/
Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Bruce Mayer, PE Licensed Electrical & Mechanical Engineer

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer - PowerPoint Presentation

ellena-manuel
ellena-manuel . @ellena-manuel
Follow
343 views
Uploaded On 2019-06-23

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer - PPT Presentation

BMayerChabotCollegeedu EngrMathPhysics 25 Chp10 SimuLink2 Learning Goals Implement Mathematical Operations in MATLAB using SimuLink Functional BlockIcons Employ FeedBack in the ID: 760169

Share:

Link:

Embed:

Download Presentation from below link

Download Presentation The PPT/PDF document "Bruce Mayer, PE Licensed Electrical &..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

Bruce Mayer, PELicensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

Engr/Math/Physics 25

Chp10:

SimuLink-2

Slide2

Learning Goals

Implement Mathematical Operations in MATLAB using

SimuLink

Functional

Block-Icons

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

Slide3

Problem 10.30

Make A subsystem Block for

It has been found that for many Valves the Flow Thru the valve is Related to the Pressure Drop

Inputs

q (kg/s)Pl & Pr (Pa)Rl & Rr ([ΔP]/[kg/s])

Using the Industry Constant of Proportionality, C

v

Slide4

Problem 10.30

Cv is essentially the NonLinear Valve CONDUCTANCE

The Valve RESISTANCE then is simply the inverse of the C

v

Then the Flow Thru a typical On/Off Valve

Slide5

Problem 10.30 (3)

To Account for potential BACK Flow under NEGATIVE ΔP Conditions use the Signed Square-Root Relation; the “SSR”

Where the SSR Fcn

Back to the Tank; ID the In-Flows Assuming Pr & Pl are Less than Pboti.e., There is OUTFLOW at the Left & Right

Slide6

SSR Digression

The SSR fcn is BUILT into SimuLinkA Quick Example

The ResultFor This Problem We’ll Build our OWNSSR

plot(tout, Yin, tout,

Yssr

,

'

LineWidth

'

, 3),

xlabel

(

't'

),

ylabel

(

'9sin(t); SSR(10sin(t))'

), grid, legend(

'

sint

'

,

'SSR'

)

Slide7

HomeMade SSR & test

Build Below from Scratch

Slide8

Problem 10.30

The Tank Flows

Next the Time-Rate-of-Change of mT is just the difference between INflow & OUTflow; Mathematically

Now the Tank mass

m

T

 Tank Mass (kg)

V  Tank Volume (m

3

)

ρ

= Fluid Density (kg/m

3)

 

Slide9

Problem 10.30

Now the OutFlows in Terms of the Fluid-Flow Resistances

p  Pressure at the BOTTOM of the Tank (Pa)And From Fluid Mechanics

A NONlinear ODE in h(t)

Next, Sub into the dm

T

/dt eqn

Slide10

Problem 10.30

Put the ODE into Integrable Form

If the Pressure in the Tank is greater than Outside

the tank, then the

ODE simplifies to

Slide11

Problem 10.30

Using 1/R = Cv in the ODE

Use the SimuLink Integrator (1/s) on the Complicated Integrand to Find Note that is a ParaMeter (i.e., a number) within the Integrator Block

 

Slide12

Problem 10.30

Now Make a SimuLink Model To Determine h(t)In This Case The Parameters will be VARIABLES with values Taken from the WORKSPACEThe Parameter List:

A

 Tank Cross-Section Area

Assumed Circular (Cylindrical Tank)

R

l,r

 Hydraulic Resistances of the LEFT & RIGHT Valves

ρ

Liquid Density

q

Liquid InFlow

h(0)

Liquid Height at t = 0

Slide13

Parameters from WorkSpace

% Bruce Mayer, PE

% ENGR25 * 21Nov11

% file = P10_30_TankBLK_Model_Test_Input_Parameters_1111.m

% Use to TEST with SINGLE tank model%

%

A = 3;

%sf

q_in

= 0.7;

% slug/sec

rho = 1.94;

% slug/cu-

ft

h_0 = 4.3;

%

ft

g = 32.2;

%

ft

/

sq

-sec

R_l = 47; R_r = 71;

% valve resistances>

%

% copy-n-paste Plot Statement into Command Window

% plot(

tout,HofT

, '

