2.1.5. The Disturbance Torque Model in Rz from Y Moves

Yixiu Sun; Lizhan Zeng; Ying Luo; Xiaoqing Li

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2.1.5. The Disturbance Torque Model in Rz from Y Moves

YS Yixiu Sun

LZ Lizhan Zeng

YL Ying Luo

XL Xiaoqing Li

This method is extracted from research article: Entropy (Basel), May 2021

Model Decoupled Synchronization Control Design with Fractional Order Filter for H-Type Air Floating Motion Platform

DOI: 10.3390/e23050633

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According to Figure 3, when the Y component moves along the Y-direction, the eccentric drive in X-direction will produce the disturbance torque in Rz. Assuming that the disturbance torque is $T_{d - y m}$ , the opposite driving torque $- T_{d - y m}$ is introduced into the control loop to act on the X component to remain the angle of the X component at 0. The dynamic equation of Y component is

where, $T_{y 1 - y m}$ is the torque of Y motor force on the centroid of the entire component, $T_{y 1 - y m} (t) = F_{y} (t) x_{F_{y} c}$ . $T_{y 2 - y m}$ is the torque of the inertia force of Y component on the centroid of the entire component, $T_{y 2 - y m} (t) = - m_{y} {\ddot{y}}_{y} (t) x_{y c}$ . $T_{y 3 - y m}$ is the air floating torque of the beam to Y component, $T_{y 3 - y m} (t) = c_{y H} d_{y} H^{2} ({\dot{θ}}_{x z} (t) - {\dot{θ}}_{y z} (t)) + k_{y H} d_{y} H^{2} (θ_{x z} (t) - θ_{y z} (t))$ . Since $θ_{x z} (t) = 0$ , then $T_{y 3 - y m} (t) = - c_{y H} d_{y} H^{2} {\dot{θ}}_{y z} (t) - k_{y H} d_{y} H^{2} θ_{y z} (t)$ .

After introducing $- T_{d - y m}$ , the angle of the X component is 0, the dynamic equation of X component is:

where $T_{x 1 - y m}$ is the torque of the Y motor stator reaction force on the centroid of the entire component, $T_{x 1 - y m} (t) = - F_{y} (t) x_{F_{y} c}$ . $T_{x 2 - y m}$ is the torque of inertia force of X component on the centroid of the entire component, $T_{x 2 - y m} (t) = m_{x} {\ddot{y}}_{x} (t) x_{x c} = - \frac{F_{y} (t) m_{x} x_{x c} s^{2}}{m_{x} s^{2} + 4 c_{x H} s + 4 k_{x H}}$ . $T_{x 3 - y m}$ is the air floating torque of Y component to the beam, $T_{x 3 - y m} (t) = - T_{y 3 - y m} (t)$ . Then the disturbance torque is obtained as,

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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