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Transfer Functions

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Introduction

 

The DynamicSystems package contains many tools for manipulating transfer functions, and visualizing their response in both the time and frequency domain.

 

Here, we demonstrate how to define a transfer function, generate a phase plot, and convert a transfer function to the time domain. Much more is possible.

 

Define a Transfer Function

 

restart:withDynamicSystems:

tfsas2+bs+c:

 

Define a transfer function object

sysTFTransferFunctiontf,parameters=a=1,b=1,c=1

module...end module

(1)

 

 

Generate a Phase Plot

 

PhasePlotsysTF,parameters=a=3,b=4,c=5

 

Convert Transfer Function to a Differential Equation

 

sysDEDiffEquationtf

module...end module

(2)

sysDE:-de

ⅆⅆtx1t=ax2tb,ⅆⅆtx2t=cbx1ta2bx2tabu1ta,y1t=x2tb

(3)

Discretization and Time-Domain Response to an Input Signal

 

Sampling time and number of samples

Ts0.025:Ns1000:

Generate the input signal

NoisyInputChirp1,0.02,0.01,hertz=true,discrete=true,samplecount=Ns,sampletime=Ts+Statistics:-SampleNormal0,0.05,Ns%T:

 

Discretize the transfer function

sysTFDToDiscretesysTF,Ts

module...end module

(4)

Simulate and plot the response

OutputResponseSimulatesysTFD, NoisyInput, parameters=a=1,b=1,c=1

_rtable18446746075371761166

(5)

plotseqi1Ts,OutputResponsei,i=1..Ns

Applications

Amplifier Gain

Bandpass Filter Design

Inverted Pendulum