bruce mayer, pe licensed electrical & mechanical engineer bmayer@chabotcollege

[email protected] • ENGR-25_Lec-25_SimuLink-1.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Chp10: SimuLink-

1



Learning Goals Implement Mathematical Operations in

MATLAB using SimuLink InterConnected Functional Blocks

Employ FeedBack in the SimuLink Environment to numerically Solve ODEs

Create Simulations of Dynamic Control Systems using SimuLink Block Models• Export Simulation result to MATLAB

WorkSpace for Further Analysis



What is SIMULINK? SIMULINK is a tool for modeling,

analyzing, and simulating a wide variety of physical & mathematical systems, including those with nonlinear elements and those which make use of continuous and discrete time

Applications Can be found in Dynamic Control Systems, Signal Processing, Communications, and other time-varying systems.



More on SimuLink SimuLink is a Graphical Environment

where Math Operations are represented by BLOCK Icons• Allows for FEEDBACK of Control Vars

Since SimuLink is used to Analyze Dynamic (time-varying) Systems, there are many References to the Variable, ‘s‘• s follows from LaPlace Transforms

–Studied in 3rd year courses on Electrical, or Dynamic Mechanical, Systems-Control



SimuLink Some More Since LaPlace Transforms, and

Dynamic-System Control Theory are beyond the scope of this Class, we will learn SimuLink by example

The Least intuitive Concept Employed will be FEEDBACK

0F dtetfstfL stThe LaPlace

Transform



Prob 10.2 Solution (book typo) Use FEEDBACK to Find y(t) for ODE

3

ydot7

y

1/5

Integ Scale

1s

2nd Integ

1s

1st Integ

secmol 3

735

mol 50

0

tdtdy

tfyyy

y

tf

y7

y3

ytf 7 yytf 73

yytf 7351

y ty

dtyytf 7351

dtdtyytf 7351



SimuLink-1 00sin10 ytdtdy

Fire Up Simulink Library Browser




Open “Model” Window/File




The “Untitled” Model” Window




Select “Sources” Library

Drag SineWave icon to Model Window




DoubleClick SineWave icon to Open Block-

Parameters Dialog Box

No ChangesNeeded




Select “Math Ops” Library

Drag Gain icon to Model Window




DoubleClick Gain icon to Open Block-Parameters

Dialog Box

Set Gainto 10




Set IC to Zero

Select Continous Library

Drag Integrator Block to Model Window

2X-Click the Icon to Open the DiaLog Box

Set the IC to Zero




Select “Sinks”Library Drag Scope Block to

Model Window




Connect The Block OutPuts & InPuts

Turns to Cross when Clik’d




Open the Config Parameters Dialog Box

Set 13s Stop-Time




Start Simulation Opens the Scope Display

Wait for “Bell” to Sound

2X Click Scope Clik Binoc’s to AutoScale




Simulation Result

tz

zzdzyty

0sin100



EX 10.2-1 (1) Export Simulation

to WorkSpace for Plotting

Add/Subtract icons

2X-Clik “To WorkSpace” icon

00sin10 ytdtdy

SINKS Library

SOURCES Library

SIGNALROUTING



EX 10.2-1 (2) Export Result Plot the Result

t ty

0 2 4 6 8 10 12 140

2

4

6

8

10

12

14

16

18

20

t

y

Example 9.2-3: Soln to dy/dy = 10sin(t) • y(0) = 0

>> plot(y(:,1),y(:,2)), xlabel('t'), ylabel('y'), grid

00sin10 ytdtdy



EX 10.2-3 (1) (with a few mods) SimuLink Model

for Thus Simulate

204sin210 ytydtdy

Integrating, Find dzyzdy

tz

z

ty

02104sin2

Note that the variables are NOT Separable• y is on BOTH sides

dzyz

tyytz

z

ty

0

2

104sin2

2

Then The Model

Sine Wave Scope

1s

Integrator

10

Gain



EX 10.2-3 (2) → Model Parameters

Sine Wave Scope

1s

Integrator

10

Gain

Chg to 2



10.2-3 (3) → Scope Result (IC=2)



