Position Control of a Cost-Effective Bellow Pneumatic Actuator Using an LQR Approach
Abstract
:1. Introduction
2. Materials and Methods
2.1. Experimental Apparatus
2.2. Numerical Modeling, PID Controller Development and Initial Experiments
2.3. Numerical Modeling, LQR Controller Development and Initial Experiments
3. Results
3.1. Position Performances of the Bellow PMA by Utilizing Indirect Vacuum Control
3.2. Position Performances of the Bellow PMA by Utilizing Direct Vacuum Control
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Motion Direction | a | b | c |
---|---|---|---|
Forward | 3.03 × 10−5 | −3.07 × 10−3 | 1.161 × 10−1 |
Backward | 1.1 × 10−5 | −1.4 × 10−3 | 8.057 × 10−2 |
τs (s) | Steady-State Error (µm) | |||
---|---|---|---|---|
Displacement (mm) | PID | LQR | PID | LQR |
5 | 0.64 | 0.675 | 227 | 17 |
10 | 0.85 | 0.644 | 291 | 30 |
20 | 0.865 | 0.665 | 620 | 90 |
30 | 0.705 | 0.725 | 830 | 100 |
40 | 0.86 | 0.89 | 1000 | 140 |
50 | 1.01 | 1.03 | 1230 | 30 |
Motion Direction | a | b | c | d |
---|---|---|---|---|
Forward | −4.6 × 10−7 | 5.724 × 10−5 | −2.442 × 10−1 | 5.929 × 10−2 |
Backward | −6 × 10−7 | 7.65 × 10−5 | −3.11 × 10−3 | 6.188 × 10−2 |
τs (s) | Steady-State Error (µm) | |||
---|---|---|---|---|
Displacement (mm) | PID | LQR | PID | LQR |
5 | 0.095 | 0.1 | 642 | 17 |
10 | 0.185 | 0.205 | 144 | 80 |
20 | 0.42 | 0.44 | 380 | 10 |
30 | 0.65 | 0.625 | 520 | 50 |
40 | 0.86 | 0.84 | 730 | 20 |
50 | 1.05 | 1.005 | 960 | 50 |
τs | Steady-State Error | |||
---|---|---|---|---|
Displacement (mm) | PIDB vs. PIDA | PIDB vs. PIDA | PIDB vs. PIDA | PIDB vs. PIDA |
5 | 85% less | 85% less | 65% more | same |
10 | 69% less | 69% less | 50% less | 62% more |
20 | 48% less | 34% less | 39% less | 90% less |
30 | 8% less | 14% less | 38% less | 50% less |
40 | same | 6% less | 28% less | 85% less |
50 | 4% more | 2% less | 22% less | 40% more |
τs (s) | Steady-State Error (µm) | |||
---|---|---|---|---|
Displacement (mm) | PID | LQR | PID | LQR |
5 | 0.205 | 0.12 | 911 | 32 |
10 | 0.23 | 0.225 | 608 | 27 |
20 | 0.435 | 0.44 | 890 | 30 |
30 | 0.63 | 0.635 | 1150 | 40 |
40 | 0.83 | 0.83 | 1410 | 30 |
50 | 1.015 | 1.085 | 1790 | 70 |
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Gregov, G.; Pincin, S.; Šoljić, A.; Kamenar, E. Position Control of a Cost-Effective Bellow Pneumatic Actuator Using an LQR Approach. Actuators 2023, 12, 73. https://doi.org/10.3390/act12020073
Gregov G, Pincin S, Šoljić A, Kamenar E. Position Control of a Cost-Effective Bellow Pneumatic Actuator Using an LQR Approach. Actuators. 2023; 12(2):73. https://doi.org/10.3390/act12020073
Chicago/Turabian StyleGregov, Goran, Samuel Pincin, Antonio Šoljić, and Ervin Kamenar. 2023. "Position Control of a Cost-Effective Bellow Pneumatic Actuator Using an LQR Approach" Actuators 12, no. 2: 73. https://doi.org/10.3390/act12020073
APA StyleGregov, G., Pincin, S., Šoljić, A., & Kamenar, E. (2023). Position Control of a Cost-Effective Bellow Pneumatic Actuator Using an LQR Approach. Actuators, 12(2), 73. https://doi.org/10.3390/act12020073