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# Thermal system input output and DC gain

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#### urnuj

##### Junior Member level 3
Hi

The output for my thermal system is the temperature(degree celcius), while the input to the system is power(watt). I set up this control system, and I am now confused while trying to find the DC gain of the system as it is not the same DC for different value of input into the system.

Is this because I am using a wrong input as it does not match the unit of the output?

What about thermal conductance, ,mass and thermal resistance of insulation and ambient?

JR,
The thermal losses will increase with the temperature above ambient, so you cannot expect the temperature to increase directly proportional to the input power.

urnuj

### urnuj

Points: 2
I see, so its normal the dc gains changes with a different value of step input that I use?

Yes thermal conductance, resistance, heat capacity has been considered and accounted in the equation.

What I am wondering is the a different value of dc gains from the experiment as I increased the value of the step input for each experiment.

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yes i understand that it will not be a linear straight line relationship. But I am comparing the DC gain of different input strength, the steady state gain.

If this is a PID control loop that you are tuning, you need to try a step changes within the normal control range.

The overall dc gain will not be linear over a very wide range, but the system when it is running, may see a fairly constant control conditions.

Cold start up may be the most extreme condition it ever sees.
But once it is going, and it settles down, and you can tune for optimum fast stable response under normal running conditions.

I understand that you are asking about the transfer function of the heater control.

If the PID controller output ("manipulated value") is translated to a proportional heater voltage or current, you get a nonlinear (quadratic) characteristic due to P = V²/R, resulting in an unwanted gain variation.

Most heater controllers are however setting the heater duty cycle which refers to a linear characteristic.

Hi

So I can define the output i want for my system according to my own equation?
And set the control gains and parameter from there?

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The setting of the heater duty cycle refers to varying the voltage being supplied to the heater is that correct?

It depends if the heater control is on/off or if the voltage is modulated.

If its on/off then the power is proportional to the duty cycle as FvM has just stated.

If the voltage is varied up and down, the resulting power will be a non linear function .

I see.
So by using power as the input and output as measured temperature, it would have a linear relationship?

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