10.2-3 (4) → Scope Result (IC=0)



EX 10.2-3 (5) → OutPut Summary

plot(y_of_t(:,1), y_of_t(:,2)),grid0 2 4 6 8 10 12 14 16 18

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

304sin41 ytydtdy

ODE Parameters Changed



EX 10.2-3 (6) → Misc 204sin210 yty

dtdy



SimuLinkHelp



SimuLink Help

3 Choices



Naming SimuLink Blocks Double-Click on the BlockName

PlaceHolder Type in a DESCRIPTIVE Name



EX 10.4-1 (1)

10s Simulation

1s

Vt

1s

THETAtt

1s

THETAt Scope

80/9

Gain

cos

Cos Fcn

pi/50

Ang Accel

100s Simulation

100cos980 2tv

The SimuLink Model



Caveat: Hidden Functions Many math Functions do NOT have

their own block. Instead they “Hide” in a PullDown menu in another icon.

ExamineSome of These.



TRIG Function Pull Down Box On MATH

OPRERATIONS can find SIN but not COS or TAN• They are HIDDEN in

the “TRIG” icon which just happens to have the label SIN– All the other Major

Trig Function reside in this block on a pull Down menu

Start with

• Change the Lower Function to COS

ty 3sin

ty 3cos : toChange



Sin to Cos by PullDown 2X clik the “sin” icon to Reveal PullDown



Sin to Cos by PullDown Clik on Cos

Changes Icon to the Cos Function• That was easy

Run Sin & Cos



All Done for Today

Running aHouse

Furnace

AVERAGE RESIDENTIAL

CUSTOMER

Nov. 2005

Oct. 2005

Percentage Change

from Oct. 2005

Nov. 2004

Percentage Change

from Nov. 2004

Therms of Gas Used

46 25 84.0% 46 0.0%

Cost of Gas Procurement (per therm)

$1.294 $1.231 5.1% $0.743 74.2%

Average Transportation Charge (per therm)

$0.41 $0.412 -0.3% $0.395 4.0%

Total Rate $1.704 $1.643 3.7% $1.137 49.8%

Public Purpose Program (PPP) Surcharge

$0.041 $0.041 0.0% $0.030 39.0%

Total Rate (including PPP Surcharge)

$1.746 $1.684 3.7% $1.167 49.6%

Total Natural Gas Bills (including PPP Surcharge)

$80.30 $42.10 90.7% $53.69 49.6%

One THERM is a unit of heating equal to 100,000 BTU.



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf



Problem 10.15 ThermoStat

Control of Bldg Temp The Governing ODE

aTqRTdtdTCR Also Solve-For, and

Plot, T(t) for Given Parameters Where did this Eqn

Come from?



Prob 10.15 (1) RELAY Block

• Relay Switch output between two constants

• Library → Discontinuities

Relay Parameters



Prob 10.15 (2) T-Stat Temp Gain

• Gain Multiply the input by a constant

• Library → Math Operations

• For Case-2 will change Gain to 40

Fnce Gain

Parameter for Case-1



Prob 10.15 (3) Ambient

Temperature Model• Sine Wave

Generate a sine wave

• Library → Sources

The Input Parameters for

t

hrFFTa 12

sin1050

Bias

Amplitude

Frequency



Prob 10.15 (4) Sin Fcn

Parameters The Summing Node

• Sum Add or subtract inputs

• Library → Math Operations



Prob 10.15 (6) Sum Parameters

1/RC Gain Block• 0.5 per HR

COPY the R*qm Gain Block in Model Space and change Parameters



Prob 10.15 (7) Now the LaPlace

Integrator• Integrator

Integrate a signal • Library →

Continuous

Integ Parameters



Prob 10.15 (8) MUX (Many-to-

One) for Ta and T• Mux Combine

several input signals into a vector or bus output signal

• Library → Signal Routing

MUX Parameters for



Prob 10.15 (9) Use

ToWorkSpace to Send Ta & T to WorkSpace for Plotting• To Workspace

Write data to the workspace

• Library → Sinks

The ToWorkSpace Parameters



Prob 10.15 (10) Connect the Dots

• Be sure to Include FeedBack Link to the ThermoStat

• Scope Added for Diagnostic PurposesBack Link to the ThermoStat



Prob 10.15 (11) Compare Cases

• Small Furnace • Large Furnace



Prob 10.15a (12) – Small Fnce% plot(tout, simout), xlabel('t (Hr)'), ylabel('T (°F)'), grid

