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Simulate ThermoStatic Control - Computational Methods - Lecture Slides, Slides of Calculus for Engineers

National Institute of Industrial EngineeringCalculus for Engineers

These are the Lecture Slides of Computational Methods which includes Thévenin’s Equivalent Circuit, Circuit Simplification, Analysis of Power Transfer, Voltage Division, Analytical Game Plan, Array Operation, Element Operations, Number of Allowable Values etc.Key important points are: Simulate Thermostatic Control, Sine Wave Function, Math Operations Library, Arbitrary Time, Simulink Model, Configuration Parameters, Engineering Analysis, Integrate to Isolate, Form of Sum, Discontinuities Librar

Typology: Slides

2012/2013

Uploaded on 03/26/2013

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Simulate ThermoStatic Control
•By Engineering Analysis the ODE with
Highest Order Term ISOLATED
( )( )
tTTqR
CRdt
dT
aH
HH
−+= 1
Integrate to Isolate T(t) on LHS
( )
( )( )
dz
CR
zTTqR
dT
t
HH
aH
tT
F∫∫
−+
=
070
( ) ( )( )
dz
CR
zTTqR
FtT
t
HH
aH
∫
−+
=−
0
70
Docsity.com
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Download Simulate ThermoStatic Control - Computational Methods - Lecture Slides and more Slides Calculus for Engineers in PDF only on Docsity!

Simulate ThermoStatic Control

  • By Engineering Analysis the ODE with

Highest Order Term ISOLATED

( qR T T ( ) t )

dt R C

dT

H a H H

 Integrate to Isolate T(t) on LHS

( ) (^) ( ( ))

dz

R C

qR T T z

dT

t

H H

H a

T t

F

∫ ∫

70 0

( )

( ( ))

dz

R C

qR T T z

T t F

t

H H

H a ∫

0

Simulate ThermoStatic Control

  • Note for
    • T(t) appears on BOTH Side of the Eqn → Use FEEDBACk
    • The Integrand is in the form of a SUM

 Also the thermostat in this case has a

2F DEADBAND

  • Implement using SimuLink’s RELAY function

( )

( ( ))

dz

R C

qR T T z

T t F

t

H H

H a ∫

0

Test Large & Small Furnaces

  • The SimuLink Model

T-Stat Scope

simout Plot Ta & T(t) (^1) s IntegratorIC = 70°F

20 R*qm^ Fnce

Temp, Ta^ Ambient

1/RC

Fnce RH (ºF-Hr/BTU)^ q^ max (BTU/Hr)^ Rq*^ max (ºF) Small 0.0389 514 20 Large (^) 0.0389 1028 40

The Output for Small Fnce

(^400 5 10 15 20 25 30 35 40 45 )

45

50

55

60

65

70

75

time (hrs)

Temperature (F)

Prob 9.15, part-a  Note

  • Small Fnce canNOT keep up with heating load when Ta drops below about 55F
  • 2 Hour Time-Lag as predicted by

Hr

F

BTU BTU Hr

R C F H H

  1. 0

1

  1. 4 1

  2. 0389

=

= × 

plot(tout,tout,simout(:,2)), simout(:,1), xlabel('time (hrs)'),...ylabel('Temperature (F)'), title('Prob 9.15, part-a')

Result for Large Fnce

  • The Large Furnace CAN Keep Up with Heat load at coldest Outside Temps

(^400 5 10 15 20 25 30 35 40 45 )

45

50

55

60

65

70

75

time (hrs)

Temperature (F)

Prob 9.15, part-a - Lg Fnce  The RH *q (^) max Product indicates the MAXIMUM Temp Difference that the Furnace+Insulation combination can accommodate  In This case (T-Ta ) (^) min = 70F – (50-10)F = 30F

  • The Small Fnce is Overwhelmed

High Power Fnce

(^400 5 10 15 20 25 30 35 40 45 )

45

50

55

60

65

70

75

time (hrs)

Temperature (F)

Prob 9.15, part-a - Lg Fnce

The Part-b SimuLink Model

1028 qm

(^1) s Energy^ Total

T-Stat

1/1e Scale Outputto Therms

R^ simout Plot Ta & T(t)

(^1) s IntegratorIC = 70°F

DeBugScope

Temp, Ta^ Ambient

1/RC

 Note the Output scaling to “PG&E” Units

  • 1 “Therm” = 100 kBTU

Energy Use

  • Small Fnce (^)  Large Fnce

(^00 4 8 12 16 20 )

time (hrs)

Cumulative Energy Use (Therms)

Prob 9.15, part-b, Lg Fnce

(^00 4 8 12 16 20 )

0.14 Prob 9.15, part-b, Sml Fnce

time (hrs)

Cumulative Energy Use (Therms)

St-Line → Fnce On 100% of time

 Fewer Therms, but Cold Inside

 Note Differing Slopes Before & After ~11hr

Prob_9_15a.mdl (2)

1/RC

Prob_9_15a.mdl (3)

s

Integrator

IC = 70°F

Prob_9_15a.mdl (5) simout

Plot Ta & T(t)

Part-a Configuration Parameters

Prob_9_15b.mdl (2)

514

qm

R

Prob_9_15b.mdl (3)

1/1e

Scale Output to Therms

1 s Total Energy