Hammerstein model

Block diagram of a Hammerstein model, which consists of the series connection of a static non-linearity in front of a linear system.

The Hammerstein model is a special model form for nonlinear dynamic systems named after Adolf Hammerstein . The characteristic is the structure, consisting of the series connection of a static non-linearity in front of a linear time-invariant dynamic system . The Hammerstein model is defined for both single- variable and multi-variable systems .

The Hammerstein model is generally used in control engineering , for example in modeling, system identification and controller design .

For single-variable systems, the mathematical description is

${\displaystyle {\tilde {u}}(t)=f(u(t))}$

${\displaystyle y(t)={\tilde {u}}(t)*g(t)}$,

where is the impulse response belonging to the transfer function of the linear system and denotes the convolution operator . ${\displaystyle g(t)}$ ${\displaystyle G(s)}$ ${\displaystyle *}$

See also

• Wiener model
• Systems theory