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Transfer Fcn

Model linear system by transfer function

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  • Library:

  • Simulink / Continuous

  • Transfer Fcn block

Description

The Transfer Fcn block models a linear system by a transfer function of the Laplace-domain variables. The block can model single-input single-output (SISO) and single-input multiple-output (SIMO) systems.

Conditions for Using This Block

转让Fcn块假设以下赖斯tions:

  • The transfer function has the form

    H ( s ) = y ( s ) u ( s ) = n u m ( s ) d e n ( s ) = n u m ( 1 ) s n n − 1 + n u m ( 2 ) s n n − 2 + … + n u m ( n n ) d e n ( 1 ) s n d − 1 + d e n ( 2 ) s n d − 2 + … + d e n ( n d ) ,

    whereuandyare the system input and outputs, respectively,nnandndare the number of numerator and denominator coefficients, respectively.num(s)andden(s)contain the coefficients of the numerator and denominator in descending powers ofs.

  • 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.

Modeling a Single-Output System

For a single-output system, the input and output of the block are scalar time-domain signals. To model this system:

  1. Enter a vector for the numerator coefficients of the transfer function in theNumerator coefficientsfield.

  2. Enter a vector for the denominator coefficients of the transfer function in theDenominator coefficientsfield.

Modeling a Multiple-Output System

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:

  1. Enter a matrix in theNumerator coefficientsfield.

    每一个rowof this matrix contains the numerator coefficients of a transfer function that determines one of the block outputs.

  2. Enter a vector of the denominator coefficients common to all transfer functions of the system in theDenominator coefficientsfield.

Specifying Initial Conditions

A transfer function describes the relationship between input and output in Laplace (frequency) domain. Specifically, it is defined as the Laplace transform of the response (output) of a system with zero initial conditions to an impulse input.

Operations like multiplication and division of transfer functions rely on zero initial state. For example, you can decompose a single complicated transfer function into a series of simpler transfer functions. Apply them sequentially to get a response equivalent to that of the original transfer function. This will not be correct if one of the transfer functions assumes a non-zero initial state. Furthermore, a transfer function has infinitely many time domain realizations, most of whose states do not have any physical meaning.

For these reasons, Simulink®presets the initial conditions of theTransfer Fcnblock to zero. To specify initial conditions for a given transfer function, convert the transfer function to its controllable, canonical state-space realization usingtf2ss. Then, use theState-Spaceblock. Thetf2ssutility provides theA,B,C, andDmatrices for the system.

For more information, typehelp tf2ssor see the Control System Toolbox™ documentation.

Transfer Function Display on the Block

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 ofs. If you specify a variable in parentheses, the block evaluates the variable.

    For example, if you specifyNumerator coefficientsas[3,2,1]andDenominator coefficientsas(den), wheredenis[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 specifyNumerator coefficientsasnumandDenominator coefficientsasden, the block looks like this:

Ports

Input

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Input signal, specified as a scalar with data typedouble.

Data Types:double

Output

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Output signal, provided as a scalar or vector with data typedouble.

  • For a single-output system, the input and output of the block are scalar time-domain signals.

  • For a multiple-output system, the input is a scalar, and the output is a vector, where each element is an output of the system.

Data Types:double

Parameters

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Define the numerator coefficients of the transfer function.

  • 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.

Programmatic Use

Block Parameter:Numerator
Type:character vector, string
Values:vector | matrix
Default:'[1]'

Define the row vector of denominator coefficients.

  • 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.

Programmatic Use

Block Parameter:Denominator
Type:character vector | string
Values:vector
Default:'[1 1]'

Tunability level of the numerator and denominator coefficients for Accelerated simulation modes and deployed simulations usingSimulink Compiler™. Set this parameter toAutoto allow Simulink to choose the appropriate level of parameter tunability.

Set this parameter toOptimizedto generate a representation of numerator and denominator coefficients in generated code for accelerated and deployed simulations that is optimized for better simulation performance.

Set this parameter toUnconstrainedto generate a fully tunable (between simulations) representation of the numerator and denominator coefficients in the generated code for accelerated and deployed simulations. To let Simulink determine the appropriate tunability level, selectAuto.

Programmatic Use

Block Parameter:ParameterTunability
Type:character vector, string
Values:'Auto'|'Optimized'|'Unconstrained'
Default:'Auto'

Absolute tolerance for computing block states, specified as a positive, real-valued, scalar or vector. To inherit the absolute tolerance from the Configuration Parameters, specifyautoor-1.

  • If you enter a real scalar, then that value overrides the absolute tolerance in the Configuration Parameters dialog box for computing all block states.

  • If you enter a real vector, then the dimension of that vector must match the dimension of the continuous states in the block. These values override the absolute tolerance in the Configuration Parameters dialog box.

  • If you enterautoor –1, then Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (seeSolver Pane) to compute block states.

Programmatic Use

Block Parameter:AbsoluteTolerance
Type:character vector, string
Values:'auto'|' 1 '| any positive real-valued scalar or vector
Default:'auto'

Assign a unique name to each state. If this field is blank (' '), no name assignment occurs.

  • To assign a name to a single state, enter the name between quotes, for example,'position'.

  • To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example,{'a', 'b', 'c'}. Each name must be unique.

  • To assign state names with a variable in the MATLAB®workspace, enter the variable without quotes. A variable can be a character vector, string, cell array, or structure.

Limitations

  • 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.

Programmatic Use

Block Parameter:ContinuousStateAttributes
Type:character vector, string
Values:' '| user-defined
Default:' '

Model Examples

Aircraft Longitudinal Flight Control

Aircraft Longitudinal Flight Control

Model flight control for the longitudinal motion of an aircraft. First order linear approximations of the aircraft and actuator behavior are connected to an analog flight control design that uses the pilot's stick pitch command as the set point for the aircraft's pitch attitude and uses aircraft pitch angle and pitch rate to determine commands. A simplified Dryden wind gust model is incorporated to perturb the system.
Open Model
Modeling an Anti-Lock Braking System

Modeling an Anti-Lock Braking System

Model a simple model for an Anti-Lock Braking System (ABS). It simulates the dynamic behavior of a vehicle under hard braking conditions. The model represents a single wheel, which may be replicated a number of times to create a model for a multi-wheel vehicle.
Open Model
Inverted Pendulum with Animation

Inverted Pendulum with Animation

一个倒立摆模型。的一个nimation is created using MATLAB® Handle Graphics®. The animation block is a masked S-function. For more information, use the context menu to look under the Animation block's mask and open the S-function for editing.
Open Model

Block Characteristics

Data Types

double

Direct Feedthrough

yes

Multidimensional Signals

no

Variable-Size Signals

no

Zero-Crossing Detection

no

Extended Capabilities

Version History

Introduced before R2006a

See Also

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