LineWidth

', 3),

xlabel

('time (sec

)'),…

ylabel

('Liquid Height, h (

ft

)'), grid

Slide14

Problem 10.30

Design a SimuLink Model to Solve for h(t) Given

Time For

Live Demo

Slide15

Tank Model

Slide16

Two-OutPut Single-Tank Model Test

SSR

Slide17

Expected Result

By Scope

By Plot

Slide18

Change Block Colors

Slide19

Problem 10.30

Now make 3-port Tank Model SubSys

Use this SubSystem Model To Analyze a CASCADING Tank System

Need to Properly MAP the I/O to use

SubSys

Model in the

Casding

format

Slide20

Map Model to 2-Tank Cascade

Need to Adapt this:

To This

=

=

Slide21

Map Model to 2-Tank Cascade

Upper Tank-1 TransFormation Profile →Note also

 

 

 

 

 

 

n/a

n/a

 

 

 

 

 

Slide22

Ref Only: Step Function Graph Code

% Bruce Mayer, PE

% MTH-15 • 29Dec16

% E25_Cascade_Tanks_qmi_Plot_BlueGreenBkGnd_161229.m

% REF: MTH15_Quick_Plot_BlueGreenBkGnd_130911.m

%

clear;

clc

; close;

%

clf

clears figure window

%

% This is a DISCRETE-point Plot

%

% The Domain Limits

xmin

= -3;

xmax

= 5;

% The FUNCTION **************************************

x = [-3, 0, 0, 5] ; y = [0, 0, 0.5, 0.5];

% ***************************************************

% the Plotting Range = 1.05*

FcnRange

<= Not used for discrete

pt

plot

ymin

= -0.11;

ymax

=0.61;

% the Range Limits

R = ymax - ymin; ymid = (ymax + ymin)/2;

ypmin = ymid - R/2; ypmax = ymid + R/2

% This Line NOT used in DISCRETE-Pt Plot

ypmin

=

ymid

- 1.025*R/2;

ypmax

=

ymid

+ 1.025*R/2

%

% The ZERO Lines

zxh

= [

xmin

xmax

];

zyh

= [0 0];

zxv

= [0 0];

zyv

= [

ypmin

ypmax

];

%

% the Plot

axes; set(gca,

'FontSize'

,12);

%

gca

stands for Get Current Axis

whitebg

([1 1 1])

% = White

BckGnd

whitebg

([0.8 1 1] = Blue-Green

plot(

x,y

,

'

LineWidth

'

, 4),grid, axis([

xmin

xmax

ypmin

ypmax

]),

...

xlabel

(

'\

fontsize

{14}t (sec)'

),

ylabel

(

'\

fontsize

{14}

q_m_i

= (slug/sec)'

),

...

title([

'\

fontsize

{16}Cascade-Tanks Mass-Flow

InPut

Profile'

,]),

...

annotation(

'textbox'

,[.15 .07 .0 .1],

'

FitBoxToText

'

,

'on'

,

'

EdgeColor

'

,

'none'

,

'String'

,

...

'E25 Cascade Tanks

qmi

Plot

BlueGreenBkGnd

161229.m'

,

'FontSize'

,7)

hold

on

plot(

zxv,zyv

,

'k'

,

zxh,zyh

,

'k'

,

'

LineWidth

'

, 2)

hold

off

Slide23

Map Model to 2-Tank Cascade

Lower Tank-2 TransFormationDetermine by SSR+Cv Calculation

 

 

 

 

 

 

 

 

 

 

n/a

n/a

Slide24

Map Model to 2-Tank Cascade

Lower Tank-2 TransFormation Detail

 

 

 

 

 

 

Slide25

Final 2-Tank-Cascading Model

 

Slide26

Result for Simulations

1200 SecondsBy Scope

300 SecondsBy Scope

Slide27

½ Hour Simulation

Dip Due to

q2(t=0) = 0 Normal Time Lag

>> plot(tout,simout), xlabel('time (sec)'), ylabel('Liquid Height, h (ft)'),...grid

h2final = 6.4 ft

h1

final

= 3.6

ft

Slide28

All Done for Today

Hoke DV1

DiaphramValve

Slide29

Bruce Mayer, PELicensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

Engr/Math/Physics 25

Appendix

Time For

Live Demo

Time For

WhtBd Demo

Slide30

May17

May17

Slide31

May17

Double

Click

to Open

Slide32

Prob 10.30 (1)

