Abstract
This paper investigates an algorithm for the tracking performance of a Takagi-Sugeno (T-S) fuzzy system using the second-order sliding mode observer/controller technique. First, the original second-order nonlinear system is represented by a T-S fuzzy model, in which most of the parameters can be computed offline. A novel fuzzy second-order sliding mode observer (FSOSMO), which combines the T-S fuzzy model and the second-order sliding mode observer (SOSMO), is then designed to estimate the velocity. Also, a new fuzzy second-order sliding mode control (FSOSMC), which combines the T-S fuzzy model and the second-order sliding mode control (SOSMC), is proposed to stabilize and guarantee the exact motion tracking for the T-S fuzzy system. By integrating the T-S fuzzy model with SOSMO/C, the resulting observer/controller scheme preserves the advantages of both techniques, such as the low online computational burden of the T-S fuzzy model, and low chattering, fast response, and finite time convergence of the SOSMO/C. Moreover, the stability and convergence of the proposed closed loop observer-based controller strategy is theoretically proven by the Lyapunov method. Finally, the simulation results of a two-link robot manipulator are presented to demonstrate the effectiveness of the proposed approach.
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Abbreviations
- FSMC:
-
Fuzzy sliding mode control
- FSOSMC:
-
Fuzzy second-order sliding mode control
- FSOSMO:
-
Fuzzy second-order sliding mode observer
- LMI:
-
Linear matrix inequalities
- SM:
-
Sliding mode
- SMC:
-
Sliding mode control
- SMO:
-
Sliding mode observer
- SMC/O:
-
Sliding mode controller/observer
- SOSM:
-
Second-order sliding mode
- HOSM:
-
High-order sliding mode
- SOSMO:
-
Second-order sliding mode observer
- SOSMC:
-
Second-order sliding mode controller
- SOSMO/C:
-
Second-order sliding mode observer/controller
- PDC:
-
Parallel distributed control
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Van, M., Kang, HJ. & Suh, YS. A novel fuzzy second-order sliding mode observer-controller for a T-S fuzzy system with an application for robot control. Int. J. Precis. Eng. Manuf. 14, 1703–1711 (2013). https://doi.org/10.1007/s12541-013-0229-1
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DOI: https://doi.org/10.1007/s12541-013-0229-1