# Washout (Discrete or Continuous)

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

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

## Description

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.

### Equations

#### Continuous

To configure the washout block for continuous time, set the Sample time property to `0`. This representation is equivalent to the continuous transfer function:

`$G\left(s\right)=\frac{Ts}{Ts+1},$`
where T is the time constant. From the preceeding transfer function, the washout defining equations are:
`$\left\{\begin{array}{c}\stackrel{˙}{x}\left(t\right)=\frac{1}{T}\left(-x\left(t\right)+u\left(t\right)\right)\\ y\left(t\right)=-x\left(t\right)+u\left(t\right)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\left(0\right)={u}_{0},\text{\hspace{0.17em}}y\left(0\right)=0,$`
where:

• u is the washout input.

• x is the washout state.

• y is the washout output.

• t is the simulation time.

• u0 is the initial input to the washout block.

#### Discrete

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:

`$G\left(z\right)=\frac{z-1}{z+{T}_{s}/T-1},$`
where Ts is the sample time. From the discrete transfer function, the washout defining equations are defined using the forward Euler method:
`$\left\{\begin{array}{c}x\left(n+1\right)=\left(1-\frac{{T}_{s}}{T}\right)x\left(n\right)+\left(\frac{{T}_{s}}{T}\right)u\left(n\right)\\ y\left(n\right)=u\left(n\right)-x\left(n\right)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\left(0\right)={u}_{0},\text{\hspace{0.17em}}y\left(0\right)=0,$`
where:

• u is the washout input.

• x is the washout state.

• y is the washout output.

• n is the simulation time step.

• u0 is the initial input to the washout block.

### Initial Conditions

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

### Bypass Filter Dynamics

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.

## Ports

### Input

expand all

Washout input signal. The block uses the input initial value to determine the state initial value.

Data Types: `single` | `double`

### Output

expand all

Washout output signal.

Data Types: `single` | `double`

## Parameters

expand all

Washout time constant. Set this value less than the Sample time to bypass the dynamics of the filter.

Washout filter sample time. Set this to `0` to implement a continuous washout block. Set this to `-1` or a positive number to implement a discrete washout block.

## References

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