Thank you sir.. for your good explaination.. I didnt know anything about control system. Then my friend Vishnu S suggested topperly. I got S in that subject.. Thank u topperly
in the isoclane method how do you define how many isoclanes you will need to do or how many are enought? and the initial point A in the graph you can always decide where it begins or some times is given?
If you want an accurate trajectory, you will need more isoclines. Basically, more isoclines means more accuracy. You can choose the initial point according to your choice. :)
Awesome video. Thank you very much. Is it correct to say that since all the examples in this video- the trajectories spiral in to the origin; systems described by the differential equations are achieving steady-state i.e. coming to rest.
Hello, At 4:35 you say that "consider a non-linear differential equation y''+y'+y=0", but that is actually a linear differential equation. Is it correct? If not did you mean a "non-linear System"? So does it mean that a differential equation can be linear but the system can be called non-linear? Moreover, I think that y''+y'+y=0 is a linear system, is it right?
Sorry about that. It's a linear ODE only. Originally, while scripting I used a nonlinear DE, but then I decided to use LDE so that it'll be comfortable for first time viewers. But forgot to change the script. Thanks for pointing out! :)
Technically speaking we can predict the system behaviour at any instance if we know the system behaviour at the previous instance. However, if your question is whether we can predict the system behaviour using initial conditions alone, the answer is no. We need to have information about all the variables throughout the time domain.
You have to manipulate that x2dx2 = f(x1,x2)dx1 such that all x1 terms are in one side of equation and x2 terms are on other side and then integrate on both sides. You'll understand this concept better if you look at some examples on integration(or if you are watching the next videos in playlist, you'll see some problems related on analytical method). :)
Hi, I didn't understand your question fully, but if you are asking about how we choose the initial point, it is completely arbitrary. In the example, I wanted to choose that as the initial point for my phase trajectory. Please feel free to come back if you still have doubts :)
@@Topperly Thanks for your kind response but I wanted to ask that, around 12:50 how you decided the intersection of the line segment from x1 axis with the line at which we have to make the Arc??
In the above methods(plots) we are assuming an initial point ryt.... can you explain why and how you made that assumption and whether the plot will look same if started from a different point
There's no particular reason - I randomly chose one. You have to choose an initial point based on the requirement. No the plots will not be same. Even closely spaced initial points results in widely varying plots - butterfly effect :)
Del curve is function of x1 and x2. Here, I just drew a random curve for representative purposes. However, in actual cases, you have to plot the function d(x1,x2).
First you have to manipulate the state equations in the form shown in video. Then you can identify the terms included in the function del(x1,x2). Now plot del(x1,x2) vs x1 or x2 depending on the case :)
@@Topperly how we manipulate the state equation Actually how to can plot the plane x1 -x2 Is this plot by any matlab code??? And how the phase of this question is plotted by matlab. Thanks for your kind support
i have a question probably a dumb one, in the analythical method why when you integrate both sides of x2dx2=-x1dx1 you get a C^2? i mean from the formula of integration don't you get X1^2/2+C=X2^2/2+C? i really dont remenber the this topic very well.
What you said is correct. But think of this way, I have a function f(x)= x. After integration, (integral f(x)) = (x^2)/2 + c, right? Now this 'c' is a constant. Let 'b' be the square root of 'c'. Therefore I can write (integral f(x)) = (x^2)/2 + c = (x^2)/2 + b^2. This is what I've done in video, so that I can obtain the equation in the form of equation of a circle.
Delta is just a function of x1 and x2. It's just like x + y = 3 in a cartesian plane. Here this straight line is a function of x and y. How do you plot this line in a cartesian plane? Just like that you should plot delta in the x1-x2 plane
at 07:30 how do we know that at N=-1 the angle should be -45deg, at N=-2 the angle should be -63deg, etc?? can you please explain that part a little bit more details? thank you in advance.
@@Topperly Thank you very much, you helped a lot with this video. Now I can finish my homework lol... please keep inspiring us with other great lecture videos... thanks again!
@Raj Anand Yeah. Desmos doesn't have that functionality. The angle was plotted using a tool in the software I use for slide preparation - Autodesk Sketchbook :) But if u like to plot the trajectories, try "pplane" toolbox in MATLAB.
It's really nice video..👏
Thank you :)
Good explanation.. much needed for tomorrow's exam.
Thanks :). Also please do keep mentioning to others about the video😁
Thanks bro this'll really help me a lot for tomorrow's exam 😁
Thanks for you support. It means a lot :)
Excellent way of teaching.... Your method is far better than our university teachers.... Keep it up bro😊
thanku bro. Good Explination.
