Identification of parallel Wiener- Hammerstein systems with a - - PowerPoint PPT Presentation

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Identification of parallel Wiener- Hammerstein systems with a - - PowerPoint PPT Presentation

Feb 21, 2024 338 likes •607 views

Identification of parallel Wiener- Hammerstein systems with a decoupled static nonlinearity M. Schoukens, K. Tiels, M. Ishteva, J. Schoukens 1 Parallel Wiener-Hammerstein Flexible Simple LTI SNL LTI 2 Identifiability Full rank linear

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Identification of parallel Wiener- Hammerstein systems with a decoupled static nonlinearity

  • M. Schoukens, K. Tiels, M. Ishteva,
  • J. Schoukens

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Parallel Wiener-Hammerstein

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Flexible Simple LTI SNL LTI

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Identifiability

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Full rank linear transform

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Identifiability

Full rank linear transform  coupled nonlinearity

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Best Linear Approximation

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Input signals

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Best Linear Approximation

Combination of dynamics!

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Input signals

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Best Linear Approximation

Combination of dynamics!

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Fixed poles Moving zeros

Input signals

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Best Linear Approximation

Common denominator

– Fixed poles – Moving zeros

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U 

Decomposing the dynamics

numerator coefficients

D V

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Partition the dynamics

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Partition the dynamics

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Partition the dynamics

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Partition the dynamics

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Decoupling

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Decoupling a Static Nonlinearity

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Decoupling a Static Nonlinearity

Homogeneous 2nd degree

 Decoupling = matrix diagonalization

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Homogeneous 3rd degree

Decoupling a Static Nonlinearity

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Homogeneous 3rd degree  Decoupling = tensor diagonalization

Decoupling a Static Nonlinearity

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Decoupling a Static Nonlinearity

Polynomial of degree n

– Combine Homogeneous Tensors of different degrees – Add constant input

 Decoupling = tensor diagonalization

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Measurement Example

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Multisine input: 5 amplitudes 20 realizations 2 periods 16384 samples System: Custom built circuit 12th order dynamics Diode-resistor NL

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Measurement Example

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Validation Error (mV) rms(e) Coupled, 3rd Degree 11.92 Decoupled, 3rd Degree 31.05 Decoupled, 15th Degree 0.66

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Measurement Example

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Measurement Example

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Conclusion

  • Different LTI models

 parallel Wiener-Hammerstein model

  • Tensor Diagonalization

 Decoupling polynomial

  • Low complexity
  • High flexibility
  • Good performance

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It works!

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Identification of parallel Wiener- Hammerstein systems with a decoupled static nonlinearity

  • M. Schoukens, K. Tiels, M. Ishteva,
  • J. Schoukens

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