ndzied1
Lifetime Supporting Member
Peter Nachtwey said:In closed loop the temperature will always go between two temperatures in the same amount of time except..... when?
The output saturates?
Peter Nachtwey said:In closed loop the temperature will always go between two temperatures in the same amount of time except..... when?
Specifically the gain and time constants. In the temperature example one knows approximately the steady state value of the temperature by mulitplying the output by the gain. However, the time constants play a big part which is why your suggestion below is so important. If the time constants are very small then the temperature will almost instantly reach the steady state temperature which results in a high rate of temperature change even if the change in set point is small.kamenges said:The true PV rate of change limit is governed by the plant
Yes.kamenges said:Artificially limiting the output simply decreases the upper limit to the PV rate of change, which is probably what you don't want to do.
Agree. That how it is done in motion control.kamenges said:It would seem more reasonable to me to limit the rate of change of the command to stay inside of the achievable rate of change of the PV. Then you can use feed forwards effectively.
Peter Nachtwey said:Tom,
The transfer function for a simple temperature system is:
G*exp(-s*d*T)/(tau1*s+1)*(tau2*s+1)
G is the gain in degrees per percent output.
tau1 is the time constant of the thermal mass
tau2 is the time constant of the temperature sensor.
T is the update time.
d is the number of update periods of dead time.
There could be a third time constant if the heater takes time to heat up to radiate heat.
The equation for this is:
Temp1 = exp(-T/tau1)* Temp1(n-1) + G*(1-exp(-T/tau1))*Control%(n-d) + Ambient temp.
Temp2 = exp(-T/tau2)*Temp2(n-1) + ( 1-exp(-T/tau2))*Temp1(n-1)
Where Temp2 is the resulting temperature as a function of the control output percentage. This implements a simple temperature with a gain ( G), deadtime ( d*T ), and two low pass filters using tau1 and tau2. Run some simulations using excel. I did this off the top of my head since I don't have access to my Mathcad right now.
I did this on the Hotrod.zip in the download area and on my ftp site.
ftp://ftp.deltamotion.com/public/PDF/Mathcad%20-%20TempPID.pdf
Tom Jenkins said:It is implicitly assumed that the energy transfer is a first order system in developing the model of the transfer function. Then the transfer function is being used to prove that the energy transfer is first order!
Peter Nachtwey said:Tom, you should post a link to your model so others can see. I still have it.