Phase Plane | Nonlinear Control Systems

Topics covered :
00:34 Phase plane analysis
02:31 Butterfly effect
03:19 Mathematical definition of Phase plane method
03:50 Symmetry of phase trajectories in phase plane
Animations by Prof. Robert Ghrist: ve42.co/Ghrist
EDIT : While discussing about symmetry with respect to x2 axis, for f(x1,x2) to be an odd function of x1, the formula should be f(x1,x2)=-f(-x1,x2)

[@krishnajithk9322]

Thank you for the explanation. I think symmetry of the phase trajectories about the X2 axis the statement is correct ie ; f(x1,x2) should be an odd function of X1 but the formula should be f(x1,x2)=-f(-x1,x2) right ?

[@Topperly]

Yes you are right! I'm sorry. This mistake slipped past while I edited the video. Thank you for notifying me!

[@philasandenxumalo192]

awesome video. very straight to the point. The whole series of NONLINEAR CONTROL SYSTEM videos have just saved my life

[@Topperly]

Thank you for your kind words :)

[@anurag8484]

next level visuals

[@Topperly]

Thank you! Hope this video was helpful. :)

[@bofasaldana6849]

This is such a great video! I loved the animations and the wonderful explanation. Thank you!

[@Topperly]

Glad to hear that :)

[@surbhi57866]

I genuinely didn't felt it was about 8 mins video. Good work!

[@Topperly]

Thank you! Your words mean a lot to us :)

[@GauravGupta-pb8mk]

Thank you sir

[@vigneyshukla2155]

Thanks you so much for this wonderful explanation with animations

[@Topperly]

Thank you for your kind words :)

[@ImthiasAhamed]

Very good and systematic lectures
Thank you

[@Topperly]

Thank you! Your appreciation means a lot :)

[@sonjababac9033]

Thanks a lot for your explanation! It helped me a lot for preparing Modeling Dynamics exam :)

[@Topperly]

Glad to hear that :)

[@saptarshisahoo5075]

great Video. Thank you

[@Topperly]

Your appreciation means a lot! Thank you :)

[@AbidAli-rz9xi]

wow.. that's pretty cool..which software have you used for visual effects and animation ?

[@Topperly]

If you see the video description, you can see that the animation credits goes to Prof. Robert Ghrist. I took permission from him to use it in this video :)

[@Callejondelgaming]

Hello and thank you for the explanation, i have only one question, when you compare the two ecuations of dx2/dx1 to get the ecuation f(x1,x2)=f(x1,-x2) why the two dividing X2 are negative? i thought that only the X2 from the ecuation dx1/dx2 in the 4th quadrant was negative.

[@Topperly]

I believe you are referring to moment 06:43 of the video. Please note that I'm simply substituting f(x1,x2) in place of f(x1,-x2) in the expression (-f(x1,-x2)/(-x2)). Hence -x2 is from the 4th quadrant itself. It's not changing. I hope this clears your doubt. If not, please comment. I'm happy to explain again :)

[@Callejondelgaming]

@@Topperly yeah thank you for your explanation, so f(x1,x2) is equal to f(x1,-x2).

[@Topperly]

Yes :)

[@blessoneasovarghese9834]

4:41 about the straight line which u plotted as f(x1,x2) : Is it the function f(x1,x2)=0? Because there is not coordinate to mark the value of 'f'. The straight line you plotted is x2=x1 or (x2-x1) = 0 or f(x1,x2)=0, where f(x1,x2)=x2-x1. Please clarify this.

[@Topperly]

Hi Blesson,
As you rightly said, we are not plotting the value of function f. We are simply plotting the function f=0 which is a function of two variables x1 and x2 in the x1-x2 plane.

[@guillermoolay4416]

really good videos, i am a study a master degree in control and one subject is non-linear systems and control and i have been looking for online curses but aren't good, this videos are really good, may be you can aboard slinding control for next control methods.

[@Topperly]

Thank you for your kind words :)

[@future_millionarie4560]

it was magical...

[@Topperly]

Thank you :)

[@ashtiw11]

Don"t you have any patreon account?

[@Topperly]

Sorry, we don't have a patreon account. Our channel is comparitively new to youtube and hence we are still building up.

[@PrasannaRoutray97]

x1 = x, x2 = x1Dot = xDot, x2Dot = xDDot = -f(x1, x2).