Position Control of Pneumatic Actuators Using Three-Mode Discrete-Valued Model Predictive Control
Abstract
1. Introduction
2. System Design and Modeling
2.1. System Design
2.2. System Model
2.3. Model Fitting and Validation
3. Control Algorithms
3.1. SMC3
3.2. DVMPC1
Algorithm 1: Prediction algorithm for DVMPC1 | |
1 | Set , , , and . |
2 | Compute |
3 | If , then use: , , and |
4 | Compute the predicted mass flow rates using: and |
5 | Compute the predicted pressure derivatives using: and |
6 | Compute the predicted pneumatic force using: |
7 | Substitute , and into (19) to obtain the predicted friction force, |
8 | Compute the predicted acceleration, , using (18), , , and |
9 | Set |
10 | If , then go to Step 2 |
11 | Stop |
3.3. DVMPC2
4. Controller Parameter Optimization
5. Experimental Verification
5.1. Testbed
5.2. Experimental Results and Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Parameter | Value | Description |
---|---|---|
0.001 s | Sampling period | |
4.91 × 10−4 m2 | Chamber A cross-sectional area | |
4.91 × 10−4 m2 | Chamber B cross-sectional area | |
293 K | Air temperature | |
0.6 m | Cylinder stroke | |
6.0 × 105 Pa | Supply pressure (absolute) | |
1.0 × 105 Pa | Atmospheric pressure (absolute) | |
2.14 kg | Nominal total mass | |
0.004 s | Valve energizing delay time | |
0.001 s | Valve de-energizing delay time | |
1.7 × 10−6 (m·kg) 0.5 | Chamber filling coefficient | |
6.1 × 10−9 m·s | Chamber discharging coefficient | |
2.65 × 10−8 m·s | Choked mass flow rate coefficient | |
54 N | Static friction force in the positive direction | |
48 N | Static friction force in the negative direction | |
81 N | Coulomb friction force in the positive direction | |
78 N | Coulomb friction force in the negative direction | |
7.9 N·s·m−1 | Viscous friction coefficient in the positive direction | |
23 N·s·m−1 | Viscous friction coefficient in the negative direction | |
0.37 m·s−1 | Stribeck velocity in the positive direction | |
0.36 m·s−1 | Stribeck velocity in the negative direction |
Controller Type | Total mass (kg) | SPS (s−1) | RMSE (mm) | ITAE (smm) | SSE (mm) | OS (mm) |
---|---|---|---|---|---|---|
SMC3 | 2.14 | 7.75 | 64.7 | 15.81 | 0.876 | 8.02 |
DVMPC1 | 2.14 | 22.08 | 51.3 | 7.98 | 1.145 | 4.16 |
DVMPC2 | 2.14 | 5.70 | 32.2 | 2.95 | 0.578 | 3.78 |
SMC3 | 3.36 | 7.80 | 63.3 | 16.99 | 1.637 | 12.56 |
DVMPC1 | 3.36 | 25.43 | 51.0 | 9.07 | 1.778 | 8.71 |
DVMPC2 | 3.36 | 7.25 | 32.3 | 3.81 | 1.172 | 8.11 |
SMC3 | 0.95 | 7.20 | 60.9 | 11.71 | 0.326 | 1.92 |
DVMPC1 | 0.95 | 36.23 | 48.5 | 6.78 | 0.968 | 0.67 |
DVMPC2 | 0.95 | 5.15 | 26.7 | 2.34 | 0.782 | 1.03 |
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Qi, H.; Bone, G.M.; Zhang, Y. Position Control of Pneumatic Actuators Using Three-Mode Discrete-Valued Model Predictive Control. Actuators 2019, 8, 56. https://doi.org/10.3390/act8030056
Qi H, Bone GM, Zhang Y. Position Control of Pneumatic Actuators Using Three-Mode Discrete-Valued Model Predictive Control. Actuators. 2019; 8(3):56. https://doi.org/10.3390/act8030056
Chicago/Turabian StyleQi, Haitao, Gary M. Bone, and Yile Zhang. 2019. "Position Control of Pneumatic Actuators Using Three-Mode Discrete-Valued Model Predictive Control" Actuators 8, no. 3: 56. https://doi.org/10.3390/act8030056
APA StyleQi, H., Bone, G. M., & Zhang, Y. (2019). Position Control of Pneumatic Actuators Using Three-Mode Discrete-Valued Model Predictive Control. Actuators, 8(3), 56. https://doi.org/10.3390/act8030056