Deriving Percent Overshoot, Settling Time, and Other Performance Metrics

In this video we examine a second order dynamic system and derive how various performance metrics (such as time to first peak, magnitude at first peak, percent overshoot, settling time, and rise time) are related to the damping ratio and natural frequency of the system.

[sethwhittington]

AE511: Thanks for breaking your videos into clear cut planned out sections. It helps with the consumption.

[morganwalker]

Another great lecture. The transition at 54:24 changed my life.

[Gholdoian]

AE 511: Thank you for the indepth explanation and derivation of the performance metrics. Previously I've only been told what they are but haven't had a derivation of each of them. Thank you

[saimafa]

oh man, you teach so much better than my controls lecturer. Thank you, I wish I was taught my systems and Controls unit by you.

[aimeepak]

AE 511: This lecture was extremely helpful in understanding the settling time, rise time, and overshoot that goes beyond just knowing the equations. It really helped me create the functions needed for the homework.

[robertattfield-kirsopp]

So helpful been looking was looking at these equations for hours without understanding them until I found this video!

[jacobcarroll]

Absolutely fantastic derivation of percent overshoot!

[elliscld]

Thank you for your help, I'd recommend implementing time stamps for different topics within for people who know a little but for example don't know the percentage overshoot

[alanlee]

AE511 - loving the summary and the identification of parameter dependency/non-dependency in the time domain analysis.

[selamhendrix]

thanks for the lecture, it's helpful to see the relationships between the different parameters

[zacharywilliams]

Great lecture; concise yet in depth derivations

[timproby]

[AE 511]
Appreciate the exchange between the theory on the white board and the use of software and it helping with understanding the theory or idea

[SMV]

Отличный урок. Теперь понятно, откуда что берётся . Большое спасибо!

[sidraman]

A great visual on step response and perfect segue into PID control

[jamesferrese]

great reminder on some cool controls topics

[julianwoo]

Good video on using Mathematica instead of Matlab for calculating percent overshoot.

[kenrickchan]

Great intro to the math behind 2nd order systems

[id-icou]

For the settling, I think you forgot to take the contribution of the sinusoïde in the amplitude of the exponential envelope. The sum of cos(.) + Csin(.) = Msin(.+a), so the amplitude of the envelope should be A*M, so M which depends on the damping ratio should also appear in the expression of the settling time

[mikerudolf]

AE511: Not sure if this was mentioned and I missed it, but some of these metrics require zeta to be between 0 & 1, correct? The term sqrt(1-z^2) runs into issues if z is not within those bounds.

From what I recall from undergrad, Tp, Mpt, and PO are all metrics of underdamped systems (zeta between 0 & 1) which is where the sqrt(1-z^2) term shows up.

[mohamedtebbo]

How would you do this for an nth order system ? Like 3rd order or 4th order