Feedback Linearization for a Generalized Multivariable T-S Model
Abstract
1. Introduction
- The development of an optimal feedback linearization-based FLC, grounded in the authors’ improved T-S modeling framework and integrated with Linear Quadratic Regulator (LQR) optimal control.
- Validation of the proposed controller through implementation on a two-link robotic manipulator, demonstrating robust performance, zero steady-state error, and effective disturbance rejection.
2. Feedback Linearization
3. Steady State Error
4. Optimal Controller Design
5. Fuzzy T-S Model Parameter Estimation
6. Implementation of the Proposed Method
- Obtain the T-S model through experimentation: , , , and C.
- Determine a central working point for the system; this may correspond to the central rule of the T-S model or the parameters from Section 5: and .
- Compute the desired system matrix and the steady-state error cancellation matrix using LQR: and K.
- Determine the matrix S.
- Update the system matrices at the current instant: , , and at the current time.
- Update the control action at the current time using Equation (7).
7. Example: Two-Link Robot
7.1. T-S Model
7.2. Proposed Optimal Controller
7.3. Case Examples
- Case 1:
- Case 2:
- Case 3:
- Disturbance effect:
- Case 4:
- Case 5:
- Case 6:
- Case 7:
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Al-Hadithi, B.M.; Blanco Rico, J.; Jiménez, A. Feedback Linearization for a Generalized Multivariable T-S Model. Electronics 2025, 14, 3129. https://doi.org/10.3390/electronics14153129
Al-Hadithi BM, Blanco Rico J, Jiménez A. Feedback Linearization for a Generalized Multivariable T-S Model. Electronics. 2025; 14(15):3129. https://doi.org/10.3390/electronics14153129
Chicago/Turabian StyleAl-Hadithi, Basil Mohammed, Javier Blanco Rico, and Agustín Jiménez. 2025. "Feedback Linearization for a Generalized Multivariable T-S Model" Electronics 14, no. 15: 3129. https://doi.org/10.3390/electronics14153129
APA StyleAl-Hadithi, B. M., Blanco Rico, J., & Jiménez, A. (2025). Feedback Linearization for a Generalized Multivariable T-S Model. Electronics, 14(15), 3129. https://doi.org/10.3390/electronics14153129