Control Gain Determination Method for Robust Time-Delay Control of Industrial Robot Manipulators Based on an Improved State Observer
Abstract
1. Introduction
2. Theory and Framework of Time-Delay Control
3. Design Method for Control Gains in Time-Delay Control
3.1. Linearized Control Gain Matrix Derivation
3.2. Identification Method of the Control Gain Matrix
3.3. Simulation Validation of Gain Identification
4. Improved State Observer Design
5. Experiments and Results
5.1. Trajectory Tracking Without Load
5.2. Trajectory Tracking with Load
6. Discussion
7. Conclusions
- Efficient control gain design: The proposed time-delay control gain determination method can be completed offline, without relying on engineer experience or introducing additional tuning parameters, enabling rapid determination of optimal control gains.
- Accurate state estimation: By integrating a model reference observer with a Kalman filter, measurement noise is effectively suppressed, allowing high-precision estimation of joint states.
- Strong engineering applicability: The method features a simple structure and low computational cost, making it suitable for practical implementation in robotic manipulator systems and offering substantial potential for wider application.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Control Gain | |||
---|---|---|---|
Mean Error | 3.89 × 10−2 | 1.07 × 10−2 | 2.35 × 10−3 |
RMS Error | 4.89 × 10−3 | 3.61 × 10−3 | 2.70 × 10−4 |
Control Gain | |||
---|---|---|---|
Mean Error | 2.73 × 10−2 | 1.19 × 10−2 | 2.26 × 10−3 |
RMS Error | 7.70 × 10−3 | 2.86 × 10−3 | 4.17 × 10−4 |
RMS/mm | Dynamic Feedforward | Adaptive TDC | Robust TDC |
---|---|---|---|
X-direction | 1.5747 | 0.3245 | 0.2430 |
Y-direction | 2.7832 | 0.5947 | 0.4356 |
Z-direction | 6.1254 | 1.1361 | 0.8711 |
Composite RMS | 6.9024 | 1.3485 | 0.9564 |
RMS/rad | Dynamic Feedforward | Adaptive TDC | Robust TDC |
---|---|---|---|
Joint 1 | 0.2775 | 0.1189 | 0.1062 |
Joint 2 | 0.8428 | 0.1554 | 0.0671 |
Joint 3 | 1.0997 | 0.2551 | 0.1175 |
Joint 4 | 0.5303 | 0.1211 | 0.0799 |
Joint 5 | 0.3398 | 0.1447 | 0.1094 |
RMS/mm | Dynamic Feedforward | Adaptive TDC | Robust TDC |
---|---|---|---|
X-direction | 1.7453 | 0.9738 | 0.5684 |
Y-direction | 3.1874 | 0.7898 | 0.3949 |
Z-direction | 3.4349 | 0.4432 | 0.2216 |
Composite RMS | 5.0004 | 1.3298 | 0.7267 |
RMS/rad | Dynamic Feedforward | Adaptive TDC | Robust TDC |
---|---|---|---|
Joint 1 | 0.3250 | 0.0616 | 0.0257 |
Joint 2 | 0.9343 | 0.6524 | 0.0451 |
Joint 3 | 1.0676 | 0.2056 | 0.0927 |
Joint 4 | 0.5229 | 0.0870 | 0.0392 |
Joint 5 | 0.3478 | 0.1010 | 0.0702 |
RMS/rad | Dynamic Feedforward | Adaptive TDC | Robust TDC |
---|---|---|---|
Joint 1 | 0.1538 | 0.0829 | 0.0742 |
Joint 2 | 0.4345 | 0.2596 | 0.1923 |
Joint 3 | 0.8078 | 0.4397 | 0.2738 |
Joint 4 | 0.3568 | 0.1924 | 0.1280 |
Joint 5 | 0.3840 | 0.2065 | 0.1375 |
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Chen, Y.; Ding, J.; Xu, T.; Liu, Y. Control Gain Determination Method for Robust Time-Delay Control of Industrial Robot Manipulators Based on an Improved State Observer. Sensors 2025, 25, 5812. https://doi.org/10.3390/s25185812
Chen Y, Ding J, Xu T, Liu Y. Control Gain Determination Method for Robust Time-Delay Control of Industrial Robot Manipulators Based on an Improved State Observer. Sensors. 2025; 25(18):5812. https://doi.org/10.3390/s25185812
Chicago/Turabian StyleChen, Yu, Jianwan Ding, Tianchang Xu, and Yanbing Liu. 2025. "Control Gain Determination Method for Robust Time-Delay Control of Industrial Robot Manipulators Based on an Improved State Observer" Sensors 25, no. 18: 5812. https://doi.org/10.3390/s25185812
APA StyleChen, Y., Ding, J., Xu, T., & Liu, Y. (2025). Control Gain Determination Method for Robust Time-Delay Control of Industrial Robot Manipulators Based on an Improved State Observer. Sensors, 25(18), 5812. https://doi.org/10.3390/s25185812