INPORT Block for Rt & Lt Pressure ValuesInport  Create an input port for a subsystem or an external input Library → Ports & Subsystems, SourcesChg Label, No Parameters

Summing Bloks for Rt & Lt

Δ

P’s = P-P

l,r

Sum

Add or subtract inputs

Library

→ Math Operations

Painful RePosition of “+” & “-” connection Locations

Top Node = |-+

Bot Node = +-|

Slide33

Prob 10.30 (2)

Fcn Blok for SSR Fcn  Apply a specified expression to the input Library → User-Defined FunctionsNeed to Implement for u = ΔP

Parameters for Fcn

Slide34

Prob 10.30 (3)

Gain Bloks for Hydraulic ResistancesGain  Multiply the input by a constant Library → Math OperationsResistance Values will come from Variables Defined in WORKSPACE

Slide35

Prob 10.30 (4)

Now

INport Blok for InflowClick on Block, and Use FORMAT to Flip & Twist Block

Sum the OUTflow = q

l

+ qr

+|+

|−+

+−|

Slide36

Prob 10.30 (5)

Then the NET INflow = q - (ql + qr)

Parameters for Scaling Gain-Blok

Now Scale Net InFlow by 1/

ρ

A

ρ

& A

values set in WorkSpace

GainBlok OutPut is the INTEGRAND

Slide37

Prob 10.30 (6)

Integrate using 1/s Block to Find h(t)Integrator  Integrate a signal Library → ContinuousThe Integrator ParametersSet IC, H(t=0) as VARIABLE h0 assigned in WorkSpace

Integrator Parameters

Slide38

Prob 10.30 (7)

Scale h(t) to Determine Pressure at the Bottom of the Tank, P

FeedBack P to Pl & Pr to find the ΔP’s

Slide39

Prob 10.30 (8)

Use OUTPORTs To pick off h(t) & POutport  Create an output port for a subsystem or an external output Library → Ports & Subsystems, Sinks The Final Model

Slide40

Prob 10.30 (9)

Test the model with some realistic Values taken from Work SpaceNeed to apply SOURCES to the Inputs

>> A = 3; %sf

>> q_in = 0.7; % slug/sec>> rho = 1.94; % slug/cu-ft>> h_0 = 4.3; % ft

>> g = 32.2; %ft/sq-sec>> R_l = 47; R_r = 71; % valve resistances>>

P9_30_TankBLK_Model_Test_Input_Parameters_0905.m

Slide41

Prob 10.30 (9a)

Parameters for STEP-Block are CRITICALLY important to obtaining the Correct Answer in the Tank-Model Test

Slide42

Prob 10.30 (10)

The Result from the Scope

Looks OK … can forge ahead

Slide43

Prob 10.30 (11)

Make the Model into a SUBSYSTEMSelect All Components with Bounding Box

Slide44

Prob 10.30 (12)

Use Menus: DIAGRAM → SUBSYTEM & MODLE Reference → CREATE SUBSYSTEM FROM SELECTION

Slide45

Prob 10.30 (13)

ReSize SubSys Blok for Readability

Move Blok w/ Mouse & Cursor Keys

Flip & Twist InFlow Blok

Increase Font Size

using Format Menu

Slide46

Prob 10.30 (14)

Copy & Paste TWICE the SubSys Block into file Prob9_30_Cascade_Tank.mdl

The Cascade Model after the Pastes

Slide47

Prob 10.30 (15)

Use CONSTANT blok to set Atmospheric pressures to ZEROConstant  Generate a constant value Library → Sources The Parameters For CONSTANT Blok

Slide48

Prob 10.30 (16)

Delete Pressure INPORTS and replace w/ Patm = 0

2x Click the SubSys block to expose its contents

COPY the SSR and R Gain-Blok from the SubSys Window

Slide49

Prob 10.30 (17)

PASTE the SSR and R Gain-Blok in Cascade-Tank Mdl

Flip the SSR & Gain BlocksReset the Gain to 1/R1

Slide50

Prob 10.30 (18)

