Zero-Pole
Modelling of the system using a zero-pole gain transfer function.
Description
Block Zero-Pole simulates a system defined by the zeros, poles and gain of the transfer function in the Laplace domain. You can use this block to model systems with one input and one output (SISO) and with one input and multiple outputs (SIMO).
This block assumes that the transfer function has the following form:
where
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- vector of zeros;
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- vector of poles;
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- gain factor of the transfer function.
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The number of poles must be greater than or equal to the number of zeros.
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Complex poles and zeros must be complex-conjugate pairs.
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For a system with multiple outputs, all transfer functions must have the same poles. The zeros may differ in value, but the number of zeros for each transfer function must be the same.
| To model a multi-output system where the transfer functions have different numbers of zeros or one zero each, use several blocks. Zero-Pole. |
Modelling systems with a single output
A single output system has scalar input and output signals in the time domain. To model this type of system:
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Enter a vector for the zeros of the transfer function in the Zeros parameters.
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Enter a vector for the poles of the transfer function in the Poles parameters.
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Enter a scalar for the gain of the transfer function in the Gain parameters.
Modelling systems with multiple outputs
A system with multiple outputs has a scalar input signal in the time domain and a vector output signal in the time domain. Each element of the vector output is an output of the system. To model this type of system:
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Enter a matrix of zeros in the Zeros parameters.
Each column of the matrix contains the zeros of a transfer function that relates the system input signal to one of the output signal elements.
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Enter a vector of poles common to all transfer functions of the system in the Poles parameters.
-
Enter the vector of gains in the Gain parameters.
Each element is the gain of the corresponding transfer function in the zeros matrix.
Ports
Input
#
IN
—
input signal
scalar
Details
The input signal of a system in the time domain, given as a real scalar.
| Data types |
|
| Complex numbers support |
No |
Output
#
OUT
—
output signal
scalar | vector
Details
A model of a system given by the zeros, poles and gain of a discrete transfer function.
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When modelling a system with a single output, the unit outputs a scalar signal in the time domain.
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When modelling a system with multiple outputs, the unit outputs a vector where each element of the vector is an output of the system.
| Data types |
|
| Complex numbers support |
No |
Parameters
Main
#
Zeros —
matrix of zeros
Arbitrary type
Details
Specifies a scalar, vector, or matrix of zeros. The number of zeros must be less than or equal to the number of poles. If poles and zeros are complex, they must be complex-conjugate pairs.
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For a system with a single output, a vector for the zeros of the transfer function is specified.
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For a system with multiple outputs, a matrix is specified. Each column of the matrix contains the zeros of the transfer function linking the input of the system to one of the outputs.
-
For a system without zeros, enter
[].
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Poles —
pole vector
Arbitrary type
Details
Specifies a scalar or vector. The number of poles must be greater than or equal to the number of zeros. If poles and zeros are complex, they must be complex-conjugate pairs.
-
For a system with one output, a vector for the poles of the transfer function is specified.
-
For a system with multiple outputs, a vector for the poles common to all transfer functions of the system or a matrix for the poles common to all transfer functions of the system is specified.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Gain —
transfer function gain
Scalar / array of real numbers
Details
Specifies a scalar or vector of gain factors.
-
For a single output system, the scalar is set.
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For a system with multiple outputs, a coefficient vector or coefficient matrix is specified. Each element is the gain of the corresponding transfer function in the Zeros parameters.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |