Transfer Fcn
A model of a linear system in the form of a transfer function.
blockType: TransferFcn
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Path in the library: |
Description
The Transfer Fcn block models a linear system using the transfer function of the variable in the form of Laplace images. The block can model systems with one input and one output (SISO) or with one input and multiple outputs (SIMO).
The block icon displays the transfer function defined by the parameters Numerator coefficients and Denominator coefficients.If the size of the block icon does not accommodate the entire expression, is displayed.
Conditions for block usage
The block Transfer Fcn assumes that the following conditions are met:
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The transfer function has the form:
where
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and - input and output signals, respectively;
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and are the number of coefficients in the numerator and denominator, respectively;
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and - coefficients of numerator and denominator in descending order of degree .
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The order of the denominator must be greater than or equal to the order of the numerator.
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For a system with multiple outputs, all transfer functions have the same denominator and all numerators have the same order.
Modelling a single output system
For a single output system, the input and output of a unit are scalar signals in the time domain. To model this system:
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Enter the vector of coefficients of the numerator of the transfer function in the field Numerator coefficients.
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Enter the vector of denominator coefficients of the transfer function in Denominator coefficients.
Modelling a system with multiple outputs
For a system with multiple outputs, the input of a block is a scalar and the output is a vector where each element is an output of the system. To model this system:
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Enter the matrix in the field Numerator coefficients.
Each row of this matrix contains the coefficients of the numerator of the transfer function that defines one of the block outputs.
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Enter the vector of denominator coefficients common to all transfer functions of the system in the field Denominator coefficients.
Setting initial conditions
The transfer function describes the relationship between input and output in the Laplace (frequency) domain. In particular, it is defined as the Laplace transform of the response (output signal) of a system with zero initial conditions to a pulsed input signal.
Operations such as multiplication and division of transfer functions depend on the zero initial condition. For example, you can decompose one complex transfer function into a number of simpler transfer functions. Apply them sequentially to get a response equivalent to that of the original transfer function. This rule does not hold if one of these transfer functions has a non-zero initial state. In addition, the transfer function has infinitely many realisations in the time domain, most of whose states have no physical meaning.
For these reasons, the initial conditions of the block Transfer Fcn are pre-set to zero. To specify the initial conditions for a given transfer function, transform the transfer function to the canonical form in the state space, then use the block State-Space.
Engee includes the ControlSystems library for the Julia language. It can be used to convert the transfer function to canonical form as follows:
tfcn = tf([1, 2, 3], [4,5,6])
states = ss(tfcn)For more information about the ControlSystems library, see. official site.
Ports
Input
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IN_1
—
input signal
scalar
Details
Input signal.
| Data types |
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| Complex numbers support |
No |
Output
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OUT_1
—
output signal
scalar | vector
Details
Output.
For a system with one output, the input and output of the block are scalar signals in the time domain.
For a system with multiple outputs, the input signal is a scalar and the output signal is a vector where each element is an output of the system.
| Data types |
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| Complex numbers support |
No |
Parameters
Main
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Numerator coefficients —
vector or matrix of numerator coefficients
Scalar / vector / matrix of real numbers
Details
Numerator coefficients of the transfer function.
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For a single output system, enter a vector for the numerator coefficients of the transfer function.
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For a system with multiple outputs, enter a matrix. Each row of this matrix contains the numerator coefficients of the transfer function that defines one of the block outputs.
| Default value |
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| Program usage name |
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| Tunable |
Yes |
| Evaluatable |
Yes |
#
Denominator coefficients —
vector or matrix of denominator coefficients
Scalar / vector / matrix of real numbers
Details
The denominator coefficients of the transfer function.
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For a single output system, enter a vector for the denominator coefficients of the transfer function.
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For a system with multiple outputs, enter a vector containing the denominator coefficients common to all transfer functions in the system.
| Default value |
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| Program usage name |
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| Tunable |
Yes |
| Evaluatable |
Yes |