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Engr/Math/Physics 25
Problem 9.15Solution
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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Simulate ThermoStatic Control

• By Engineering Analysis the ODE with Highest
  Order Term ISOLATED

• Integrate to Isolate T(t) on LHS

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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 SimuLinks RELAY function

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The Part-a SimuLink Model

• RELAY ? Discontinuities Library
• MUX ? Commonly Used Blocks Library

• SINE WAVE FUNCTION ? Math Operations Library
• TO WORKSPACE (simout)? Sinks Library

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Test Large Small Furnaces

• The SimuLink Model

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The Output for Small Fnce

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

plot(tout, simout(,1), tout,simout(,2)),
xlabel('time (hrs)'),... ylabel('Temperature
(F)'), title('Prob 9.15, part-a')
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Low Power Fnce
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Result for Large Fnce

• The RHqmax Product indicates the MAXIMUM Temp
  Difference that the FurnaceInsulation
  combination can accommodate
• In This case (T-Ta)min 70F (50-10)F 30F
• The Small Fnce is Overwhelmed

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

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High Power Fnce
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Part b Daily Energy Use

• To Determine Daily Energy Use, E, Need to
  time-integrate the fnce Power Output over 24hrs

• For an Arbitrary time

• Refine the Part-a model to
• Gain Access to qmax alone
• Use the integrator Block to find E

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The Part-b SimuLink Model

• Note the Output scaling to PGE Units
• 1 Therm 100 kBTU

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Energy Use

• Small Fnce

• Large Fnce

St-Line ? Fnce On 100 of time

• Note Differing Slopes Before After 11hr

• Fewer Therms, but Cold Inside

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Engr/Math/Physics 25
AppendixModel Construction
Bruce Mayer, PE Licensed Electrical Mechanical
EngineerBMayer_at_ChabotCollege.edu
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Prob_9_15a.mdl (1)
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Prob_9_15a.mdl (2)
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Prob_9_15a.mdl (3)
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Prob_9_15a.mdl(4)
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Prob_9_15a.mdl (5)
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Part-a Configuration Parameters
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Prob_9_15b.mdl (1)

• Non GREEN Blocks are the same as in part-a

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Prob_9_15b.mdl (2)
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Prob_9_15b.mdl (3)
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Part-b Configuration Parameters