| Simulink® | |
Continuous
The Transfer Fcn block models a linear system by a transfer function of the Laplace-domain variable s. The block can model both single-input single-output (SISO) and single-input multiple output (SIMO) systems.
This block assumes that the transfer function has the following form
where u and y are the system's input and outputs, respectively, 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. This block also assumes that the transfer functions for the outputs of a multiple output system have the same denominator and that the numerators of the transfer functions have the same order.
To model a single-output system, enter a vector containing the system transfer function's numeric coefficients in the Numerator coefficient field in the block's parameter dialog box. Enter a vector containing the transfer function's denominator coefficients in the Denominator coefficient field. In this case, the input and output of the block are scalar time-domain signals.
To model a multiple-output system, enter a matrix in the Numerator coefficient field where each row of the matrix contains the numerator coefficients of a transfer function that determines one of the block's outputs. Enter a vector containing the denominator coefficients common to the system's transfer functions in the Denominator coefficient field. In this case, the block's input is a scalar and the block's output is a vector each of whose elements is an output of the system modeled by the block.
Initial conditions are preset to zero. If you need 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 consult the Control System Toolbox™ documentation.
The numerator and denominator are displayed on the Transfer Fcn block depending on how they are specified:
If each is specified as an expression, a vector, or a variable enclosed in parentheses, the icon shows the transfer function with the specified coefficients and powers of s. If you specify a variable in parentheses, the variable is evaluated. For example, if you specify Numerator as [3,2,1] and Denominator as (den) where den is [7,5,3,1], the block looks like this:
If each is specified as a variable, the block shows the variable name followed by (s). For example, if you specify Numerator as num and Denominator as den, the block looks like this:
By default Simulink® software uses the absolute tolerance value specified in the Configuration Parameters dialog box (see Absolute tolerance) to solve the states of the Transfer Fcn block. If this value does not provide sufficient error control, specify a more appropriate value in the Absolute tolerance field of the Transfer Fcn block's dialog box. The value that you specify is used to solve all the block's states.
The Transfer Fcn block accepts and outputs signals of type double.
The row vector of numerator coefficients. A matrix with multiple rows can be specified to generate multiple output. The default is [1].
The row vector of denominator coefficients. The default is [1 1].
Absolute tolerance used to solve the block's states. You can enter auto or a numeric value. If you enter auto, Simulink software determines the absolute tolerance (see Specifying Variable-Step Solver Error Tolerances). If you enter a numeric value, Simulink software uses the specified value to solve the block's states. Note that a numeric value overrides the setting for the absolute tolerance in the Configuration Parameters dialog box.
Use this to assign a unique name to each state. The state names apply only to the selected block. If left blank, no name is assigned.
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 number of states must be evenly divided by the number of state names. There can be fewer names than the number of states, but there cannot be more names than states.
For example, you can specify two names in a system with four states. Simulink software will assign the first name to the first two states and the second name to the last two.
To assign state names with a variable that has been defined in the MATLAB® workspace, enter the variable without quotes. A variable can be a string, cell, or structure.
Direct Feedthrough | Only if the lengths of the Numerator and Denominator parameters are equal |
Sample Time | Continuous |
Scalar Expansion | No |
States | Length of Denominator -1 |
Dimensionalized | Yes, in the sense that the block expands scalar input into vector output when the transfer function numerator is a matrix. See the preceding block description. |
Zero Crossing | No |
| To Workspace | Transfer Fcn Direct Form II | |
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