# Estimating transfer function of a system with input and output values as well as kp and ki values

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Keaton Looper on 16 Nov 2023
Commented: William Rose on 1 Dec 2023
I am trying to estimate the transfer function of a heat transfer system I am studying. I have the input voltage value and the output corresponding voltage for the temperature sensor. I am using set Kp and Ki values for the system. Is there a way for matlab to calculate the transfer function based and the input, output, and kp and ki values?
Sam Chak on 22 Nov 2023
Based on your description of the Thermal System, I think that the block configuration looks as shown in the image below. To make it easier for @William Rose to guide you in identifying the Thermal System, can you provide the data of Control Voltage in Scope 1 (Vc) and the Output Voltage in Scope 2 (Vo)? I presume that the values for Kp and Ki are fixed.
Terminology:
• Tr = Reference temperature
• Vr = Reference voltage
• Ve = Error voltage
• Vc = Control voltage (measured input)
• Vo = Output voltage (measured output)
• u = Heat from the heating element (energy supplied to the thermal system)
• y = Output temperature of the thermal system

William Rose on 16 Nov 2023
Yes you can.
You can estimate the overall transfer function from Vin(t) to Vout(t) by using tfestimate(), if you have the signal processing toolbox. If you don't have that toolbox, then compute the Fourier transforms of Vin and Vout. Then compute complex ratio Vout(f)/Vin(f) at each frequency. This the (estimate of) the overall transfer function.
Since you mention kp and ki, you must referring to a negative feedback control system. Maybe you want to estimate the open loop transfer function. Let's call it G(f). The overall transfer function which you computed above is .
You know H(f), right? It is, therefore . So you use the known H(f) and the estimated , and you solve for G(f). That leaves a little for you to work out on your own. Good luck!
Keaton Looper on 30 Nov 2023
i am tyring to graph the data and the estimates but i am unable to get it to graph based on the new Tsim2 function
William Rose on 1 Dec 2023
Keaton, can you share what you tried that didn’t work? Thanks. I am traveling and don’t have a computer with Matlab.

William Rose on 24 Nov 2023
Keaton, what do you get if you analyze the new data with code used to analyze the earlier data? What differences between the transfer functions of the old and new data stand out to you?

Branko on 24 Nov 2023
I am also a student and would like to simulate a heating system with a heat pump.
The heat pump is controlled as on/off or by adjusting the inflow curve from -5 C to 5 C.
Thank you.
Regards,
Branko