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

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 transform 3

Identifiability Full rank linear transform  coupled nonlinearity 4

Best Linear Approximation Input signals 5

Best Linear Approximation Input signals Combination of dynamics! 6

Best Linear Approximation Input signals Combination of Fixed poles dynamics! Moving zeros 7

Best Linear Approximation Common denominator – Fixed poles – Moving zeros 8

Decomposing the dynamics numerator coefficients D U  V 9

Partition the dynamics 10

Partition the dynamics 11

Partition the dynamics 12

Partition the dynamics 13

Decoupling 14

Decoupling a Static Nonlinearity 15

Decoupling a Static Nonlinearity Homogeneous 2 nd degree  Decoupling = matrix diagonalization 16

Decoupling a Static Nonlinearity Homogeneous 3 rd degree 17

Decoupling a Static Nonlinearity Homogeneous 3 rd degree  Decoupling = tensor diagonalization 18

Decoupling a Static Nonlinearity Polynomial of degree n – Combine Homogeneous Tensors of different degrees – Add constant input  Decoupling = tensor diagonalization 19

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

Measurement Example Validation Error (mV) rms(e) Coupled, 3 rd Degree 11.92 Decoupled, 3 rd Degree 31.05 Decoupled, 15 th Degree 0.66 21

Measurement Example 22

Measurement Example 23

Conclusion • Different LTI models  parallel Wiener-Hammerstein model • Tensor Diagonalization  Decoupling polynomial • Low complexity • High flexibility • Good performance It works! 24

Identification of parallel Wiener- Hammerstein systems with a decoupled static nonlinearity M. Schoukens, K. Tiels, M. Ishteva, J. Schoukens 25