## Derive Non-Linear Transfer Function

## Derive Non-Linear Transfer Function

(OP)

Hello engineers:

I have an question of derive transfer function in nonlinear control system, as title.

Generally, a linear system can easy derive transfer function like the picture, but it is difficult to derive transfer function when it include friction model.

I want to ask every excellent engineers can derive the transfer function?

Friction model is a velocity function : F(w) = (Fs-Fc)exp(-(w/ws)^2)+Fc*sgn(w)+q2*w

Fs, Fc, ws and q2 is known

Thank you!!

I have an question of derive transfer function in nonlinear control system, as title.

Generally, a linear system can easy derive transfer function like the picture, but it is difficult to derive transfer function when it include friction model.

I want to ask every excellent engineers can derive the transfer function?

Friction model is a velocity function : F(w) = (Fs-Fc)exp(-(w/ws)^2)+Fc*sgn(w)+q2*w

Fs, Fc, ws and q2 is known

Thank you!!

## RE: Derive Non-Linear Transfer Function

xnuke

"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand,

Atlas Shrugged.Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

## RE: Derive Non-Linear Transfer Function

## RE: Derive Non-Linear Transfer Function

This is an example of why I say that serious simulations use differential equations instead of Laplace transforms or state space.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: Derive Non-Linear Transfer Function

I don't disagree with you about simulations, Peter. Simulations using differential (really, difference) equations allow systems that cannot be solved analytically to be solved numerically. I

xnuke

"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand,

Atlas Shrugged.Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

## RE: Derive Non-Linear Transfer Function

Yes, this friction model is Stribeck friction model, and I tried to derive W_out(t)'s differential equations, but it is too difficult to get W_out(t).

I will try to linearize Stribeck friction model, and wish it can get good result.

## RE: Derive Non-Linear Transfer Function

I was once hired by a construction company that was replacing the dam gates on a dam just down stream from Pittsburg, PA.

The army corp of engineers ( ACE ) didn't want the dam gates to drop due to leakage so they insisted that the hydraulic cylinders lifting the gates had no leak ( read too tight to move easily ) seals. The dam gates would vibrate at they moved which could damage the dam since the gates weighed about 100 tons a piece. The ACE accused the construction company of putting in the gates wrong. We monitored to the gates with position, acceleration and pressure sensors and used this data to make a model. The Stribeck friction was severe and causing the slip-stick motion. I was able to show it was the seal friction from the no leak seals that was the problem not the construction company's installation that was at fault. This got the construction off the hook and the ACE had to admit it was the seals

If you want to get the job done and model the system accurately then use differential equations.

Start with the two differential equations shown in equations 3 and 4 here

http://ctms.engin.umich.edu/CTMS/index.php?example...

Convert your force(omega) to Torque(omega) and insert it into equation 3.

Peter Nachtwey

Delta Computer Systems

http://www.deltamotion.com

http://forum.deltamotion.com/

## RE: Derive Non-Linear Transfer Function

Thank you for your sharing, it is an interesting experience, and RK method is very useful.

I used RK method calculated the results of W, and it is right result compare with Simulink.

I learned a lot of knowledge! Thank you so much. Today is very lucky! You are my Santa this year.

CCLIUTW

## RE: Derive Non-Linear Transfer Function

xnuke

"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand,

Atlas Shrugged.Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.