How to model a servo motor transfer function

2022 3 24
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Hello! So I got into this university project on an Acrome 2D Ball-Balancing (Ball and Plate system). The servos are linked through and Arduino to the computer. I have as an input the voltage of the ball with respect to the x axis and y axis. We, as a team, are actually trying to estimate the servo transfer function. We have got a couple of measurements to start with, in particular: the angular position in radians of the servo motor at a correspondent voltage. The servo motor model is a Hitec 5485HB RC Servo Motor. Thank you in advance for any help :)

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Sam Chak
Sam Chak 2022-3-24

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Hi @Mario Malizia
If your lab has the System Identification Toolbox, it can be used for constructing or estimating the transfer function of the servomotor from the measured input-output data.
https://www.mathworks.com/products/sysid.html
Read the paper: Virtual Torque Sensor for Low-Cost RC Servo Motors Based on Dynamic System Identification Utilizing Parametric Constraints
https://www.researchgate.net/publication/328910852_Virtual_Torque_Sensor_for_Low-Cost_RC_Servo_Motors_Based_on_Dynamic_System_Identification_Utilizing_Parametric_Constraints
Else, find the relevant codes on FileExchange that do not requires the System Identification Toolbox. For example:
https://www.mathworks.com/matlabcentral/fileexchange/32365-system-identification

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Mario Malizia
Mario Malizia 2022-3-26
Thank you very much for your answer.
We imported a dataset with iddata with a 1800ish input/output measurements and we were able to estimate the transfer function V(s) [Volt applied to the servo] -> Theta(s) [angular position of the servo]
Sam Chak
Sam Chak 2022-3-26
Hey @Mario Malizia
Good to know that it helped. 👍
Mario Malizia
Mario Malizia 2022-3-31
I am sorry, I got another question.
The model identification app in MatLab was very helpful, the data was measured in this way:
V(S) (input), we manually collected all the voltages given in input by a potentiometer (letting it variate) and THETA(S) as an output (angular position of the motor in rad).
We got a 1800ish datas in vector with Sampling time 0.01s and obtained a transfer function of grade 1 (1pole/no zero) with a fitting of 97.4%.
The professor however told us that the measured we have obtained was not accurate due to the fact that the system is not excited.
We hence re-executed the measurements with a sine-sweep excitation of the system and we obtained again a 2000ish data for input/output and placed it into a model.
We are having troubles though, to evaluate a new transfer function (obtaining poor results such as 27.4%ish).
Do you know how we can properly evaluate a transfer function starting from this?
Thank you very much in advance.
Sam Chak
Sam Chak 2022-4-1
Hi @Mario Malizia
Technically, the transfer function of a servomotor is given by
.
but because , the transfer function is usually approximated as a 2nd-order system to describe process behavior. Perhaps, try identifying from the sine-sweep input/output data using a 2nd-order model (a process model with 1 pole and an integrator).
https://www.mathworks.com/help/ident/ug/building-and-estimating-process-models-using-system-identification-toolbox.html
https://www.mathworks.com/help/ident/ref/idproc.html
For more details, pleasel check:
https://www.mathworks.com/products/sysid.html#app

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