are studied by varying the values of system parameters. It is found that when the values of the system parameters are smaller, the PMSM operates in stable domains, no matter what the values of control gains are. With the values of parameters increasing, the unstability appears and PMSM falls into chaotic operation. Furthermore, the complex dynamic behaviors are verified by means of simulation.Third, based on LaSalle invariant theory, an adaptive law of controlling chaos was presented in this paper, which can avoid the influence of undeterministic equilibrium of system. Simulation results show that the designed control law is effective and its control property is better than that of others. On the other hand, to control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to beconstructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulationresults show the proposed controller is very effective.Fourth, a straightforward adaptive chaos controller based on Lyapunov asymptotical stability theory is designed to control chaos in PMSM with v/f controller. Simulation results show the proposed control law is very effective and robust against both the uncertainties in system parameters and external noise interference.Fifth, a passivity-based adaptive control law is presented, which transforms the PMSM with v/f controller into an equivalent passive system. It is proved that the equivalent system can be asymptotically stabilized at different equilibrium points without influence of undeterministic parameters. Simulation results show the proposed control law is very effective and robust against the uncertainty in system parameters.Sixth, we study the effect of Gaussian white noise on erosion of safe basin in a two- generator system whose safe basin is integral in the absence of noise. The stochastic Melnikov method is first applied to predict the onset of basin erosion when the noise excitation is present in system. And then the eroded basins are simulated according to the necessary restrictions for the system’s parameters. These studies imply that random noise excitation can induce and enhance basin erosion in power system... |
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