transfer function

[hamshie.k@gmail.com]

i need a help to obtain transfer function for a tank, where a heater is placed. the liquid temperature should be maintained at 45C . no inlet or out let. how to obtain the transfer function?? for analysisng about the controller?

 

[hamshie.k@gmail.com]

please guide me soon

 

[Jugurtha]

Hello,

I'm working on something similar, but with a Bang-Bang control. i.e : Two thresholds, heater fully on until high threshold is reached, turn off heater, liquid cools off until temperature hits a low threshold, then turn heater fully on, etc...

Either this, or if you need to maintain it exactly at 45 °C, you can look up PID control or something like that.

PS: Do not forget to circulate the fluid so that your temperature reading is more pertinent.

 

[misterT]

Here is some help:
**broken link removed**

 

[MrAl]

Hi,

A simple way to look at this is to use the electrical analog. The tank is just an RC low pass filter excited by the heating element temperature. Replace the RC time constant with the thermal time constant, replace the drive voltage with the hot temperature of the heating element. The tank temperature is the value of the 'voltage' across the 'capacitance'.

The RC low pass filter is:
E1=E0/(s*R*C+1)

replacing RC with the electrical time constant tau:
E1=E0/(s*tau+1)

Now replacing E0 with T0 and E1 with T1:
T1=T0/(s*Tau+1)

where
T0 is the hot temperature of the heating element,
T1 is the temperature of the tank,
Tau is the thermal time constant of the tank.

To find Tau you can measure the temperature of the tank at t0, turn on the heating element, then measure the temperature of the tank at t1. With t0=0 and when the temperature of the tank reaches 63.2 percent of the max temperature that is one time constant the value of Tau.

If you prefer, you can use:
E*(1-e^(-t/Tau))

and fit two or three or more temperature measurements to this curve which will provide a value for Tau:
T1=T0*(1-e^(-t/Tau))

This assumes that the ambient temperature is relatively stable and that the measured temperature in the tank represents the temperature everywhere in the tank.

A better model yet is:
E1=E0*A*(1-e^(-t/(Tau)))

with transfer function:
E0*A/(s*Tau+1)

The extra variable comes from the fact that the tank cools by a different thermal resistance than it heats by.

Of course all of the above assumes a first order system where the tank thermal time constant dominates the system response. If you have a very small tank this may not be true and you'd need to consider a second order system where the time constant of the heating element also has to be taken into account.



In the past i have used the bang bang method too where you use two temperature settings, one to turn on and one to turn off. It works pretty well really.

 

[crutschow]

You need the mass of the water in the tank, the heat loss from the tank versus the delta temperature from the tank to ambient , and the heater power to determine the transfer function (rate of temperature rise per unit time versus ambient temperature).

 

[hamshie.k@gmail.com]

whether this transfer function could be obtained for setpoint temperature and actual value of temperature. i have the values of mass and heater power. how to relate it? i have to get the transfer function for analysisng the controllers

 

[cachehiker]

I need to consult notes that are unfortunately not here at my workplace (getting paid for thermodynamics doesn't happen often) but if I recall correctly you will end up with:

dT/dt = CP - K(T- ambient) where P is the power being supplied to the heating element and C and K are constants that can be calculated using a thermometer and stopwatch. Raise the tank temperature to 45°C, shut off the power, and measure how long it takes to lose 63.2% of its temperature rise, and you will have K. Apply a fixed amount of power to the element, measure how long it takes to attain 63.2% of it eventual, stabilized, temperature rise and you will have C.

You can also calculate K from the mass of the water and the thermal resistance of the tank walls, but I would trust real world measurements over theoretical calculations for real world predictions. The same goes for C.

 

[MrAl]

Hi,

You can get the heat capacity for the water and so the mass would help there, but remember it is not constant for water.

 

[hamshie.k@gmail.com]

Heating coil is placed inside the water. Btw how to obtain resistance. since it is water capacitance is 4200 ryt??

 

[hamshie.k@gmail.com]

could u please suggest a theoretical method

 

[hamshie.k@gmail.com]

can u suggest me a link for further refference

 

[hamshie.k@gmail.com]

Actually the system is like this. a tank is placed inside another tank. consider outer tank as A and inner as B. the heating coil is placed inside tank B, for the purpose of heat distribution in the liquid inside tank A. tank A has inlets and outlet.
but tank B water level is stationary no inflow or out flow. assume there wont be a mass loss as vapour.
the required temp in outer tank A is 40 C. so i have build the relationship and obtain transfer function.

please guide me . plzzzzzz

 

[MrAl]

Hello,


This sounds like it might be a different problem other than just a tank and a heater. If you have water flowing into the tank that changes it a little. I think you should draw a diagram of the entire system so we know what is really supposed to be happening here.

 

[hamshie.k@gmail.com]

View attachment 65161View attachment 65162

 

[hamshie.k@gmail.com]

yes the heater is placed inside the tank with dotted lines

 

[MrAl]

Hi,


Nice drawing.
What is that rectangular thing near the upper left corner?
What is the small rectangular thing between the pump and outer tank just above the word "Wood" ?
What is the pump doing? If it is moving fluid, where is the fluid moving from and to?
I guess the "Wood" holds the pump?

It looks like the "Motor" spins the mixer in the outer tank.

 

[cachehiker]

could u please suggest a theoretical method

I suppose I could dig into my textbooks to construct a theoretical model taking convected, radiated, and conducted heat flow into account along with the thermal resistivity, surface area, and fluid flow of all the materials involved. Depending on how many simplifications I make, it will take anywhere from a few hours to a few days to construct and take anywhere from a few paragraphs to a few pages to explain.

And in the end, it will only be close, give or take maybe 20% or maybe even 40%.

Actual tests would still be necessary to refine the model to within a few percent.

At that point the model would probably prove useful for accurately predicting the effect of potentially expensive or time consuming changes in tank sizes, materials, and fluid flow. Without the need for accurately predicting the effect of such changes though, the time spent constructing a theoretical model would be better spent performing a few tests.