Transfer equation of a Voice coil motor for dissertation

[rude man]

Where does the refrence input (x_ref) come from? Is this what measures surface irregularities?

 

[deamonata]

the desired height comes from a modified hertzian contact theory essentially the person pressed down on a force sensor and this is converted into the desired height, this happens before the controller so it shouldn't make too much difference to the system.

 

[rude man]

See next post ...

 

[rude man]

OK, here's my understanding of your system. Itobviously doesn't include the digital interface but you should be able to associate all my variables with your system.

 

[rude man]

OK, one more time ...

 

[deamonata]

I will try this in a MATLAB simulation tomorrow and get back to you but it looks sensible, one question though? what is V_offset?

 

[rude man]

I will try this in a MATLAB simulation tomorrow and get back to you but it looks sensible, one question though? what is V_offset?

It's the "30" in $v(t)=2.5x(t)+30$[/QUOTE]

 

[deamonata]

Ok so update. I have now got the system successfully modeled. and the response matches the physical devicemThe model is shown below:

YOu may notice it is slightly different to what you suggested but, I think that is probably because of misunderstandings, due to my trying to explain the system over the internet. However you put me on the right tracks to understand how to include gravity.

I'm now trying to design a lead lag compensator, my tutor advised that as the gain for V is 400 and the gain for the disturbance is 0.129, the effects are negligible, and as such for the purposes of designing a controller it can be ignored.

however following the normal steps, (using the bode plot) improves the response but doesn't get rid of the steady state error, matlab's auto tuner can remove it how ever so it must be possible. any thoughts?

EDIT: Note the controller is not shown in the system model as I was comparing the response. to the system response without a controller.

 

[rude man]

Ok so update. I have now got the system successfully modeled. and the response matches the physical devicemThe model is shown below:

.

One problem is the output of block Fcn3. You have a constant input into a gain block that has infinite gain at dc. So the output of that block never stabilizes but goes out to infinity.

It's been a while since I worked this problem with you & I fear I have lost touch with the basic functioning of your system. Maybe you could re-describe it. I don't mean equations etc. just the basic thing you're trying to accomplish with the entire system, including how gravity fits into the picture. How about something in writing you were given as an assignment? I think I understand your voice-coil transfer function but the rest of the picture is still fuzzy to me. E.g. I just noticed mention of a force sensor. How does it fit into the picture?

You should try to draw a new block diagram showing the main components and describing what each is supposed to do. Leave out any math.

 

[iawia]

Just a quick comment on Voice Coil Transfer Function

Hi,

I know this post is super old, but I read through it and it did not seem like anyone really answered it. This is for anyone else who is still interested.

You can not apply the Laplace Transform to non-linear equations like yours which include gravity. For a system to be linear, it must follow the principles of homogeneity and additivity. The equations containing gravity violate the homogeneity.

However, since the gravitational effects are constant, they can be removed from the equation and the system can still be characterized by a transfer function. (think of this situation as if the voice coil was fixed in outer space far away from any gravitational fields, the system would still behave the same with the only difference being that the initial conditions will be zero).

If you are looking for voice coil displacement/input, ie Xvc/Vin, I have solved it for you here:

Xv/Vin = (Bl/mvL)/(s(s^2+R/L*s + Bl*Kb/mvL))
where B = magnetic flux, l = length of wire used to form the coil, mv = mass of the voice coil assembly that will move, L = inductance, & Kb = back EMF motor constant.

It is a third order equation but you can break it up into the standard form by equating the R/L = 2ζ*ω and ω^2 = BlKb/mv*L

Hence, the damping ratio ζ = R/2Lω or (R/2L)*(mvL/Bl*Kb)^1/2 and the natural frequency ω^2 = Bl*Kb/mvL

(sorry first time using this forum and have not used the math scripts yet)

If you still want to include gravity, matlab's Simulink can handle it quite well as I sure you already know. All that is required are the correct force dynamic equations of motion, then include -mv*g as one of the forces.