×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Derive Non-Linear Transfer Function

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!!

RE: Derive Non-Linear Transfer Function

Transfer functions only exist for linear time-invariant systems.

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

(OP)
Thank you for your answer, xnuke.

RE: Derive Non-Linear Transfer Function

Why can't a transfer function be expressed as a non-linear differential equation or system of non-linear differential equations? I do this all the time for hydraulic simulations. It looks like CCLIUTW is trying to add Stribeck friction to his simple motor system in velocity mode.

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

A transfer function (in the continuous-time domain) is the ratio of the output of a linear time-invariant system to the input of the system, in the s-domain, when all initial conditions are zero. I believe the requirement for linearity comes from the application of the Laplace transform to convert from the time domain to the complex frequency domain. Typically, some method is used to linearize a nonlinearity like sgn(ω) (e.g., using the describing function of ideal relay for the sgn function in this case) when an approximate transfer function is required so that analytical methods can be used.

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

(OP)
Thanks for all response.

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

CCLIUTW, use differential equations then integrate with Runge Kutta.
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

(OP)
Hello Nachtwey,

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

Not surprising. I think the first solver Simulink tries (when VariableStepAuto is selected - the default for continuous-time models) is ode45 - which is a variable time-step version of the RK(4,5) integration method. You've essentially repeated what Simulink did using a slightly different numerical integrator. I'm happy you learned something, though.

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.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login


Resources

Low-Volume Rapid Injection Molding With 3D Printed Molds
Learn methods and guidelines for using stereolithography (SLA) 3D printed molds in the injection molding process to lower costs and lead time. Discover how this hybrid manufacturing process enables on-demand mold fabrication to quickly produce small batches of thermoplastic parts. Download Now
Design for Additive Manufacturing (DfAM)
Examine how the principles of DfAM upend many of the long-standing rules around manufacturability - allowing engineers and designers to place a part’s function at the center of their design considerations. Download Now
Taking Control of Engineering Documents
This ebook covers tips for creating and managing workflows, security best practices and protection of intellectual property, Cloud vs. on-premise software solutions, CAD file management, compliance, and more. Download Now

Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close