Thank you. Means a lot :)
Thank you sir.. for your good explaination.. I didnt know anything about control system. Then my friend Vishnu S suggested topperly. I got S in that subject.. Thank u topperly
Ur friend is awesome! 😂
U got 'S'! Congratulations 👏
"S" grade? Ee guruvinu thiruppathi ayada...thiruppathi ayi! (salimkumar.jpeg)
Awesome!!!!
Thank you :)
wow sir
Subscribe for more updates🤗
Thanks 🙏
Top class
Glad to hear that :)
Nice explanation
Thanks :)
Thanks a lot😊
Thank you! Your appreciation means a lot :)
Thank you :)
Thank you! Means a lot :)
Nice one.
More videos pls Sir...
Thank you! That means a lot! Yeah, I'm planning to make more :)
in the isoclane method how do you define how many isoclanes you will need to do or how many are enought? and the initial point A in the graph you can always decide where it begins or some times is given?
If you want an accurate trajectory, you will need more isoclines. Basically, more isoclines means more accuracy.
You can choose the initial point according to your choice.
:)
Awesome video. Thank you very much. Is it correct to say that since all the examples in this video- the trajectories spiral in to the origin; systems described by the differential equations are achieving steady-state i.e. coming to rest.
Yes, if the trajectories spiral into origin, system is achieving steady state :)
@@Topperly . Thank you very much for the reply.
Hello, At 4:35 you say that "consider a non-linear differential equation y''+y'+y=0", but that is actually a linear differential equation. Is it correct? If not did you mean a "non-linear System"? So does it mean that a differential equation can be linear but the system can be called non-linear? Moreover, I think that y''+y'+y=0 is a linear system, is it right?
Sorry about that. It's a linear ODE only. Originally, while scripting I used a nonlinear DE, but then I decided to use LDE so that it'll be comfortable for first time viewers. But forgot to change the script. Thanks for pointing out! :)
What is the software that u r using here to draw the phase plane potrait using isocline method????
I'm not using any software. It's Desmos graphing website.
Sir how to find the value of angle in isocline method
Angle = taninverse(N). Also note that the angle is taken with respect to positive X axis. :)
What software have you used to draw angles in isocline?
It's an inbuilt tool that comes with autodesk sketchbook :)
Thanks for sharing the video... I want to ask about isocline method have the ability to predict the system behavior in the future?
Technically speaking we can predict the system behaviour at any instance if we know the system behaviour at the previous instance.
However, if your question is whether we can predict the system behaviour using initial conditions alone, the answer is no. We need to have information about all the variables throughout the time domain.
how to choose initial point 'A', in isocline method?? randomly??
Yes, initial point is chosen randomly as per our choice :)
I have another question how do you get the integral of -f(x1,x2)dx1 in the analythical method?
Can you please mention the timestamp of instant you are referring to?
@@Topperly minute 2:20
You have to manipulate that x2dx2 = f(x1,x2)dx1 such that all x1 terms are in one side of equation and x2 terms are on other side and then integrate on both sides. You'll understand this concept better if you look at some examples on integration(or if you are watching the next videos in playlist, you'll see some problems related on analytical method). :)
nicely explained but wanna to know that when we plot isoclines for different values of N ,on what values of angles we have to plot these isoclines ???
Thank you!
Angle = arctan(N). Sorry I forgot to mention that in the video.
At 12:53 How we decided the intersection point of yellow line with white line and made the arc ?
Hi,
I didn't understand your question fully, but if you are asking about how we choose the initial point, it is completely arbitrary. In the example, I wanted to choose that as the initial point for my phase trajectory.
Please feel free to come back if you still have doubts :)
@@Topperly Thanks for your kind response but I wanted to ask that, around 12:50 how you decided the intersection of the line segment from x1 axis with the line at which we have to make the Arc??
Please watch from 11:56. That point(initial point) is chosen first. It's arbitrarily chosen in the phase plane.
@@Topperly got it. Thank you very much, you are doing a great job ❤
In the above methods(plots) we are assuming an initial point ryt.... can you explain why and how you made that assumption and whether the plot will look same if started from a different point
There's no particular reason - I randomly chose one. You have to choose an initial point based on the requirement.
No the plots will not be same. Even closely spaced initial points results in widely varying plots - butterfly effect :)
Nolan explain cheyyo ithreyum nannayit ....💥💥... topperly uyir
He he....ithokke enth (salimkumar.jpeg)
@@Topperly veendum malayali
Thanks for the video. But I'm not understanding how you are obtaining the state equations.
