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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

Engr/Math/Physics 25. Problem 9.15 Solution. Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Simulate ThermoStatic Control. By Engineering Analysis the ODE with Highest Order Term ISOLATED. Integrate to Isolate T(t) on LHS. Simulate ThermoStatic Control.

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Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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  1. Engr/Math/Physics 25 Problem 9.15Solution Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  2. Simulate ThermoStatic Control • By Engineering Analysis the ODE with Highest Order Term ISOLATED • Integrate to Isolate T(t) on LHS

  3. 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

  4. The Part-a SimuLink Model • RELAY → Discontinuities Library • MUX → Commonly Used Blocks Library • SINE WAVE FUNCTION → Math Operations Library • TO WORKSPACE (simout)→ Sinks Library

  5. Test Large & Small Furnaces • The SimuLink Model

  6. 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')

  7. Low Power Fnce

  8. The Large Furnace CAN Keep Up with Heat load at coldest Outside Temps Result for Large Fnce • The RH*qmax 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

  9. High Power Fnce

  10. To Determine Daily Energy Use, E, Need to time-integrate the fnce Power Output over 24hrs Part b – Daily Energy Use • For an Arbitrary time • Refine the Part-a model to • Gain Access to qmax alone • Use the integrator Block to find E

  11. The Part-b SimuLink Model • Note the Output scaling to “PG&E” Units • 1 “Therm” = 100 kBTU

  12. Small Fnce Energy Use • Large Fnce St-Line → Fnce On 100% of time • Note Differing Slopes Before & After ~11hr • Fewer Therms, but Cold Inside

  13. Engr/Math/Physics 25 AppendixModel Construction Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

  14. Prob_9_15a.mdl (1)

  15. Prob_9_15a.mdl (2)

  16. Prob_9_15a.mdl (3)

  17. Prob_9_15a.mdl(4)

  18. Prob_9_15a.mdl (5)

  19. Part-a Configuration Parameters

  20. Prob_9_15b.mdl (1) • Non GREEN Blocks are the same as in part-a

  21. Prob_9_15b.mdl (2)

  22. Prob_9_15b.mdl (3)

  23. Part-b Configuration Parameters

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