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DynamicSystems[TransferFunction] - create a transfer function system object

Calling Sequence

TransferFunction(opts)

TransferFunction(sys, opts)

TransferFunction(tf, opts)

TransferFunction(z, p, k, opts)

TransferFunction(num, den, opts)

TransferFunction(a, b, c, d, opts)

TransferFunction(de, invars, outvars, opts)

Parameters

sys

-

System; system object

tf

-

algebraic or Matrix(algebraic); transfer function

z

-

list(algebraic) or Matrix(list(algebraic)); zeros

p

-

list(algebraic) or Matrix(list(algebraic)); poles

k

-

algebraic or Matrix(algebraic); gain(s)

num

-

list(algebraic) or Matrix (list(algebraic)); numerator coefficients

den

-

list(algebraic) or Matrix (list(algebraic)); denominator coefficients

a

-

Matrix; state-space matrix A

b

-

Matrix; state-space matrix B

c

-

Matrix; state-space matrix C

d

-

Matrix; state-space matrix D

de

-

equation or list(equation); diff-equations

invars

-

name, anyfunc(name) or list of same; input variables

outvars

-

name, anyfunc(name) or list of same; output variables

opts

-

(optional) equation(s) of the form option = value; specify options for the TransferFunction command

Description

• 

The TransferFunction command creates a transfer function (TF) system object. The frequency-domain behavior of the object is modeled by rational functions (ratpoly) corresponding to transfer functions in the frequency domain.

• 

If the system option cancellation is set to true with DynamicSystems[SystemOptions], then during the conversion pole zero cancellation will be performed.  The system option relativeerror is used to match poles and zeros to cancel.

• 

The input can be specified as one of several representations: transfer function (TF), zero-pole-gain (ZPK), coefficients (Coeff), state-space (SS), or diff-equations (DE).

• 

If no input is provided, a unity-gain TF system is created.

• 

The optional parameter sys is a system object; it is converted to the TF representation. All options are ignored.

• 

The optional parameter tf is the transfer function of a TF system. For a single-input/single-output system, tf is a rational function (ratpoly). For a multi-input/multi-output system, tf is a Matrix of rational functions. The indeterminate of the polynomials depends on whether the system is continuous or discrete; a continuous system typically uses s while a discrete system typically uses z as the indeterminate. The actual names are assigned by DynamicSystems[SystemOptions].

• 

The optional parameters z, p, and k are the zeros, poles, and gain, respectively, of a ZPK system. For a single-input/single-output system, z and p are lists and k is an algebraic expression. For a multi-input/multi-output system, z and p are Matrices of lists and k is a Matrix of algebraic expressions.

• 

The optional parameters num and den are the coefficients of the numerator and denominator, respectively, of a Coeff system. For a single-input/single-output system, num and den are lists, the first element being the coefficient of the highest order term. For a multi-input/multi-output system, num and den are Matrices of lists.

• 

The optional parameters a, b, c, and d are the four state-space matrices, A, B, C, and D, respectively, of an SS system.

• 

The optional parameter de is the difference/differential equation(s) of a DE system. A list is used to specify more than one equation.

• 

The parameters invars and outvars specify the input and output variables of difference/differential equations. They are not required, but if either is not specified then the corresponding keyword parameter inputvariable or outputvariable must be assigned. If both positional and keyword parameters are specified, the keyword parameter take precedence.

Examples

withDynamicSystems:

sys1:=TransferFunction:

PrintSystemsys1

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=1

(1)

sys2:=TransferFunctionss3+5s2+7s+6:

PrintSystemsys2

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=ss3+5s2+7s+6

(2)

sys3:=TransferFunction1,2,1,2,3:

PrintSystemsys3

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=s+2s2+2s+3

(3)

sys4:=TransferFunction,5+1I,51I,1:

PrintSystemsys4

Transfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1stf1,1=1s2+10s+26

(4)

ss_a:=Matrix1,2,0,4

ss_a:=1204

(5)

ss_b:=Matrix3,7,9,6

ss_b:=3796

(6)

ss_c:=Matrix5,6,5,2

ss_c:=5652

(7)

ss_d:=Matrix0,0,0,0

ss_d:=0000

(8)

sys5:=TransferFunctionss_a,ss_b,ss_c,ss_d,discrete,sampletime=0.001,systemname=Example discrete MIMO system:

PrintSystemsys5

Transfer Functiondiscrete; sampletime = .1e-2systemname=Example discrete MIMO system2 output(s); 2 input(s)inputvariable=u1z,u2zoutputvariable=y1z,y2ztf1,1=69z24z25z+4tf2,1=33z+12z25z+4tf1,2=71z116z25z+4tf2,2=47z92z25z+4

(9)

See Also

DynamicSystems, DynamicSystems[Coefficients], DynamicSystems[DiffEquation], DynamicSystems[StateSpace], DynamicSystems[SystemObject], DynamicSystems[SystemOptions], DynamicSystems[ZeroPoleGain]


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