Control Theory Lab 4

Modeling of Physical-SİMULİNK

Simulink

• Simulink is a graphical interface that allows the user to create programs that are actually run in MATLAB. When these programs run, they create arrays of the variables defined in Simulink that can be made available to MATLAB for analysis and/or plotting.

Simulink uses blocks to write a program. Blocks are arranged in various libraries according to their functions. Properties of the blocks and the values can be changed in the associated dialog boxes. Some of the blocks are given below.

SUM (Math library): Represented

Y=x1+x2-x3

GAIN (Math library): represented

INTEGRATOR (Continuous library)

a- implicite initial condB-explicite initial cond

CONSTANTS (Source library)

STEP (Source library)

SIGNAL GENERATOR (Source library)

repetitive signals

2 click:sine, square,ramp etc choose frequency .......

SCOPE (Sinks library)

The system response can be examined graphically

Think of it as an oscilloscope

CLOCK (Sources library) To Workspace (Sinks library)

The To Workspace block is used to return the results of a simulation to the MATLAB workspace, where they can be analyzed and/or plotted. Any variable in a Simulink diagram can be connected to a ToWorkspace block.

Problem1: We need to simulate the resonant circuit and display the current waveform as we change the frequency dynamically.

varies from 0 to 2000 rad/s

10 100 uf

0.01 HV(t)=5sinwt

Observe the current. What do we expect ?

The amplitude of the current waveform will become maximum at resonant frequency, i.e. at = 1000 rad/s

How to model our resonant circuit ?

V(t)=5sin wt

10 100 uf

0.001H

Using KVL

idtC1

dtdi

LiRv

I

Differentiate wrt time and re-arrange:

LCi

dtid

LR

dtdi

dtdv

L1

2

2

Taking Laplace transform:

LCI

IssILR

LsV 2

LC1

sLR

sIL

sV 2

Thus the current can be obtained from the voltage:

LC1

sLR

s

)L/1(sVI

2

LC1

sLR

s

)L/1(s2

V I

Constructing the model using Simulink:

‘Drag and drop’ block from the Simulink library window to the untitled window

1

s+1

Transfer Fcn

simout

To WorkspaceSine Wave

Constructing the model using Simulink:

LC1

sLR

s

)L/1(s2 62 101s1000s

)100(s

100s

s +1000s+1e62

Transfer Fcn

v

To Workspace1

i

To WorkspaceSine Wave

TF continous

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1

-0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5

0

5

Example in class

100s

s +1000s+1e62

Transfer Fcn

0.802

SliderGain

Scopes

1

Integrator

sin

ElementaryMath

Dot Product2

5

Constant1

2000

Constant

Show the teacher the output on the scope

Problem1:

a. Reproduce the same block diagram using simulink.b. From the simulink blockk diagram fing the transfer function both in time and

frequency domain

Problem 2:

Problem3:

Find on the internet the transfer function of a power 2 (or higher) low pass filter.a)Define all the parameters and variable b) change the transfer function in time/frequency domainc) Use simulink to analyse the behaviors of the filter bewteen 0<t<5 cycles.