I don't like to operate with complex numbers so I use this, imo, simpler way to find the critical gain. L(s) = 4K/(4+s) exp(-0.6s) L(jω) = 4K/(4+jω) exp(-j0.6ω) We can divide the loop gain in two parts, absolute value and phase. |L(jω)| = 4K/√(4^2+ω^2) ∟L(jω) = -atan(ω/4)-0.6ω Then make the phase equal to "-π" to find the critical frequency. ∟L(jω) = -π atan(ω/4) + 0.6ω = π This equation is (more or less) the same as the one shown in the video "ω/4 + tan(0.6ω)=0", but it doesn't have infinite solutions, just one. So when using an iterative method to find the solution, any starting value can be choosen. That's and advantage imo. ω = 3.94 rad/s. Once the critical frequency is found, just calculate the absolute value of the loop gain. |L(j3.94)| = 4K/√(4^2+3.94^2) = 0.712K Since we said that the phase was equal to "-π", that loop gain must be a negative real number. L(j3.94) = -0.712K -0.712K = -1 --> K = 1.404 No need to operate with complex numbers haha.
Even though you are saying that there is no need to operate with complex numbers, the way you work out the problem make use of complex numbers. What is the reason for dividing the loop gain into absolute value and phase? Here, you assume that the loop gain is a complex expression. You can call the method or numbers anything you want, but it is still the same, so there is a NEED for complex numbers. That is not really funny, I know :)
@@CanBijles I think there was a misunderstoodment. I don't want to avoid complex numbers at all, in fact I like them, what I don't enjoy is making huge operations with them. For example, if there is a long product of complex numbers in the denominator and I want to "put" them in the numerator... That can be kind of messy. "Even though you are saying that there is no need to operate with complex numbers, the way you work out the problem make use of complex numbers" It is true that there are complex numbers written in my comment, I mean, the whole point is to make s=jω, that's unavoidable. But didn't operte with them so I don't see any contradiction there. "What is the reason for dividing the loop gain into absolute value and phase? Here, you assume that the loop gain is a complex expression" The loop gain is L(jω), isn't it? That is a complex expression, so it can be divided in absolute value and phase, like in the Bode diagrams. Why don't do it if it helps to solve the problem? For example, if we take the loop of your next video (of this topic): L(s) = 160K/((s+4)(s+5)(s+8)) exp(-0.2s) L(jω) = 160K/((4+jω)(5+jω)(8+jω)) exp(j(-0.2ω)) Absolute value and phase |L(jω)| = 160K/√((4^2+ω^2)(5^2+ω^2)(8^2+ω^2)) ∟L(jω) = -(0.2ω + atan(ω/4) + atan(ω/5) + atan(ω/8)) Make phase equal to "-π". 0.2ω + atan(ω/4) + atan(ω/5) + atan(ω/8) = π This, got the equation to find the critical frequency pretty much straight forward. Once calculated, next steps are trivial: plug it in the absolute value, make it negative, equal it to "-1" and isolate "K". On the other hand, to get to a similar equation in that video, several operations with complex numbers were made... That's what I meant when I said "there is no need to operate with complex numbers". This is not a critique btw lol, I like your videos, they are helping me a lot to understand this subject. The way to solve the problems is perfect too. Just wanted to point that thing out.
@@ilPescetto There are definitely other ways to work out a problem, but the structured way to work out a problem is by using the official route, even more when you explain this to others. There are special cases which allows us to work out a problem faster, also with some experience, you can almost feel what the answer might be. I also use them, but merely for myself as a short cut. My objective with these videos on this channel is how one can do this step by step without using any short cuts and not knowing what is going on. Once you master this, you can always shorten the work by using some short cuts and special cases. Thanks for your comments, I like to read them. Keep us all active. Good luck!
Depending on the subject and problem, you can apply the techniques and methods in control systems in real-world systems. In reality, you determine the system parameters (e.g. transfer function) from a transient response or frequency response or combined. After this step, there is always some iteration and tuning going on, which will get you closer to the actual model of the system. This will then allow you to design a proper controller according to the specifications. You may consult a good book where they discuss practical problems, for example: Control Systems Engineering, Norman S. Nise
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Спасибо за отличный урок, за знания!
Thanks for your message. You are welcome!
Wow, thank you for making such a good effort to discuss the topic of time-delay in control systems.😀🙏
You are welcome!
could do for PI controller?
What do you mean exactly?
)
(*-*)
I don't like to operate with complex numbers so I use this, imo, simpler way to find the critical gain.
