Girish Mahajan (Editor)

Integral sliding mode

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In 1996, V. Utkin and J. Shi proposed an improved sliding control method named integral sliding mode control (ISMC). In contrast with conventional sliding mode control, the system motion under integral sliding mode has a dimension equal to that of the state space. In ISMC, the system trajectory always starts from the sliding surface. Accordingly, the reaching phase is eliminated and robustness in the whole state space is promised.

Control Scheme

For a system x ⋅ = f ( x ) + B ( x ) u + h ( x ) ,

an integral sliding surface can be designed as σ ( t ) = G x ( t ) − G x ( 0 ) + ∫ 0 t [ G B u 0 ( τ ) + G f ( x ( τ ) ) ] d τ so that σ ( 0 ) = 0 is guaranteed and the reaching mode during which the system is sensitive to noise in normal sliding mode is eliminated.

References

Integral sliding mode Wikipedia
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