Performance Characterisitics Given a Zero in the System

[Kuriger9]

I have the equations to determine the rise time, peak time, percent overshoot, and settling time for a generic second-order system with no zeros in the system. Given a unit step input for the open-loop transfer function G(s)=(s+1)/(s²+2s+1) how do I analytically determine the performance characteristics (aside from using MATLAB)?


Thanks in advance!

 

[milesyoung]

In general, you're going to have to find the inverse Laplace transform of the response you're interested in and do a bit of calculus to derive relationships for rise time etc. These can quickly become unwieldy, so you often find that people just simulate the response and tune the parameters to fit their specifications.

That's not to say they're doing it blind though. If you read up a bit on how zeros affect the transient behavior of systems, you can get the hang of predicting their influence.

 

[Kuriger9]

In general, you're going to have to find the inverse Laplace transform of the response you're interested in and do a bit of calculus to derive relationships for rise time etc. These can quickly become unwieldy, so you often find that people just simulate the response and tune the parameters to fit their specifications.

That's not to say they're doing it blind though. If you read up a bit on how zeros affect the transient behavior of systems, you can get the hang of predicting their influence.

Thank you this certainly helps!

 

[milesyoung]

If you really want to find those relationships, I recommend you follow a text where they derive them for a second order system using calculus.

Then you can try to do it for the system you're interested in and get help with the specifics here if you get stuck.