type2 servo 1

[kishoregv]

Trying to understand the importance of type2 servo. I read in books that to get zero velocity lag, type2 system is suitable. I have difficulty understanding this concept intutively, while mathematically I am clear. A type 2 has two poles at origin. This means, double integeration. A ramp input integerated twice gives an expression to the power of 3. How does it all work.

 

[xnuke]

This is known as the internal model principle. If you want to have zero steady-state error to a given input signal, the negative feedback loop must possess a model of that signal within the blocks inside it. In this case, to perfectly track a ramp input, which has two poles at the origin, there needs to be two poles at the origin in the transfer functions of the blocks in the loop.

To get zero steady-state error to a ramp input (assuming a sensor with no poles), if the system transfer function already has a pole at the origin, the controller would have to provide one. If the system transfer function has no poles, the controller would have to provide both.

To get zero steady-state error to a step input, which has a single pole at the origin, the loop must have a single pole at the origin inside it, which explains why PI or PID controllers can perfectly track step inputs for many systems. The integrator in the controller adds the pole at the origin those system transfer functions lack.

The internal model principle explains why, for most systems, a PID can't perfectly track a sine wave - there's no model of the sine wave in the feedback loop. This lead to the development of proportional-resonant controllers, which have a sinusoid model in the controller, for control of power electronic inverters tracking power grid sine waves (though other control methods have since replaced PR).

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
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[kishoregv]

"In this case, to perfectly track a ramp input, which has two poles at the origin, there needs to be two poles at the origin in the transfer functions of the blocks in the loop"

Got it. I tried to simulate (1/s^2)forming a closed loop in simulink. For a Ramp the output is simply unstable. Literature recommends a zero-pole pair to compensate for a phase lag. So two integerators in series leads to instability. My question is how to now fix the location of zero and the pole for a system that takes in ramp input and the output is expected to follow without lag.

 

[PNachtwey]

Trying to understand the importance of type2 servo

It really isn't that important. Motion systems that are controlling position get one pole from integrating velocity to position. A PI or PID adds the second pole. However, the closed loop poles are usually not at the origin but as far to the left in the s-plane so the error will decay quickly.

I have never seen an integrator with a double integrator yet motion controllers can follow a ramp or sine wave without any significant errors without sine wave feed back or double integrators.

I read in books that to get zero velocity lag, type2 system is suitable

It works in theory but that is not how its done. You are reading books written by people that have don't have any real experience. A steady state ramp? How ridiculous. Eventually the ramp must end. In motion control they end pretty quickly.

To get zero steady-state error to a ramp input (assuming a sensor with no poles), if the system transfer function already has a pole at the origin, the controller would have to provide one.

No!

a PID can't perfectly track a sine wave - there's no model of the sine wave in the feedback loop.

A sine wave model in the feed back loop isn't required. You are talking theory again but this is not how its done. Do you really expect the controller to change its feedback every time the motion profile generator changes?

For a Ramp the output is simply unstable. Literature recommends a zero-pole pair to compensate for a phase lag. So two integerators in series leads to instability

Yes! So much for theory.

Sine waves without a sine wave feed back with a pneumatic system!!
This uses only position feed back from the Temposonic rod.

https://www.youtube.com/watch?v=m_X4g86-B7s

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

 

[kishoregv]

Yeah, Thanks for all your replies. I still need the answer for choosing location of pole and a zero for a type2 compensator. Also difference between tracking rate and bandwidth. Why two terms? It looks alike.

 

[PNachtwey]

I still need the answer for choosing location of pole and a zero for a type2 compensator.

A good safe start is placing all the closed loop poles on the negative real axis in the s-plane.
The closed loop response is sure to be stable but will also act like a low pass filter in response to an input.
You need one gain for every closed loop pole to do this. If you plant is K/s^2 then a PD controller will work.
The PD controller will also add one zero. The phase lag will be at most 90 degrees.
Do you know how to do pole placement?

My question is why? What system do you have that is type 2?





Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

 

[kishoregv]

I was just studying about PLL and that's how ended up over type2 servo. Any automated way of calculating poles and zeroes

 

[PNachtwey]

Like I said, use pole placement.
Use Ackermann's method if working in the digital domain.
Use my symbolic method if working in the s domain.

I added the constant acceleration ramp to a worksheet I had done years ago.
The pole placement is trivial but there are practical limits.

http://deltamotion.com/peter/Mathcad/Mathcad - t2 pd.pdf

The digital and symbolic solutions converge as the sample interval approaches 0.

Edit:
Here is the PID solution

http://deltamotion.com/peter/Mathcad/Mathcad - T2 PID.pdf

There are 3 practical solutions. PD, PID and Lead/Lag.

I hadn't review these files since 2009. They are now updated. I have solutions for just about any practical system and control options.

All three solutions ( PD, PID and Lead/Lag) are pretty simple. I don't understand why there should be confusion or misunderstandings about how to control a double integrator system. Unless...

Now I will rant again. Matlab and Simulink do not provide understanding. They are good and providing answers only. I have doubts about a lot of text books too. Most seem to be written by PhDs that have little real experience. They make the math look complicated to hide how simple the math really should be. In the three examples I posted the symbolic formulas for the controller gains could be easily calculated by hand in a few minutes. The math shouldn't be that complicated once you really understand what and why.

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

 

[IRstuff]

Peter, thanks for that. Is it possible to post the actual Mathcad?

Thanks


TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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[PNachtwey]

IRStuff, e-mail me. I am easy to find. Put Mathcad in the title so I find it easily in case it goes in my spam folder.

edit,
I updated the file. Some of the wording wasn't right because I just did a quick copy and paste.
I also updated my Lead/Lag version

http://deltamotion.com/peter/Mathcad/Mathcad - t2 lead lag.pdf

The lead/lag version has an extra close loop pole so it is slower than the PD version.

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/