Understanding and Sketching the Root Locus

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. Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/main/Controls15 Additional videos in this series: -Introduction to Root Locus (https://youtu.be/V3iveC_fa04) -Understanding and Sketching the Root Locus (https://youtu.be/gA-KOk3SAb0) -Using ‘rlocus’ in Matlab to Plot the Root Locus (https://youtu.be/im19KuzjWwo) -Using the Control System Designer in Matlab (https://youtu.be/RPzFLzKkQGs) Additional resources/references on root locus -Erik Cheever’s website on root locus (https://lpsa.swarthmore.edu/Root_Locus/RootLocus.html) -Brian Douglas’ discussion on zeros at infinity (https://youtu.be/eTVddYCeiKI?t=606) All Control Theory videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o) #Control #ControlTheory You can support this channel via Patreon at https://www.patreon.com/christopherwlum. Thank you for your help!