Comparative Experiment and Analysis
(1)Comparing the method of this paper with the conventional PI closed loop control method. In this experiment, the
reference value of angular speed is a magnitude of 30rad/s step signal. In Fig. 4, we can see that the conventional PI
closed loop control method track the reference angular speed about 5 seconds. But the Triple-step nonlinear method can track the reference angular speed in about 1 second. Thus the method of this paper has better transient response characteristics.

(2)In order to verify the proposed method for the tracking ability of sinusoidal signal, we conduct experiment and compare with the conventional PI closed loop control method. In this experiment, the reference of angular speed is sinusoidal signal ω∗(t) = 30 sin(2πt)(rad/s) in Fig. 5 and ω∗(t) = 4 sin(2πt)(rad/s) in Fig. 6. Fig. 5(a) and Fig. 6(a) use the conventional PI controller. In Fig. 5(b) and in Fig. 6(b) use the nonlinear control method in this paper. When the motor speed through the zero point(motor rotation transformation), due to lower motor speed, there is a clear dead zone phenomenon when the conventional PI is used. But the Triplestep nonlinear method can lead to a smooth transition in the zero crossing. When the amplitude of reference angular speed is low, the motor has serious dead zone phenomenon. The conventional PI closed loop control method has a great tracking error and poor control effect. However, the Triplestep nonlinear method has better signal tracking effect.
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