In order to improve the performance of external disturbance rejection of permanent magnet synchronous motor (PMSM) in speed control, sliding mode control with extended state observer is adopted in this paper. First, an exponential function-based sliding mode reaching law (ESMRL) is developed. The ESMRL can dynamically adapt to the variations of the controlled system, which decrease the reaching time in reaching stage and void chattering in sliding motion stage while maintaining high tracking accuracy of the servo system. Then, an extended state observer (ESO) is introduced to the controller to simultaneously estimate external disturbance and compensate the uncertainties. Simulation results demonstrate that the proposed method has better suppression of chattering effect and disturbance rejection ability while ensuring dynamic performance.

Aiming at solving the problem of the multi-low-frequency mechanical resonances appearing in the large optical telescope control system, this paper proposes a novel control method based on nonlinear active disturbance rejection control (NADRC) and proportional-integral (PI) control. In the proposed control framework, a nonlinear tracking differentiator (NTD)-based feedforward control is designed to improve the tracking performance of the system. Then, the principle of suppression of mechanical resonance of this method is analyzed. Compared with the most commonly used acceleration feedback control (AFC) method, the theoretical analysis shows that the proposed method is more effective for suppressing the low-frequency mechanical resonance. Finally, the proposed method is applied to a large optical telescope, and the experimental results show that the proposed method is better than AFC.INDEX TERMS Mechanical resonance suppression, active disturbance rejection control (ADRC), acceleration feedback control (AFC), nonlinear tracking differentiator (NTD), optical telescope.

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