Permanent magnet synchronous motor (PMSM) will demonstrate chaotic phenomena when its parameters fall into a certain area. The performance of PMSM will degrade because of chaos. Therefore, chaos should be suppressed or eliminated. According to the features of this practical plant, the drawbacks of existing control methods are analyzed, and the nonlinear feedback control method is suggested to control the chaos in PMSM. The nonlinear feedback principle is developed using the direct axis and the quadrature axis stator voltage as manipulated variables. The control target will become a unique asymptotically stable equilibrium under the nonlinear feedback principle, by this way, the controlled states can reach the target and the control objective can be implemented. This method can be physically realized using nonlinear state feedback. The control forces can be put into effect at any time. The target of the method may be any point in the strange attractor. The influence of the model error and the measurement noise upon the control performance is studied via simulations. Simulation results show the effectiveness of this method under the presence of the model error and the measurement noise

Nonlinear feedback control of chaos in permanent magnet synchronous motor

Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor

This paper aims to address the stabilization problem of permanent magnet synchronous motor (PMSM) based wind energy conversion system (WECS) through a novel adaptive fractional fuzzy integral sliding mode control scheme in contrast to the traditional integer order control schemes. The main objective of modeling the fractional order control for nonlinear PMSM is to enhance the convergence rate which is effectively better when compared to integer order control schemes. In addition, this paper intensively investigates the performance of fractional order controllers in both PMSM and surface-mounted PMSM-based WECS through analyzing the global stability of closed-loop system based on Lyapunov stability theory. In this regard, the nonlinear PMSM model is transformed into equivalent linear submodels through an effective Takagi–Sugeno fuzzy membership rules. Then, a novel automated (adaptive) controller is designed along with fractional sliding surface, which involves an integral term to control the considered PMSM. In general, adaptive controllers are much more effective than manual controllers. Further, the sufficient conditions are derived in terms of linear matrix inequalities via constructing the novel fractional fuzzy Lyapunov functional with quadratic terms, which guarantees the global stabilization of PMSM-based WECS. Overall performance and effectiveness of the proposed theoretical results are demonstrated through numerical simulations.

Adaptive Fractional Fuzzy Integral Sliding Mode Control for PMSM Model

The Permanent Magnet Synchronous Motor (PMSM) is known to exhibit chaotic behavior under certain conditions. This paper proposes to use an instantaneous Lyapunov exponent control algorithm to control the PMSM. One of the objectives of the control approach is to bring order to the PMSM and to drive it to any user-defined desired state. Simulation results under different operating conditions indicate that the proposed control scheme works well. Moreover, the proposed Lyapunov exponent control scheme is able to induce chaos on the permanent magnet synchronous motor. Simulation results show the effectiveness of the proposed control scheme in chaotifing the response of the motor.

Controlling chaos in the permanent magnet synchronous motor

Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement

This paper characterizes the complex dynamics of the permanent-magnet synchronous motor (PMSM) model with a non-smooth-air-gap, extending the work on the smooth case studied elsewhere. The stability, the number of equilibrium points, and the pitchfork and Hopf bifurcations are analyzed by using bifurcation theory and the center manifold theorem. Numerical simulations not only confirm the theoretical analysis results but also show some more new results including the period-doubling bifurcation, cyclic fold bifurcation, single-scroll and double-scroll chaotic attractors, ribbon-chaotic attractor, as well as intermittent chaos that are different from those reported in the literature before. Moreover, analytical expressions of an approximate stability boundary are given, by computing the local quadratic approximation of the two-dimensional stable manifold at an order-2 saddle point. Combining the existing results with the new results reported in this paper, a fairly complete description of the complex dynamics of the PMSM model is now obtained.

Chang Yu

Papers

Complex dynamics in a permanent-magnet synchronous motor model