×
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

Transfer Function from Difference Equations

Transfer Function from Difference Equations

Transfer Function from Difference Equations

(OP)
If you had a difference equation model of say x(k+1) = 0.2x(k)+u(k) and y(k+1)=-0.4y(k)+x(k)+u(k-1), how would you develop a transfer function in the discrete time domain.

Likewise, working backwards, if you were given a transfer function in the continous domain of say (s+3)/(s^2+4s+16), sampled every 0.05s, how would you find a set of difference equations.

Thanks for your time.

RE: Transfer Function from Difference Equations

Quote:


If you had a difference equation model of say x(k+1) = 0.2x(k)+u(k) and y(k+1)=-0.4y(k)+x(k)+u(k-1), how would you develop a transfer function in the discrete time domain.
What is x and what is y?
This is for what kind of application because it doesn't make much sense.
I looks like you just made this up.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

RE: Transfer Function from Difference Equations

(OP)
Y is the output and U is the input. X is an intermediate variable I suppose.

I did not make this up.

RE: Transfer Function from Difference Equations

OK, but you didn't answer my question. What is the real application? What does x and y really represent? It could be some unreasonable question a college professor would ask. Yes I could solve it. There are situations where x may be position and y may velocity or the rate of change of x but there is no context to the question which is why I think it is a question a professor made up so then it is just an exercise.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

RE: Transfer Function from Difference Equations

(OP)
Oh sorry, yes it is a made up exercise. It's not homework or anything, I would just like to understand maybe in a more general sense how difference equations relate to discrete transfer functions like differential equations relate to continuos time transfer functions.

RE: Transfer Function from Difference Equations

Your question is still backwards. Usually one starts out with the transfer function as a differential equation or Laplace transform and then calculates the difference equation, not the other way around. The controller gains are also calculated as PID gains but then it is possible convert the PID controller to a difference equation. Working the problem backwards can be done but it would require solving for multiple unknowns from multiple equations. Like I said above, it can be done but why?

For instance a digital PID controller can be implemented as
u(n)=u(n-1)+K0*e(n)+K1*e(n-1)+K2*e(n-2)
where
K0=Ki*T+Kp+Kd/T
K1=-Kp-2*Kd/T
K2=Kd/T
So if I know K0,K1,K2 and T I can calculate Ki, Kp and Kd but why? Usually one starts with Ki,Kp, and Kd then calculates K0, K1, K2.

Peter Nachtwey
Delta Computer Systems
http://www.deltamotion.com
http://forum.deltamotion.com/

RE: Transfer Function from Difference Equations

(OP)
Oh, that PID example actually cleared up another confusion I had. Thanks for taking the time, really appreciate it.

RE: Transfer Function from Difference Equations

To the OP, you may use z-transforms to resolve you first problem. As for the second, it you must specify where the sampling takes place first.

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