Controllability of a Linear System: The Controllability Matrix and the PBH Test скачать в хорошем качестве

Controllability of a Linear System: The Controllability Matrix and the PBH Test

In this video we explore controllability of a linear system. We discuss two methods to test for controllability, the controllability matrix as well as the PBH test. Topics and time stamps: 0:00 – Introduction and definition. 1:04 – Controllability of a dog. 3:48 – Controllability matrix. 7:18 – Example 1: Controllable system. 11:10 – Example 2: Uncontrollable system. 17:36 – Example 3: Make an uncontrollable system controllable. 22:11 – Example 4: System is controllable using single input. 28:54 – Example 5: Symmetry makes system uncontrollable with single input. 31:38 – PBH test history and background. 35:09 – PBH test statement and analysis. 45:31 – Example 6: PBH test. 1:29:22 – Example 7: System that needs multiple control inputs to be controllable. 1:35:46 – Summary and conclusions. Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/... Additional videos in this series: -Controllability of a Linear System: The Controllability Matrix and the PBH Test (   • Controllability of a Linear System: The Co...  ) -Introduction to Full State Feedback (   • Introduction to Full State Feedback Control  ) -Practical Implementation Issues with a Full State Feedback Controller (   • Practical Implementation Issues with a Ful...  ) -Introduction to Linear Quadratic Regulator (LQR) Control (   • Introduction to Linear Quadratic Regulator...  ) Overview of engineering videos and curriculum located at http://faculty.washington.edu/lum/Edu... Additional resources: -Steve Brunton’s discussion on controllability (   • Controllability [Control Bootcamp]  ) -Steve Brunton’s discussion on the PBH test (   • Controllability and the PBH Test [Control ...  ) -Hautus Lemma - https://en.wikipedia.org/wiki/Hautus_... -Rank Nullity Theorem (https://en.wikipedia.org/wiki/Rank%E2...) You can support this channel via Patreon at   / christopherwlum  . Thank you for your help!