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Describing Function Method for Chattering Analysis

Describing Function Method for Chattering Analysis. Unmodeled dynamics. When chattering occurs at high frequency. where the vectors a and b are constant. Parameters of Oscillations. = Equivalent Control. * Frequency. ( k = 0, 1, 2, … ). Relay Gain Adaptation.

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Describing Function Method for Chattering Analysis

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  1. Describing Function Method for Chattering Analysis Unmodeled dynamics When chattering occurs at high frequency where the vectors a and b are constant.

  2. Parameters of Oscillations = Equivalent Control * Frequency (k = 0, 1, 2, … )

  3. Relay Gain Adaptation State-dependent Gain Method Relay gain depends on system states Unmodeled Dynamics

  4. Relay Gain Adaptation State-dependent Gain Method Unmodeled Dynamics

  5. R Relay Gain Adaptation Equivalent-control-dependent Gain Method Relay gain depends on the equivalent control

  6. Relay Gain Adaptation Equivalent-control-dependent Gain Method (i) Gf >0 -1 < η< 1 (M0≥ |g|) → Sliding mode exists (ii) Gf <0

  7. Relay Gain Adaptation Equivalent-control-dependent Gain Method

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