How to model a servo motor transfer function

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 :)

Answer 1

[Sam Chak]

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

[Mario Malizia]

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]

Hey @Mario Malizia

Good to know that it helped. 👍

[Mario Malizia]

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]

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