Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking
Abstract
:1. Introduction
- The designed controller achieves the desired tracking precision without requiring precise modeling or precise a priori knowledge of the system;
- By formulating a Barrier Composite Energy Function (BCEF) and integrating it into the controller design, the tracking control challenge associated with a LMDGS subject to state variables constraints is properly addressed;
- By incorporating the contributions of the controller’s output fault term, the designed control scheme can effectively mitigate to a significant extent the adverse effects of actuator failures, ensuring system’s convergence.
- By introducing in the design the desired trajectory correction function, non-repetitive desired trajectories can be effectively tracked while ensuring convergence of the system’s tracking error.
2. Problem Statement and Preliminaries
3. Modification of Reference Trajectories
- (1)
- are 2nd order differentiable;
- (2)
- are uniformly bounded over ;
- (3)
- whereas , where representes the ith order time derivative;
- (4)
- , over , where .
4. Controller Design and BCEF
5. Convergence Analysis
5.1. Finiteness of
5.2. Convergence of State Tracking Errors
5.2.1. Fictitious State Tracking Errors
5.2.2. State Tracking Errors
5.3. Boundedness of System States
6. Experimental Results and Discussion
6.1. Experimental Platform
6.2. Validation Experiments
6.2.1. TMILC Performance Experiment
6.2.2. Comparison of TMARC, TMPID, and TMILC
7. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
n | Number of iterations |
j | Order number, . |
System states at n-th iteration. | |
Expected trajectory at n-th iteration. | |
The revised expected trajectory at n-th iteration. | |
trajectory modifier functions. | |
System state tracking errors at n-th iteration. | |
System fictitious state tracking errors at n-th iteration. | |
The parametric uncertainty at n-th iteration. | |
External disturbances and unknown system dynamics at n-th iteration. | |
The unknown control input gain function. | |
Control input at n-th iteration. | |
the control input subject to actuator faults at n-th iteration. | |
System output, . | |
barrier composite energy function at n-th iteration. | |
First derivative of • | |
Estimated value of • | |
Error between and •, i.e., | |
The constraint function of system position state tracking error at the n-th iteration |
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Index | m | f | ||||
---|---|---|---|---|---|---|
Unit | kg | N·s/mm | N | 1 | N/V | 1 |
X | 15 | 0.1 | 3 | 0.03 | 10 | 9.738 |
Y | 25 | 0.1 | 3 | 0.03 | 80 | 30.531 |
Index | TMILC | TMARC | TMPID |
---|---|---|---|
Max | 1.0315 | 1.9304 | 7.3413 |
Max | 1.1047 | 1.2986 | 3.9029 |
RMS | 3.3453 | 5.3372 | 9.7100 |
RMS | 5.3772 | 7.6146 | 6.6105 |
Index | TMILC | TMARC | TMPID |
---|---|---|---|
Max | 6.9881 | 2.6380 | 4.3013 |
Max | 7.2846 | 1.7175 | 1.4549 |
RMS | 1.4865 | 4.0457 | 6.8210 |
RMS | 1.1971 | 7.3033 | 4.3452 |
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Yu, C. Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking. Mathematics 2024, 12, 1673. https://doi.org/10.3390/math12111673
Yu C. Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking. Mathematics. 2024; 12(11):1673. https://doi.org/10.3390/math12111673
Chicago/Turabian StyleYu, Chaohai. 2024. "Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking" Mathematics 12, no. 11: 1673. https://doi.org/10.3390/math12111673
APA StyleYu, C. (2024). Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking. Mathematics, 12(11), 1673. https://doi.org/10.3390/math12111673