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Matlab/Simulink Program

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Function of Block: Transfer Function (1)

Posted by Shahrul






  • Description


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.


  • Transfer Fcn Display

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


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