Nonlinear Extended Observer-Based ADRC for a Lower-Limb PAM-Based Exoskeleton
Abstract
:1. Introduction
- We build a mathematical model of the PAM-based exoskeleton robot named BK-Gait.
- We improve the tracking performance of the robot by implementing an NLESO-based ADRC controller, which utilizes a nonlinear ESO that can accurately approximate the system disturbance.
- We develop a feedback controller based on the Lyapunov stability theory. The controller shows outstanding effectiveness when guiding the robot to follow a gait pattern trajectory.
2. Problem Statement
2.1. System Description
2.2. System Modeling
3. Nonlinear Eso-Based ADRC Controller
- Tracking Differentiator (TD), which avoids a sharp deviation of the output signal from its reference. Alternatively, one can create a desirable reference orbit that is physically feasible;
- Extended State Observer (ESO), which estimates the function to remove the unknown component in the model control;
- Nonlinear Feedback Controller (), which controls the state variables of the model to follow the desired trajectory.
3.1. Tracking Differentiator (Td)
3.2. Extended State Observer (Eso)
- •
- is bounded for any ,
- •
- ,
- •
- .
- •
- uniformly in , for every constant .
- •
- For any , there is , so that , where is an initial value independent constant.
3.3. Feedback Controller
4. Experimental Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PAM | Pneumatic Artificial Muscle |
ADRC | Active Disturbance Rejection Control |
ESO | Extended State Observer |
LESO | Linear Extended State Observer |
NLESO | Nonlinear Extended State Observer |
TD | Tracking Differentiator |
RMSE | Root Mean Square Error |
EMG | Electromyography |
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Parameters | ||||
Value | 25 | 25 | 35 | 30 |
Parameters | ||||
Value | 15 | 20 | 0.015 | 0.01 |
Parameters | |||||
Value | 25 | 25 | 35 | 30 | 15 |
Parameters | |||||
Value | 20 | 0.015 | 0.01 | 0.9 | 0.9 |
Joint | Signal Frequency | RMSE | |
---|---|---|---|
LESO | NLESO | ||
Hip | 0.5 Hz | 1.075 | 0.923 |
0.5 Hz (Disturbance) | 1.753 | 1.534 | |
Knee | 0.5 Hz | 1.598 | 1.271 |
0.5 Hz (Disturbance) | 2.657 | 2.342 |
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Dao, Q.-T.; Dinh, V.-V.; Trinh, M.-C.; Tran, V.-C.; Nguyen, V.-L.; Duong, M.-D.; Bui, N.-T. Nonlinear Extended Observer-Based ADRC for a Lower-Limb PAM-Based Exoskeleton. Actuators 2022, 11, 369. https://doi.org/10.3390/act11120369
Dao Q-T, Dinh V-V, Trinh M-C, Tran V-C, Nguyen V-L, Duong M-D, Bui N-T. Nonlinear Extended Observer-Based ADRC for a Lower-Limb PAM-Based Exoskeleton. Actuators. 2022; 11(12):369. https://doi.org/10.3390/act11120369
Chicago/Turabian StyleDao, Quy-Thinh, Van-Vuong Dinh, Minh-Chien Trinh, Viet-Cuong Tran, Van-Linh Nguyen, Minh-Duc Duong, and Ngoc-Tam Bui. 2022. "Nonlinear Extended Observer-Based ADRC for a Lower-Limb PAM-Based Exoskeleton" Actuators 11, no. 12: 369. https://doi.org/10.3390/act11120369