Is designing a machine to measure transfer functions a feasible senior project?

[leright]

I am taking a control class right now, which I find quite interesting. I had an idea for a senior project where I'd design and build a machine that allows one to hook up a motor and it will compute the torque/voltage transfer function or the angular speed/voltage transfer function of an electromechanical system.

I would design the machine to input a unit impulse voltage to the system and the machine would measure torque response or angular speed response. This response would then be fit to an equation and a computer algorithm would determine the laplace transform. The laplace transform of the unit impulse response would of course be transfer function.

Has this been done? Is this too simple of a project? Too hard? Not interesting enough? Any comments?

 

[leright]

anyone have an opinion?

 

[leright]

No comments? Surprising.

 

[LeBrad]

I am taking a control class right now, which I find quite interesting. I had an idea for a senior project where I'd design and build a machine that allows one to hook up a motor and it will compute the torque/voltage transfer function or the angular speed/voltage transfer function of an electromechanical system.

I would design the machine to input a unit impulse voltage to the system and the machine would measure torque response or angular speed response. This response would then be fit to an equation and a computer algorithm would determine the laplace transform. The laplace transform of the unit impulse response would of course be transfer function.

Has this been done? Is this too simple of a project? Too hard? Not interesting enough? Any comments?

It's hard to comment on the hardness and interestingness of the idea without knowing more about the level of your class.

So you're saying you want to take some physical system, give it an impulse as an input, and then measure the output which would be the impulse response h(t). Then you're going to transform that into H(s). That sounds like it will work.

Do you have to actually implement this? Is this just a thought experiment or is it actually supposed to be something practical? I ask that because it seems like it would be a lot simpler to measure H(s) directly if that's what you're after, but if you're just trying to demonstrate system relationships, then your way is better. Are you assuming it's difficult to compute H(s) analytically based on your system? Are you trying to predict H(s) with experiment or verify a hand-computed H(s) with experiment? It seems like this type of thing would be more useful for extremely complicated systems where the transfer function is not obvious.

The only thing I would worry about if you actually have to implement it is that error in h(t) would be magnified/distorted in H(s). For example if you have some noise in h(t) to make it appear a little jumpy, you will end up with a lot of high frequency junk in H(s). But I guess you can always measure H(s) and compare.

 

[leright]

It's hard to comment on the hardness and interestingness of the idea without knowing more about the level of your class.

So you're saying you want to take some physical system, give it an impulse as an input, and then measure the output which would be the impulse response h(t). Then you're going to transform that into H(s). That sounds like it will work.

Do you have to actually implement this? Is this just a thought experiment or is it actually supposed to be something practical? I ask that because it seems like it would be a lot simpler to measure H(s) directly if that's what you're after, but if you're just trying to demonstrate system relationships, then your way is better. Are you assuming it's difficult to compute H(s) analytically based on your system? Are you trying to predict H(s) with experiment or verify a hand-computed H(s) with experiment? It seems like this type of thing would be more useful for extremely complicated systems where the transfer function is not obvious.

The only thing I would worry about if you actually have to implement it is that error in h(t) would be magnified/distorted in H(s). For example if you have some noise in h(t) to make it appear a little jumpy, you will end up with a lot of high frequency junk in H(s). But I guess you can always measure H(s) and compare.

No, this must be fully designed and it must be a working prototype. If it were just a thought experiment it would be rather trivial.

Ans I hope to be able to measure the transfer functions of many mechanical systems (beyond motors) where the analysis is not obvious. I want an accurate way to determine transfer functions of mechanical systems where analytically they cannot easily be determined, or maybe even not at all.

The biggest part of this project, imo, would be designing a means of measuring h(t) very accurately, so when I fit the response to a function with a computer algorithm these oscillations don't show up...however, I am thinking that when I fit the response to a function the accuracy of the curve fitting will not be high enough to detect low level oscillations anyways.

 

[LeBrad]

Ans I hope to be able to measure the transfer functions of many mechanical systems (beyond motors) where the analysis is not obvious. I want an accurate way to determine transfer functions of mechanical systems where analytically they cannot easily be determined, or maybe even not at all.

The biggest part of this project, imo, would be designing a means of measuring h(t) very accurately, so when I fit the response to a function with a computer algorithm these oscillations don't show up...however, I am thinking that when I fit the response to a function the accuracy of the curve fitting will not be high enough to detect low level oscillations anyways.

Ok, I missed the part about fitting h(t) to a curve the first time. What kind of setup are you going to use for this? I think the most important thing to get an accurate h(t) is to generate a good impulse.

If you just want to find H(s), since you know y(t) = H(s)u(t) for sinusoidal inputs, why not just use a sinusoid for the input with amplitude=1 and sweep the frequency while measuring the amplitude of the output, which would be H(s)?

 

[rbj]

i understand how you might measure the input voltage and current of the moter and i have an idea for how you might measure angular position from which angular velocity and acceleration might be derived. how are you planning to directly measure torque? are you indirectly going to do it by knowing the mass or moment of inertia of what gets attached to the motor shaft and then derive the torque from the angular acceleration? you still won't know the torque due to friction/resistance.

 

[leright]

i understand how you might measure the input voltage and current of the moter and i have an idea for how you might measure angular position from which angular velocity and acceleration might be derived. how are you planning to directly measure torque? are you indirectly going to do it by knowing the mass or moment of inertia of what gets attached to the motor shaft and then derive the torque from the angular acceleration? you still won't know the torque due to friction/resistance.

I was considering using a torque transducer to measure torque. However, I suppose I could determine the torque by knowing the angular acceleration, but I may not always know what the moment of inertia is for the machine I am attaching. The point of this device is to allow engineers to determine the transfer functions of various devices with little to no information about the device's characteristics.

 

[leright]

Ok, I missed the part about fitting h(t) to a curve the first time. What kind of setup are you going to use for this? I think the most important thing to get an accurate h(t) is to generate a good impulse.

If you just want to find H(s), since you know y(t) = H(s)u(t) for sinusoidal inputs, why not just use a sinusoid for the input with amplitude=1 and sweep the frequency while measuring the amplitude of the output, which would be H(s)?

It would be simpler if I could just generate a good impulse. That way I wouldn't need to sweep a bunch of frequencies. It seems that this way would be a bit quicker. Regardless of the technique I use, I will need to program an embedded system of some sort that would run this procedure and then collect data that could be sent back to the computer as a MATLAB file. At that point, I could just write a MATLAB algorithm that could take it from there.