Understanding and Sketching the Root Locus

Показать описание

In this video we discuss how to sketch the root locus for a system by developing a series of 5 core rules augmented by 5 supplemental rules (for a total of 10 rules). These rules will help us gain an understanding and intuition on how the root locus behaves as the parameter K increases from 0 to infinity.

Topics and time stamps:
0:00 – Introduction
1:26 –Block diagram architecture.
3:35 – Example system 1 – brute force, numerical solution to root locus.
12:20 – Rule 1: Number of poles is unchanged.
17:05 – Example system 2 to illustrate rule 1.
19:22 – Rule 2: Closed loop poles start at open loop poles and go to open loop zeros or zeros at infinity.
23:58 – Example system 3 to illustrate rule 2.
35:06 – Rule 3: Valid regions on real axis are to the left of odd numbered pole/zeros (start numbering from right to left).
1:12:41 – Example system 4 to illustrate rule 3.
1:29:31 – Rule 4: Angle of asymptotes and centroid of asymptotes.
1:29:56 – Example system 5 to illustrate rule 4.
1:44:45 – Example system 6 to illustrate rule 1, 2, 3, and 4.
1:54:19 – Rule 5: Angle of departure from complex poles.
1:54:41 – Example system 7 to illustrate rule 5.
2:19:38 – Summary of core 5 rules.
2:27:01 – Rules 6, 7, 8, 9, and 10.
2:34:08 – Example system 8 to illustrate all rules.
2:54:38 – Conclusions and next steps.

Additional videos in this series:
-Introduction to Root Locus (TBD)

Additional resources/references on root locus

Рекомендации по теме

Комментарии

AE511: Boiling down the root locus manual sketch into 5-10 rules was very helpful! Walking through each step by step really helped me learn the fundamentals of the root locus, something I didn't get too much from undergrad

zaneyosif

This is the best explanation on this topic that I have ever come across. Thanks for the efforts and for sharing.

karthikmurthy

Christopher, On last example time 2:43:00 when You calculated Centrum =-11/3 = -3.67 I think you made a mistake it should be Centrum=-7/3= -2.33 and that is when you did -30.75 degree angle of departure it didn't come smoothly!

MR-hxee

AE511: Wow, I cannot express how much easier this material came across through the use of some real examples of varying complexity. I was feeling pretty shaky on root locus but the last example helped tie it all together.

ahungryflyer

Thank you so much for this. Someone please give this man a cold drink, he deserves it after the amount of time he spent on this video 🥂

montage

A sincere thank you, I have an exam on this tomorrow and just couldn't get an intuition until now. Best explanation I have found :)

nicholasziglio

Appreciate that you took the time to correct yourself on the vector drawing, this stuff is a lot of effort

mattschierholtz

AE511: Thanks for all the examples! The step-by-step structure of the video with examples for each step is very helpful.

philipcasey

I've just spent 3 hours without any boredom learning and solving with you. thank you so much for this great content <3

Andrew_k_

Просто шикарный урок! Фундаментальный!

SMV

I need teachers like you when I was in college.

rahulbhavsar

[AE 511] 58:30
The visualization of rule 3 with the vectors is very helpful to understanding the math behind rule 3

timproby

Thank you for such a well organized easy to follow lecture!

selamhendrix

Great content, can't thank you enough. The only thing i missed is, in last example, if there was a criterion for determining which poles go to infinity and which poles are attracted to zeros. I sketched p1-> z1 and p2 -> z2 with p4 and p5 going to infinity but MatLab proved me wrong.

davidebenedettivalentini