Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. (English) Zbl 1207.93079
Summary: Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional-order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first-order sliding mode control technique. The second scheme is based on the chattering-free second-order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by a Lyapunov analysis. The simulation results confirm the expected performance.
MSC:
| 93D09 | Robust stability |
| 93D20 | Asymptotic stability in control theory |
| 34K37 | Functional-differential equations with fractional derivatives |
| 93C41 | Control/observation systems with incomplete information |
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