Linear motor active disturbance rejection control design method based on Taylor tracking differentiator

[0063]Examples:

[0064]In order to verify the feasibility of the active disturbance rejection control design method based on Taylor tracking differentiator provided by the present invention, thefigure 2 Verification in the linear motor control system shown:

[0065]Based on the control design method proposed in this article, the attachedfigure 2 The load of the linear motor system in the system is a weight with a total mass of 1.4kg, the mass of the linear motor mover is 1.79kg, the drive constant Ka=0.84A/V, the thrust coefficient is Km=15N/A, and then use them to separate them in sequence Substitute into formulas (1)-(6).

[0066]Comparing the design method of auto disturbance rejection control based on Taylor tracking differentiator provided by the present invention with the traditional auto disturbance rejection control design method, the controllers all use PD controllers with feedforward compensation, among which the linearity of traditional auto disturbance rejection controllers The expanded state observer is designed as follows:

[0067]

[0068]Among them, if ωoWhen a larger value is taken, it can be guaranteed that when t→∞,

[0069]Comprehensively considering the response speed and noise sensitivity of the system, the parameters of the Taylor tracking differentiator are set to: ε = 0.02, the RESO parameter is set to: r = 20, and the linear expansion state observer designed by formula (7) is set to: ωo=50, the PD controller parameter setting with feedforward compensation is: ωc= 30. The desired signal is: ξ(t)=0.2sin(2πf×t), f represents the frequency.

[0070]The sine signals of different frequencies are set, and the feasibility of the design method provided by the present invention is verified by comparing the tracking effect with the traditional active disturbance rejection control. f is set to the elements in the set {0.2, 0.3, 0.4, 0.5, 0.6} in turn. The experimental results are attachedFigure 3-4Shown. Withimage 3 Indicates the tracking error of the Taylor tracking differentiator-based ADRC and the traditional ADRC corresponding to the expected signals of different frequencies. Refer to the attachmentimage 3 It can be clearly seen that the accuracy of the auto disturbance rejection controller based on Taylor tracking differentiator is obviously better than that of the traditional auto disturbance rejection controller.

[0071]For a more precise descriptionimage 3 The tracking effect shown, define the root mean square error (RMSE): And calculate the attachedimage 3 The root mean square error of the Taylor tracking differentiator-based active disturbance rejection controller and the traditional active disturbance rejection controller corresponding to the different frequencies in theFigure 4 Shown.

[0072]Reference attachmentFigure 4 It can be seen that the root mean square of the tracking error of the active disturbance rejection controller based on the Taylor tracking differentiator at different frequencies is less than that of the traditional active disturbance rejection controller.

[0073]In summary, combined withimage 3 AndFigure 4 The experimental results can verify the feasibility of the active disturbance rejection controller based on Taylor tracking differentiator.