Solving a Problem with LPHW Radiator

[jami8337]

I am trying to solve a problem regarding an LPHW radiator, of which the heat output is controlled by adjusting the LPHW flow rate. The relationship between the flow rate and the radiator output can be approximated by a first order transfer function with a time constant of 1 minute. The heat output is adjusted by a control signal directed to a final control device that determines the LPHW flow rate.

I now need to draw two open loop block diagrams The first showing the relationship between the control signal and the radiator heat output. The second of the relationship between the heat output and the room temperature.

I am at a loss on what to do for the first diagram, however it may just be me overthinking it. Would it simply be:

i ----> Controller -----> LPHW Valve -------> Heat Output

Any insight would be greatly appreciated

Thanks

 

[CWatters]

I think you probably need to add a block showing the first order transfer function. Something like..

I---> Controller -> LPHW Valve --> LPHW Flow rate ---> Transfer function ----> Heat Output

Replace "Transfer function" with the actual equation.

Not sure how to do the second one. I'm familiar with steady state heat loss calculations (you need thing like the thermal resistance of the walls and the temperature gradient across them) but your question suggest a dynamic situation (for which you probably need information on the thermal mass?).

Sorry that's the best I can manage.

 

[jami8337]

Thanks for your help, I think i can draw both the block diagrams, but I am hitting a wall when having to derive the transfer function for the first one. This would be based on the energy balance equation i believe, but i am a bit lost trying to derive that. I have come up with:

(T_W-T_i)/R

Where T_w is the temperature of the LPHW, and T_i is the room temp...

 

[jami8337]

Okay here is what i have come up with:

Temperature LPHW = θ_L
Temperature Output = θ_O
Heat Flow rate = Q

Q=(θ_L-θ_O)/R

Assuming no losses. The heat transferred from the LPHW alone determines the 'Radiator output' to the room. Therefore the rate of heat transfer will determine the rate of change of the radiator output, hence:

dθ_O/dt = Q/C (C = Capacitance)

Then:

dθ_O/dt = (θ_L-θ_O)/RC

I can then rearrange this and take a laplace transform to give me the transfer function. Does this sound like the right sort of track to be on?

Thanks!

 

[CWatters]

Sorry it's been a long time since I did any control theory but I found..

http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc-2011/data/papers/1806.pdf

See bottom of page 4408 which has..

"The relationship between room air temperature and radiator output heat can be well approximated by a 1st order transfer function..."

and gives the transfer function.

 

[Ashique]

Whats up? Any further news regarding these efforts?