Documentation

## Library

Simscape / Electrical / Specialized Power Systems / Control & Measurements / Filters ## Description

The Lead-Lag Filter block implements the following transfer function:

`$H\left(s\right)=\frac{1+{T}_{1}s}{1+{T}_{2}s}$`

where

This type of filter is used mainly for implementing lead-lag compensation in control systems. The key characteristics of the Lead-Lag Filter block are:

• Input accepts a vectorized input of N signals, thus implementing N filters. This feature is particularly useful for designing controllers in three-phase systems (N=3).

• The same block is used for continuous or discrete model. Changing the sample time Ts from 0 to a positive value automatically discretizes the filter, and vice versa.

• Filter states can be initialized for specified DC inputs and outputs.

## Parameters

Time constant T1 (s)

Specify the filter time constant(s) T1 in seconds. Default is `5e-3`.

Time constant T2 (s)

Specify the filter time constant(s) T2 in seconds. Default is `20e-3`.

DC initial input and output

Specify the DC initial value of input and output signals. If the input signal is vectorized, specify a 1-by-N vector, where each value corresponds to a particular input. Default is `0`.

Sample time

Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block. Default is `0`.

## Characteristics

 Direct Feedthrough Yes Sample Time Specified in the Sample Time parameter Continuous if Sample Time = 0 Scalar Expansion Yes, of the parameters States One state per filter Dimensionalized Yes

## Examples

The `power_LeadLagFilter` example shows two uses of a vectorized Lead-Lag Filter.

The model sample time is parameterized with variable Ts (default value Ts = 50e-6). To simulate continuous filters, specify Ts = 0 in the MATLAB® Command Window before simulating the model.