Which part?
How we can draw the phase trajectory at 10.49
Which software we use and what is the procedure sir....
It's really required for me
That I drew by hand on a Desmos Graph.
I think pplane toolbox in Matlab will be more useful for you :)
Please explain how to draw isocline graph in another video.
Btw nice explanation of other methods.
Thank you for your feedback :) . I was planning to make a video showing how to solve a question using isocline method.
@@Topperly thanks for rewerting back!
how to plot the angles of the respective slopes?
like at which point are you taking the reference and plotting the angles?
Which method are you referring to?
@@Topperly isocline
All angles are w.r.t x-axis
@@Topperly ok on x-axis from which point will be taken as reference?
Angles are always measured w.r.t a line not a point
how did you draw the del curve in delta method?
Del curve is function of x1 and x2. Here, I just drew a random curve for representative purposes. However, in actual cases, you have to plot the function d(x1,x2).
@@Topperly d(x1,x2) will be a 3- dimensional plot with d-magnitude along a plane perpendicular to x1, x2 plane
del is just a function of just two variables - x1 and x2. So, it is a 2 dimensional plot only.
one more example of analytical method please.
At 11.55 how we draw the graph of del(x1,x2) on x1 and x2 plane
First you have to manipulate the state equations in the form shown in video. Then you can identify the terms included in the function del(x1,x2). Now plot del(x1,x2) vs x1 or x2 depending on the case :)
@@Topperly how we manipulate the state equation
Actually how to can plot the plane x1 -x2
Is this plot by any matlab code???
And how the phase of this question is plotted by matlab.
Thanks for your kind support
@Deepak Gupta To understand delta method further, please refer this book(thesis) :)
core.ac.uk/download/pdf/36706161.pdf
i have a question probably a dumb one, in the analythical method why when you integrate both sides of x2dx2=-x1dx1 you get a C^2? i mean from the formula of integration don't you get X1^2/2+C=X2^2/2+C? i really dont remenber the this topic very well.
Can you please mention the timestamp of instant you are referring to?
@@Topperly starting the 3:42
What you said is correct. But think of this way,
I have a function f(x)= x. After integration, (integral f(x)) = (x^2)/2 + c, right?
Now this 'c' is a constant. Let 'b' be the square root of 'c'. Therefore I can write (integral f(x)) = (x^2)/2 + c = (x^2)/2 + b^2.
This is what I've done in video, so that I can obtain the equation in the form of equation of a circle.
@@Topperly ok i undestand so for you "K" in the video is your "b", i got confused because you writed it first as C^2.
No 'c' in the video is 'b'. 'k^2' in video is equal to '2*c^2' after cross-multiplication :)
what is meant by plotting delta function?
Does it mean delta=0 is the equation of the curve?
Yes, you are right :)
@@Topperly where to plot the magnitude of delta? On x1 axis?
If so what to do if delta is a function of x1 only?
Delta is just a function of x1 and x2.
It's just like x + y = 3 in a cartesian plane. Here this straight line is a function of x and y. How do you plot this line in a cartesian plane? Just like that you should plot delta in the x1-x2 plane
at 07:30 how do we know that at N=-1 the angle should be -45deg, at N=-2 the angle should be -63deg, etc?? can you please explain that part a little bit more details? thank you in advance.
Angle = arctan(N)
N is the slope of line :)
@@Topperly Thank you very much, you helped a lot with this video. Now I can finish my homework lol... please keep inspiring us with other great lecture videos... thanks again!
Haha...Glad to hear that :)
how to find the angle in 2nd method
Angle = taninverse(N). Also note that the angle is taken with respect to positive X axis. :)
@@Topperly thank u buddy
Sir where u r plotting graph I mean which app
I'm not using any graphs. I'm drawing on Desmos graph :)
@@Topperly thank u sir , I got it .
Sir , I m using demos graph first time , i don't getting that line for plotting angle. like u adjusting line according to angle . Pls help
@Raj Anand Yeah. Desmos doesn't have that functionality. The angle was plotted using a tool in the software I use for slide preparation - Autodesk Sketchbook :)
But if u like to plot the trajectories, try "pplane" toolbox in MATLAB.
@@Topperly thank u sir
At n how theta come up
Eg at n=-1 how theta - 45° in isocline method
Thetha = arctan(n)
Ok got it thnks
Only 4 hr remaining to my exam 😂 13:18
Haha...Hope the exam was good for you :)
@@Topperly बहुत अच्छा गया मेरे भाई तुमको ढूढ़ रहा मै
Nice explanation
Thank you! Means a lot :)