Convert Pb1 to q1 using Cv1 = 1/R1Connect q1 to InFlow Port on Tank2 subsys

Slide51

Prob 10.30 (19)

Now Use STEP block for qmi Step  Generate a step function Library → Sources The Parameters for the step blok

Slide52

Prob 10.30 (20)

Document Heights by MUXing height Outputs to ScopeMUX BlockMux  Combine several input signals into a vector or bus output signal Library → Signal Routing

Scope Block

Scope, Floating Scope, Signal Viewer Scope

Display signals generated during a simulation

Library

→ Sinks

Slide53

Prob 10.30 (21)

InterConnects Completed

Now Need to Edit INSIDE SubSys block for new Variable Names

Slide54

Prob 10.30 (22)

Edit Values in Tank1 SubSys

Slide55

Prob 10.30 (23)

Edit Values in Tank1 SubSys

Slide56

Prob 10.30 (24)

Edit Values in Tank1 SubSysBe Sure to Change the INITIAL CONDITIONSomewhat Hidden in the 1/s block

Slide57

Prob 10.30 (25)

Edit Values in Tank2 SubSys

Slide58

Prob 10.30 (26)

Edit Values in Tank2 SubSys

Slide59

Prob 10.30 (27)

Edit Values in Tank2 SubSysBe Sure to Change the INITIAL CONDITIONSomewhat Hidden in the 1/s block

Slide60

Prob 10.30 (28)

Simulate for 1hr = 3600 seconds

Simulate for 1hr = 3600 seconds

Slide61

Prob 10.30 (29) To WorkSpace

Prob9_30_Cascade_Tank_ToWorkSpace.mdl

Note: SimOut Sends Tank Heights ONLY to WorkSpace

tout

is AutoMatically sent to WorkSpace by SimuLink

Slide62

Test Values to paste into WkSpc

A = 3q_in = .7rho = 1.94h_0 = 4.3g = 32.2R_l = 47R_r = 71

For Model Test

For Cascade Test

A1 = 3; % sq-ftA2 = 5; % sq-ftg = 32.2; %ft/sq-secR1 = 30;R2 = 40;rho = 1.94; % slug/cu-ftq_mi = 0.5; % slug/sech1_0 = 2; % fth2_0 = 5; % ft

P9_30_TankSYS_Model_Input_Parameters_0712.m

Slide63

MALAB 2010 has Built in SSR

Slide64

Tank Model & Test

Slide65

Parameters for q_in on Test

Step Time MUST be Zero

Slide66

Parameters in m-file

% Bruce Mayer, PE

% ENGR25 * 21Nov11

% file = P10_30_Model_Input_Parameters_1111.m

% for use with files

%* Prob10_30_3port_Tank_SubSys_TEST_1111.mdl

%* Prob10_30_Cascade_Tank_1111.mdl

%

%

clc

disp

(

'

SubSys

Test parameters'

)

A =3

q_in

= 0.7

rho = 1.94

h_0 = 4.3

g = 32.2

R_l

= 47

R_r

= 71

disp

(

' '

)

%

disp

(

' '

)

disp

(

' Dual Tank Full-Systems Test Parameters'

)

A1 = 3

A2 = 5

R1 = 30

R2 = 40

rho = 1.94

q_mi

= 0.5

h1_0 = 2

h2_0 = 5

%

% copy-n-paste Plot Statement into Command Window

% plot(

tout,hOFt

),

xlabel

('time (sec)'),

ylabel

('Liquid Height, h (

ft

)'), grid

%

% TRY ALSO:

q_mi

= .45 &

TimeSim

=

1000

Slide67

1304 SubSys Design1304

P10_30_TankModel_SubSys_1304.mdl

Slide68

1304 Subsys Test 1304

P10_30_TankModel_Test_1304.mdl

Slide69

Tank Cascade 1304

Slide70

Final Model

P10_30_2TankSystem_1611.slx

Slide71

P9-30 Notes Pg-1

Slide72

P9-30 Notes Pg-2

Slide73

P9-30 Notes Pg-3

Slide74

Using a Fixxed Step Size

Apr07

No. of Time Pts appears to max out at 1000

Slide75

Cascading Tanks

Slide76

Cascading Tanks

Slide77

Final Model