Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach
Abstract
:1. Introduction
2. System Modeling
- The top plate fixed frame T is a right-handed coordinate system whose origin is at the mass center of the plate; the Z-axis points upward, the X-axis points forward, the counterclockwise is the positive rotation direction. This coordinate system is depicted by red-colored vectors in Figure 1.
- The bottom plate fixed frame B has its origin at the centroid of the bottom plate. Translation and rotation directions are similar to frame T.
- is the displacement of the origin O in the x-, y-, and z-directions;
- is the rotation about x-, y-, and z-axes of the upper plate;
- and are the displacement and the angular position of the bottom plate, respectively;
- m is the mass of the sprung weight;
- is the inertia tensor of the sprung mass;
- is the force in the j-axis direction generated by the ith actuator in the same direction;
- is the force in the j-axis direction generated by the four springs;
- is the distance in the j-axis direction from the center of mass to the sensor measuring the velocity in the i-axis direction (m);
- is the distance in the j-axis direction from the center of mass to the actuator that generates the force in the i-axis direction (m).
- is the state vector;
- is the system output vector;
- is the control signal vector;
- is the disturbance vector from the bottom plate.
3. Noninteracting Control Design
3.1. Conditions for a Decoupled Performance
3.2. Design of the State Feedback Matrix F
3.3. The LMI-Based Design of the Feedback Matrix G
4. Simulation Studies
4.1. Implementation
4.2. Simulations
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
a [m] | 0.4 | m [kg] | 288 | lzy [m] | 0.53 |
b [m] | 0.6 | Jxx [kg.m2] | 34.8 | lxz [m] | 0.015 |
c [m] | 0.2 | Jyy [kg.m2] | 15.6 | lzx [m] | 0.37 |
kx, ky, kz [N/m] | 14,180 | Jzz [kg.m2] | 49.92 | lxy [m] | 0.53 |
cx, cy, cz [Ns/m] | 100 | lxx [m] | 0.29 | lyz [m] | 0.015 |
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Lee, D.-H.; Kim, Y.-B.; Chakir, S.; Huynh, T.; Park, H.-C. Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach. Appl. Sci. 2021, 11, 7693. https://doi.org/10.3390/app11167693
Lee D-H, Kim Y-B, Chakir S, Huynh T, Park H-C. Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach. Applied Sciences. 2021; 11(16):7693. https://doi.org/10.3390/app11167693
Chicago/Turabian StyleLee, Dong-Hun, Young-Bok Kim, Soumayya Chakir, Thinh Huynh, and Hwan-Cheol Park. 2021. "Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach" Applied Sciences 11, no. 16: 7693. https://doi.org/10.3390/app11167693