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A novel fuzzy second-order sliding mode observer-controller for a T-S fuzzy system with an application for robot control

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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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Authors and Affiliations

  1. Graduate School of Electrical Engineering, University of Ulsan, Ulsan, South Korea, 689-749

    Mien Van

  2. School of Electrical Engineering, University of Ulsan, Ulsan, South Korea, 689-749

    Hee-Jun Kang & Young-Soo Suh

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  1. Mien Van
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  2. Hee-Jun Kang
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  3. Young-Soo Suh
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Correspondence to Hee-Jun Kang.

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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

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