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Lead-Lag Filter

Implement first-order lead-lag filter


Control and Measurements/Filters


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



s=Laplace operatorT1,T2=time constants

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.


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.


Direct FeedthroughYes
Sample TimeSpecified in the Sample Time parameter
Continuous if Sample Time = 0
Scalar ExpansionYes, of the parameters
StatesOne state per filter


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.

Introduced in R2013a

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