Sir i am your new subscriber. I yesterday subscribed your channel and l really appreciate you authentic and genuine way of teaching.. May God Bless You !
If it is the same first example and I want to find the closed loop transfer function for nonlinear system, is it just compensation or a derivation of the function and compensation?
Once you replace the nonlinear element with describing function, you are basically linearising the system. So, you can treat it just like any linear system block diagram model.
Please solve this problem to me I thank you before it The input x(t) and the outout y(t) of nonlinear system are related through the nonlinear differential equation . Y=x²dx/dt +2x Determine the describing function of the system .
1. Nonlinear Control Systems by Alberto Isidori 2. Nonlinear Systems by Hassan K Khalil 3. Modern Control Engineering by Mohandas K P These are some books I refer :)
Sorry, we haven't covered this topic in our video since it was out of scope. You can check out the matlab tutorials in youtube. They will hopefully be of great help to you:)
Sorry, we haven't covered this topic in our video since it was out of scope. You can check out the matlab tutorials in youtube. They will hopefully be of great help to you:)
Hey Topperly, what if we had a nonlinearity in the form of u = f(e) = { e , for e < -e0 or e > e0 a*e, for -e0 < e < e0} ? How do we handle the f(x1) then , (because now it contains terms of x1) ? I mean, how do we use the dx2/dx1 method?
Hi, This method only works if an explicit solution exists for the resulting differential equation. I suggest you to dive into the mathematics of 'solutions to DE' to find answer to your question. Meanwhile, I'll also check for the same :)
@@Topperly Thank you for your prompt answer. You have been quite helpful for my nonlinear control system class. About the solutions to DE, what bothers me is that in the case I mentioned the type of the equation changes and I get confused on what is supposed to happen. I mean we can't solve it using Laplace in a proper way (at least now in a way I know). Also, I use MATLAB's ode45 to solve the system by writing an extra function to describe the system's error state equations, using IF statements to define x2dot differently according to x1 values (using the f mentioned above). What I don't get is whether this form with if statements is correct or if I have to change the code according to the solution that I will do by hand (the method that I will follow to solve the state equations and describing the phase portrait). Thank you in advance Topperly
I believe this use of IF statements will work. It doesn't matter at which step you are substituting the value of f(x1). Please do drop a reply if you found the solutions to ODE for the question. Thank you :)
@@Topperly If the region is x1>1, shouldn't the initial conditions(x1(0) and x2(0)) be considered at x1(1) and x2(1)? Thank you for this amazing video!
Sir i am your new subscriber. I yesterday subscribed your channel and l really appreciate you authentic and genuine way of teaching.. May God Bless You !
So nice of you!
How to find the values of x1(0) & x2(0)?
At 4:40, How did you integrate both sides as if 'f(x1)' is function of 'x1'?
It is because if you look at how we defined f(x1), you can see that f(x1) doesn't contain any terms of x1, but just constants.
@@Topperly but integration of constants, for example integration of 1 is x not jzt a constant
If you see it's {constant/z) and the integral of that will be constant×ln(z)
If it is the same first example and I want to find the closed loop transfer function for nonlinear system, is it just compensation or a derivation of the function and compensation?
Once you replace the nonlinear element with describing function, you are basically linearising the system. So, you can treat it just like any linear system block diagram model.
Yes
Hello Topperly, Could you please share the name of the software that you are using as a whiteboard. Thank you for the lecture, it was very helpful
I'm using Autodesk Sketchbook.
Also, thank you for your contribution to our cause. We really appreciate it :)
@@Topperly Thank you for the prompt reply Topperly.
Please solve this problem to me
I thank you before it
The input x(t) and the outout y(t) of nonlinear system are related through the nonlinear differential equation .
Y=x²dx/dt +2x
Determine the describing function of the system .
Please watch the first question in this video :)
th-cam.com/video/dpllW3Je4b0/w-d-xo.html
Can you please tell me which text are you following for this topic... To find more examples which text I should follow
1. Nonlinear Control Systems by Alberto Isidori
2. Nonlinear Systems by Hassan K Khalil
3. Modern Control Engineering by Mohandas K P
These are some books I refer :)
@@Topperly Thank you
@@Topperly how can I get a PDF of modern control engineering by P Mohandas....
Please discuss how to plot the phase trajectories by using matlab.... foe question 1
Sorry, we haven't covered this topic in our video since it was out of scope. You can check out the matlab tutorials in youtube. They will hopefully be of great help to you:)
Phase trajectories plotted in analytical & isocline methods doesn't seem to match. Why?
That shouldn't happen. Could you please recheck?
Please discuss how to plot the phase trajectories by using matlab.....
Sorry, we haven't covered this topic in our video since it was out of scope. You can check out the matlab tutorials in youtube. They will hopefully be of great help to you:)
Hey Topperly, what if we had a nonlinearity in the form of u = f(e) =
{ e , for e < -e0 or e > e0
a*e, for -e0 < e < e0} ?
How do we handle the f(x1) then , (because now it contains terms of x1) ?
I mean, how do we use the dx2/dx1 method?
Hi,
This method only works if an explicit solution exists for the resulting differential equation. I suggest you to dive into the mathematics of 'solutions to DE' to find answer to your question. Meanwhile, I'll also check for the same :)
@@Topperly Thank you for your prompt answer. You have been quite helpful for my nonlinear control system class. About the solutions to DE, what bothers me is that in the case I mentioned the type of the equation changes and I get confused on what is supposed to happen. I mean we can't solve it using Laplace in a proper way (at least now in a way I know). Also, I use MATLAB's ode45 to solve the system by writing an extra function to describe the system's error state equations, using IF statements to define x2dot differently according to x1 values (using the f mentioned above). What I don't get is whether this form with if statements is correct or if I have to change the code according to the solution that I will do by hand (the method that I will follow to solve the state equations and describing the phase portrait). Thank you in advance Topperly
I believe this use of IF statements will work. It doesn't matter at which step you are substituting the value of f(x1).
Please do drop a reply if you found the solutions to ODE for the question. Thank you :)
How to plot non linear State Space in Matlab? Can you please give reference to learn?
There's a toolbox called 'pplane' which will help you. But I'm not sure if it's available for the latest version of MATLAB :)
Mam is it possible to draw phase trajectory using isocline method without initial value.
No. Bcz you always need a starting point to understand how the system evolves after that.
Ok mam but what is the initial value taken in the first question
I took some random value, nothing specifically :)
Ok mam thank you
@@Topperly Are you taking random values of N at 12:13?
In region 1 (X1>0)
For X1=0 then F(X1)=0.
So, Why have you taken F(X1)=1 for X1>0?
Region 1 is X1>1
Could you please mention the timestamp of the moment you are referring to?
5.30
Sorry, there's been a mistake. I intended to say x1>1. Thanks for pointing it out :)
This videos are very informative. Thank you.
@@Topperly If the region is x1>1, shouldn't the initial conditions(x1(0) and x2(0)) be considered at x1(1) and x2(1)?
Thank you for this amazing video!