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

**Library:**Simscape / Electrical / 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 (Discrete or Continuous) block for
continuous time, set the **Sample time** property to
`0`

. This representation is equivalent to the continuous
transfer function:

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

where *T* is the time constant. From the
preceding transfer function, the washout defining equations are:

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

where:

*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 block._{0}

To configure the washout Washout (Discrete or Continuous) 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:

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

where *T _{s}* is the
sample time. From the discrete transfer function, the washout defining equations
are defined using the forward Euler method:

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

where:

*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 block._{0}

To specify the initial conditions of this block, set
**Initialization** to:

`Inherited from block input`

— The block sets the state and output initial conditions to the initial input.`Specify as parameter`

— The block sets the state initial condition to the value of**Initial state**.

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:

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

In the continuous case, the sample time and time constant must both be zero.

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