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This paper focuses on an improved square root unscented Kalman filter (SRUKF) and its application for rotor speed and position estimation of permanent magnet synchronous motor (PMSM). The approach, which combines the SRUKF and strong tracking filter, uses the minimal skew simplex transformation to reduce the number of the sigma points, and utilizes the square root filtering to reduce computational errors. The time-varying fading factor and softening factor are introduced to self-adjust the gain matrices and the state forecast covariance square root matrix, which can realize the residuals orthogonality and force the SRUKF to track the real state rapidly. The theoretical analysis of the improved SRUKF and implementation details for PMSM state estimation are examined. The simulation results show that the improved SRUKF has higher nonlinear approximation accuracy, stronger numerical stability and computational efficiency, and it is an effective and powerful tool for PMSM state estimation under the conditions of step response or load disturbance.

This paper presents an adaptive nonsingular terminal sliding mode controller for a bearingless permanent magnet synchronous motor. In order to rapidly converge state variables associated with terminal sliding mode control, an adaptive variable-rated exponential reaching law, in which the L1 norm of state variables is introduced, is proposed for the second-order uncertain nonlinear dynamical system. Exponential and constant reaching speed can adaptively adjust according to the distance between state variable and equilibrium point, which can shorten the reaching time and weaken system chattering. The mathematical models for rotating speed and the rotor radial displacement of the bearingless permanent magnet synchronous motor system are set up. The proposed method is then applied to the speed and radial displacement control. Simulation results are provided to validate the effectiveness of the proposed method.

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An improved rotating high-frequency signal injection method based on a finite impulse-response filter for state estimation of bearingless permanent magnet synchronous motor sensorless control is developed in this article. A novel equiripple optimal approximation finite impulse-response filter, which can achieve that the maximum error of pass-band and stop-band is minimum than other finite impulse-response filter under the conditions of the same-order magnitude, is introduced to extract the high-frequency current signal and realize minimum extraction error. The rotor position error signal can be extracted using heterodyning processing to the high-frequency current. The proposed method can effectively eliminate the synchronous shaft filter and reduce the complexity of the system. Linear-phase compensation is used in the finite impulse-response filter to achieve minimum delay of rotor speed and position estimation. The BPMSM sensorless vector control system is set up based on this estimation approach. Simulation results indicate that the proposed method integrated off-line optimization of a finite impulse-response filter and linear-phase compensation can accurately estimate the rotor position and speed in the full-speed range.