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Continuous
The Transfer Fcn block models a linear system by a transfer function of the Laplace-domain variable s. The block can model single-input single-output (SISO) and single-input multiple output (SIMO) systems.
The Transfer Fcn block assumes the following conditions:
The transfer function has the form
where u and y are the system input and outputs, respectively, and nn and nd are the number of numerator and denominator coefficients, respectively. num and den contain the coefficients of the numerator and denominator in descending powers of s.
The order of the denominator must be greater than or equal to the order of the numerator.
For a multiple-output system, all transfer functions have the same denominator and all numerators have the same order.
For a single-output system, the input and output of the block are scalar time-domain signals. To model this system:
Enter a vector for the numerator coefficients of the transfer function in the Numerator coefficients field.
Enter a vector for the denominator coefficients of the transfer function in the Denominator coefficients field.
For a multiple-output system, the block input is a scalar and the output is a vector, where each element is an output of the system. To model this system:
Enter a matrix in the Numerator coefficients field.
Each row of this matrix contains the numerator coefficients of a transfer function that determines one of the block outputs.
Enter a vector of the denominator coefficients common to all transfer functions of the system in the Denominator coefficients field.
Initial conditions are preset to zero. To specify initial conditions, convert to state-space form using tf2ss and use the State-Space block. The tf2ss utility provides the A, B, C, and D matrices for the system. For more information, type help tf2ss or see the Control System Toolbox™ documentation.
The Transfer Fcn block displays the transfer function depending on how you specify the numerator and denominator parameters.
If you specify each parameter as an expression or a vector, the block shows the transfer function with the specified coefficients and powers of s. If you specify a variable in parentheses, the block evaluates the variable.
For example, if you specify Numerator coefficients as [3,2,1] and Denominator coefficients as (den), where den is [7,5,3,1], the block looks like this:
If you specify each parameter as a variable, the block shows the variable name followed by (s).
For example, if you specify Numerator coefficients as num and Denominator coefficients as den, the block looks like this:
The Transfer Fcn block accepts and outputs signals of type double.
Define the row vector of numerator coefficients.
Default: [1]
For a single-output system, enter a vector for the numerator coefficients of the transfer function.
For a multiple-output system, enter a matrix. Each row of this matrix contains the numerator coefficients of a transfer function that determines one of the block outputs.
See Block-Specific Parameters for the command-line information.
Define the row vector of denominator coefficients.
Default: [1 1]
For a single-output system, enter a vector for the denominator coefficients of the transfer function.
For a multiple-output system, enter a vector containing the denominator coefficients common to all transfer functions of the system.
See Block-Specific Parameters for the command-line information.
Specify the absolute tolerance for computing the block output.
Default: auto
You can enter auto or a numeric value.
If you enter auto, Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (see Solver Pane) to compute the block output.
If you enter a numeric value, that value overrides the absolute tolerance in the Configuration Parameters dialog box.
See Block-Specific Parameters for the command-line information.
Assign a unique name to each state.
Default: ' '
If this field is blank, no name assignment occurs.
To assign a name to a single state, enter the name between quotes, for example, 'velocity'.
To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.
The state names apply only to the selected block.
The number of states must divide evenly among the number of state names.
You can specify fewer names than states, but you cannot specify more names than states.
For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.
To assign state names with a variable in the MATLAB workspace, enter the variable without quotes. A variable can be a string, cell array, or structure.
See Block-Specific Parameters for the command-line information.
Direct Feedthrough | Only if the lengths of the Numerator coefficients and Denominator coefficients parameters are equal |
Sample Time | Continuous |
Scalar Expansion | No |
States | Length of Denominator coefficients -1 |
Dimensionalized | Yes, the block expands scalar input into vector output when the transfer function numerator is a matrix. |
Zero-Crossing Detection | No |
 | To Workspace | Transfer Fcn Direct Form II |  |
Learn more about Simulink through this collection of videos, articles, technical literature and the Getting Started with Simulink Guide.
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