A Quasi Time-Optimal Control for PMSM in the Condition of Current Constraints

A quasi time-optimal control strategy is proposed to improve the dynamic performance of PMSM. The time-optimal speed error convergence trajectory is deduced under the current constraint condition, and the shortcoming of time-optimal trajectory in practical applications are analyzed. After that, time-optimal convergence trajectory is improved by utilizing the saturation property of the tanh function. Thus, the designed speed error convergence trajectory is time-optimal when the tanh is saturated, and is finite-time convergence when tanh is not saturated. Therefore, the speed response approximates the time optimum but avoids the drawbacks of the true time-optimal. Afterwards, smoothing is added to the designed error convergence trajectory, which reduces the chattering caused by the fractional power term while retaining its strong disturbance rejection capability. Subsequently, the control law is deduced according to above designed convergence trajectory. Then, the extended state observer (ESO) is designed to compensate the disturbance terms in the control law. An open/closed-loop hybrid ESO is proposed to compensate the inner-loop disturbances. Thus, it avoids the effect of the transient processes of ESO on the system while maintaining steady-state accuracy. And a linear ESO is used to compensate outer-loop disturbances. Furthermore, the stability of the system is analyzed, and parameter tuning methods is given. Finally, the proposed method is experimentally verified.