Nyquist Diagram | Stability Criterion | Example #1

In this video, we will discuss the Nyquist diagram and stability of a third-order system in closed-loop configuration. The system is controlled by a proportional controller. We will calculate the required proportional controller gain to have a stable closed-loop system. We follow a logical procedure and provide the solutions step by step such that it clear for you what and why we carry out a specific action.
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[@ivancalvimoreno629]

Excelent, simple and practical. Thanks!

[@CanBijles]

Great to know you liked the video! You're welcome!

[@SMV1972]

Спасибо за ваш труд. Спасибо за отличный урок!

[@CanBijles]

Thanks for your message! Glad you liked the video. Share the knowledge :)

[@kaedeumi2072]

Excellent video, well explained👍

[@CanBijles]

Thanks, you are welcome!

[@kaique081000]

Excellent explanation!! Very didactic. But I have a question. I just cannot fully understand why -1 and 180 phase is bad for the stability of a system. Can you make a comment about that ? Thank you very much

[@CanBijles]

Thanks, you are welcome! Share the knowledge :)
There are many ways to describe this, but here is my version:
The stated problem considers a negative feedback system, this is required for stable systems, like amplifier and filters. Having a negative feedback, the total closed-loop system has a sign inversion in the loop, which means 180 degrees. Now, if an additional 180 degrees occurs due to components, frequency of operations or for any reason, then the total phase in the loop will be 360 degrees. Phase shift of 360 degrees means positive feedback and this can cause the system to oscillate or get out of control if there is no enough damping in the system.
I hope this clarifies the situation. Just let me know if you have further questions.

[@user-ti1to9kb6x]

Hi, thank you for your videos. They are very helpful. I have a question, if you don't mind answering. In this example you found Wgm by setting Φ(w)=-180. In another example, you found Wgm by multiplying the numerator and denominator of the TF by the conjugate of the denominator then setting the imaginary term=0. Can I use any method at any time to find Wgm or is there a specific occasion for each method? Thanks a lot

[@CanBijles]

Thanks for your message. Glad to know you liked the videos :)
You can use both methods, but depends on the problem which one is faster and easier. When you make the imaginary part zero, you will only have the real part, having the phase 180 degrees.

[@maheralfadel5490]

Thank you for the useful information Can you please explain to me how you obtained the value of w=7.21 rad/sec? I have tried a lot, but I haven't obtained anything. I need these steps for my exam.?

[@CanBijles]

You're welcome! You need to set up the transfer function of the loop gain. The phase expression of the loop gain transfer function must be equated to -180 degrees and you need to solve for the omega, you should do this numerically. I actually discuss this from the start of the video, maybe you can check it again. Good luck.

[@dienau6313]

I have a question, if G(s) = 400/s(s+2)(s+3), which method should I use to solve?

[@CanBijles]

It depends on what do you want. In general, it does not depend on the transfer function.