Hey people!

I have a set of questions which I want to complete and understand, they are shown below. All of these questions are relevant to the image of a control system I have attached which is a simulink schematic in matlab. I am essentially trying to estimate a transfer function for a ac/dc motor which is labeled in the image.



A sine and step input can be applied, as shown in the image.

questions:

1. Work out the DC gain of the motor velocity output (use a unit step input);
2. The noise amplitude on the velocity output.
3. Identify the gain of the system at a few different frequencies.
4. Using yoour knowledge of Bode plots, and the DC gain that you measured earlier, to generate a transfer function of this input/output relationship, Ω(s)/V(s)





Above shows a sine response to the motor at a frequency of 1 rad/sec, and a unit step response to the system. This shows a plot of the velocity output ω(t) and the input v(t) which is the yellow line.

From the step response data I calculate the DC gain to be 9.54dB? 20log(3)? I think?

As you can see the output is very noisy, which when when a sinusoidal input is applied and the frequency varied, the higher frequencies become impossible to take any accurate gain measurements, the max readable frequency = 10 rads/s or 1.59hz. So generating a bode plot becomes impossible? Are these measurements alone enough to identify a transfer function?

This is where I become suck. I do not know how to derive the transfer function for the motor with the data I can read accurately. I would know If I had a bode plot! But I cannot get enough frequency measurements for a bode plot.

So how do I come up with this transfer function? Is it possible to identify the system by examining the step response alone, but the question states to use my knowledge of bode plots? I'm stumped! Some guidance please?

Regards,

Mitch



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You appear to show only the step input response and not the sinusoidal input response.

 

Hey thanks for your reply, I have now put up a sine response at a frequency of 1 rad/s.

 

Any body any ideas?

 

You indicate you could proceed with your analysis if you had a Bode plot. Why do you think you can't extract a bode plot? Presumably you can plot the output response vs the sinusoidal input signal in terms of both magnitude and phase. Looking at the output response at 1rad/sec you appear to have nearly 90° phase shift which would possibly indicate something to you in terms of where the transfer function pole (or poles) lie on the frequency axis.

A typical approach in the absence of a known transfer function is to assume the system can be modeled as a first order lag plus pure dead time. Are you familiar with this concept?