Pre-Compensation Strategy for Tracking Error and Contour Error by Using Friction and Cross-Coupled Control
Abstract
:1. Introduction
2. Modeling and Identification of Friction
2.1. LuGre Friction Modeling
2.2. Multi-Parameter Identification of Friction Model
2.3. Tracking Error Modeling
3. Friction Compensation and Control Strategy
3.1. Friction Feedforward Control Design
3.2. Experiment of Friction Compensation Control
4. Contour Error Modeling and Controlling
4.1. Contour Error Modeling
4.2. Influence of the Dynamic Parameter on Contour Error
- (1)
- When the motion time and dynamic gains of each axis are equal, the second and third terms of equation (26) become zero. Consequently, the error er is solely influenced by the first servo dynamic characteristics. In this scenario, the error is dependent on both the frequency of the servo bandwidth and the size of the design path.
- (2)
- When the motion time constants Tx and Ty of each axis are different, but the motion gains Kcx and Kcy are the same, the Equation (26) can be rewritten as follows:
- (3)
- Except for the first item, error er is affected by two parts based on (27). One part is constant and independent of time. The other part consists of elliptic trajectories that vary with time. These trajectories have a major axis distributed in the direction of 45° or 135°, and their radius is related to the system dynamic parameter ωt.
- (4)
- When the motion time constants Tx and Ty are equal, but the motion gains Kcx and Kcy are different, Equation (26) can be rewritten as follows:
- (5)
- When Tx, Ty and Kcx, Kcy are all different, Equation (27) can be rewritten as follows:
4.3. Design of Cross-Coupled Control Strategy
5. Machining Experiment Verification
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Design Values | Least Square Algorithm | Genetic Algorithm | Ant Colony Algorithm | Proposed Algorithm | |
---|---|---|---|---|---|
(N) | 30.00 | 30.51 | 30.63 | 30.21 | 30.12 |
(rad/s) | 0.500 | 0.479 | 0.485 | 0.490 | 0.498 |
(N/m) | 560.0 | 549.4 | 554.1 | 556.7 | 550.6 |
(N/(m/s)) | 300.0 | 291.0 | 294.2 | 303 | 299.8 |
Least Square Algorithm | Genetic Algorithm | Ant Colony Algorithm | Proposed Algorithm | |
---|---|---|---|---|
(N) | 0.279 | 0.229 | 0.251 | 0.119 |
(rad/s) | 0.0292 | 0.0166 | 0.0112 | 0.0052 |
(N/m) | 26.92 | 19.98 | 21.97 | 14.34 |
(N/(m/s)) | 23.45 | 16.19 | 20.74 | 11.57 |
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Liu, M.; Zhu, Y.; Xu, H.; Liu, W.; Yang, H.; Gao, X. Pre-Compensation Strategy for Tracking Error and Contour Error by Using Friction and Cross-Coupled Control. Machines 2024, 12, 593. https://doi.org/10.3390/machines12090593
Liu M, Zhu Y, Xu H, Liu W, Yang H, Gao X. Pre-Compensation Strategy for Tracking Error and Contour Error by Using Friction and Cross-Coupled Control. Machines. 2024; 12(9):593. https://doi.org/10.3390/machines12090593
Chicago/Turabian StyleLiu, Minghao, Yongmin Zhu, Hongliang Xu, Weirui Liu, Hui Yang, and Xingjun Gao. 2024. "Pre-Compensation Strategy for Tracking Error and Contour Error by Using Friction and Cross-Coupled Control" Machines 12, no. 9: 593. https://doi.org/10.3390/machines12090593