0 5 10 15 20 25 30 35 40 45 5040

45

50

55

60

65

70

75Prob 9.15 • Thermostatic Control - Small Furnace

t (Hr)

T (°

F)

Ambient TempInside Temp

Unstable Inside Temp



Prob 10.15a (13) – Large Fnce

0 5 10 15 20 25 30 35 40 45 5040

45

50

55

60

65

70

75

t (Hr)

T (°

F)

Prob 9.15 • Thermostat Control - Large Furnace

Ambient TempIInside temp

T-S

tat

Sco

pesi

mo

ut

Plo

t T

a &

T(t

)

1 s

Inte

gra

tor

IC =

70

°F

40 Fn

ce

R*q

m

Am

bie

nt

Te

mp

, T

a

0.5 1/R

CSTABLEInsideTemp



Prob 10.15b (14) Part (B) → For

Stable Temp Control Find Energy Used

The Modify Previous Model

Separate Gain Blok R*qm to gain Access to qm

Scale qm to get scale comparable to T(t)

Copy & Modify Bloks• Gain• Integrator



Prob 10.15b (15) The Energy Integrator Model

1028

qm

1s

TotalEnergy

T-Stat

1/100

Scale Output

0.0389

Rsimout

Plot Ta & T(t)

1s

IntegratorIC = 70°F

DeBugScope

AmbientTemp, Ta

0.5

1/RC



Prob 10.15b (16) – Energy Use

0 5 10 15 20 250

20

40

60

80

100

120

140Prob 9.15b • Total Energy Used - Large Furnace

t (Hr)

T (°

F), E

/100

(BTU

/Hr)

Inside TempFurnace Energy Use

Daily Use = 12400 BTU/Day = 0.124 Therm/Day → 21.7 ¢/DayBut This Fnce is Microscopic; My Fnce rating is 80 kBTU/Hr



10.2



Prob 10.2



SimuLink ↔ ODE45



Problem 10.2-1



0 2 4 6 8 10 12 14 16 18 20-1

0

1

2

3

4

5

6

t

y(t)

Bruce Mayer, PEENGR25 * 30Apr13

y(t)

1s

To yDotIC = 2

1s

To yIC = 5

yoft

To Workspace

Product

eu

MathFunction

13

Gain3

3

Gain2

7

Gain1

1/5

Gain-1/20

Constant

Clock

2013735 teyyy



P10.2 with various forcing fcns

2013

717.73.4sin50

:fcns Forcingte

ttt

tf



mck Exmpl (1) 2X Mass, Spring,

Damper System

How Do x1 & x2 respond to the SUDDEN Application of a UNIT Pull (1lb or 1N)?

C1

C2

x1

x2

f(Pull Force)

k1

k2



EX mck (2) m1 = 5 m2 = 3 c1 = 4 c2 = 8 k1 = 1 k2 = 2

C1

C2

x1

x2

f(Pull Force)

k1

k2



EX mck (3) 2X Mass, Spring,

Damper System

Set Simulation Time and check by 2X click Scope



EX mck (4) Simulation

Time = 10s

Auto Scaling the Axes

Positions have NOT Yet Stabilized• Try 100s StopTime



EX mck (5) StopTime = 100s

Stabilizes after about 25s• Use 25s for Stop

Final Offsets• x1 = 1.0• x2 = 1.25



P10.2 with various forcing fcns

20137.73.4sin50

:fcns Forcingtett

tf

bruce mayer, pe licensed electrical & mechanical engineer bmayer@chabotcollege

Documents

pe engineeringmathphysics

computational methodssimulink

computational methodsprob

computational methodsmore

computational methodswhat

simulink environment

simulink library

dynamic timevarying