Discrete-time or continuous-time washout or high-pass filter

**Library:**Simscape / Power Systems / Simscape Components / Control / General Control

The Washout (Discrete or Continuous) block implements a
washout filter in conformance with IEEE 421.5-2016^{[1]}.
The washout is also known as a high-pass filter.

You can switch between continuous and discrete implementations of the integrator using
the **Sample time** parameter.

To configure the washout block for continuous time, set the **Sample
time** property to `0`

. This representation is
equivalent to the continuous transfer function:

$$G(s)=\frac{Ts}{Ts+1},$$

$$\{\begin{array}{c}\dot{x}(t)=\frac{1}{T}\left(-x(t)+u(t)\right)\\ y(t)=-x(t)+u(t)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x(0)={u}_{0},\text{\hspace{0.17em}}y(0)=0,$$

*u*is the washout input.*x*is the washout state.*y*is the washout output.*t*is the simulation time.*u*is the initial input to the washout block._{0}

To configure the washout block for discrete time, set the **Sample
time** property to a positive, nonzero value, or to
`-1`

to inherit the sample time from an upstream block. The
discrete representation is equivalent to the transfer function:

$$G(z)=\frac{z-1}{z+{T}_{s}/T-1},$$

$$\{\begin{array}{c}x(n+1)=\left(1-\frac{{T}_{s}}{T}\right)x(n)+\left(\frac{{T}_{s}}{T}\right)u(n)\\ y(n)=u(n)-x(n)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x(0)={u}_{0},\text{\hspace{0.17em}}y(0)=0,$$

*u*is the washout input.*x*is the washout state.*y*is the washout output.*n*is the simulation time step.*u*is the initial input to the washout block._{0}

The block sets the state initial condition to the initial input, making the initial output zero.

Set the time constant to a value smaller than or equal to the sample time to ignore the dynamics of the filter. When bypassed, the block feeds the input directly to the output:

$$T\le {T}_{s}\to y=u\text{\hspace{0.17em}}.$$

[1] *IEEE Recommended
Practice for Excitation System Models for Power System Stability
Studies.* IEEE Std 421.5-2016. Piscataway, NJ: IEEE-SA,
2016.

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