L(s) = 4K/(4+s) exp(-0.6s)
L(jω) = 4K/(4+jω) exp(-j0.6ω)
We can divide the loop gain in two parts, absolute value and phase.
|L(jω)| = 4K/√(4^2+ω^2)
∟L(jω) = -atan(ω/4)-0.6ω
Then make the phase equal to "-π" to find the critical frequency.
∟L(jω) = -π
atan(ω/4) + 0.6ω = π
This equation is (more or less) the same as the one shown in the video "ω/4 + tan(0.6ω)=0", but it doesn't have infinite solutions, just one.
So when using an iterative method to find the solution, any starting value can be choosen. That's and advantage imo. ω = 3.94 rad/s.
Once the critical frequency is found, just calculate the absolute value of the loop gain.
|L(j3.94)| = 4K/√(4^2+3.94^2) = 0.712K
Since we said that the phase was equal to "-π", that loop gain must be a negative real number.
L(j3.94) = -0.712K
-0.712K = -1 --> K = 1.404
No need to operate with complex numbers haha.
Even though you are saying that there is no need to operate with complex numbers, the way you work out the problem make use of complex numbers. What is the reason for dividing the loop gain into absolute value and phase? Here, you assume that the loop gain is a complex expression.
You can call the method or numbers anything you want, but it is still the same, so there is a NEED for complex numbers. That is not really funny, I know :)
@@CanBijles
I think there was a misunderstoodment.
I don't want to avoid complex numbers at all, in fact I like them, what I don't enjoy is making huge operations with them.
For example, if there is a long product of complex numbers in the denominator and I want to "put" them in the numerator... That can be kind of messy.
"Even though you are saying that there is no need to operate with complex numbers, the way you work out the problem make use of complex numbers"
It is true that there are complex numbers written in my comment, I mean, the whole point is to make s=jω, that's unavoidable. But didn't operte with them so I don't see any contradiction there.
"What is the reason for dividing the loop gain into absolute value and phase? Here, you assume that the loop gain is a complex expression"
The loop gain is L(jω), isn't it? That is a complex expression, so it can be divided in absolute value and phase, like in the Bode diagrams. Why don't do it if it helps to solve the problem?
For example, if we take the loop of your next video (of this topic):
L(s) = 160K/((s+4)(s+5)(s+8)) exp(-0.2s)
L(jω) = 160K/((4+jω)(5+jω)(8+jω)) exp(j(-0.2ω))
Absolute value and phase
|L(jω)| = 160K/√((4^2+ω^2)(5^2+ω^2)(8^2+ω^2))
∟L(jω) = -(0.2ω + atan(ω/4) + atan(ω/5) + atan(ω/8))
Make phase equal to "-π".
0.2ω + atan(ω/4) + atan(ω/5) + atan(ω/8) = π
This, got the equation to find the critical frequency pretty much straight forward. Once calculated, next steps are trivial: plug it in the absolute value, make it negative, equal it to "-1" and isolate "K".
On the other hand, to get to a similar equation in that video, several operations with complex numbers were made...
That's what I meant when I said "there is no need to operate with complex numbers".
This is not a critique btw lol, I like your videos, they are helping me a lot to understand this subject. The way to solve the problems is perfect too.
Just wanted to point that thing out.
@@ilPescetto There are definitely other ways to work out a problem, but the structured way to work out a problem is by using the official route, even more when you explain this to others. There are special cases which allows us to work out a problem faster, also with some experience, you can almost feel what the answer might be. I also use them, but merely for myself as a short cut.
My objective with these videos on this channel is how one can do this step by step without using any short cuts and not knowing what is going on. Once you master this, you can always shorten the work by using some short cuts and special cases.
Thanks for your comments, I like to read them. Keep us all active. Good luck!
How can i use the control theory in reality sir ?
Depending on the subject and problem, you can apply the techniques and methods in control systems in real-world systems. In reality, you determine the system parameters (e.g. transfer function) from a transient response or frequency response or combined. After this step, there is always some iteration and tuning going on, which will get you closer to the actual model of the system. This will then allow you to design a proper controller according to the specifications. You may consult a good book where they discuss practical problems, for example: Control Systems Engineering, Norman S. Nise
how did you solve the value for omega? didn't get the same value
I show this from step 2 in the video. See from 00:02:30. Remember that omega must be in rad/sec and also set your calculator to radian.
@@CanBijles -4tan(0.6w), what value of omega did you put here?
@@ganeshneupane1721 You need to solve the equation w = -4tan(0.6w). This will give you w = 3.94 rad/sec.
@@CanBijles -4tan(0.6w) here the omega doesn't have any value. my question is what value of omega should I use there? is it 1, 2, 3, ......?
@@ganeshneupane1721 Did you solved the equation?