when you put Zpi = 0.5 angle criterion at 14:20 does not satisfy. We have found PHI of (Zpd) = 83, since total of PHI of (Zpi) + PHI of (Zpd) = 226, PHI of (Zpi) = 143. And we know that Zpi is between 0 and -1 so we should find tan(180 - 143) = 6/x (x is the bottom edge of triangle) from this equation we get x = 7.96 so Zpi = 0.04. I dont understand why you put Zpi = 0.5 directly. Can you please explain where am i wrong? thanks for the great videos.
Thank you for your helpful video and the step-by-step guide. I have a question. When I calculate my PI controller, using the angle criterion, the angle came out to be larger than 180 degree, what should I do in such an occasion? My plant has 2 complex poles.
Thanks for your message and you are welcome! I am glad you liked the video. About your questions about the phase criterion in the root locus method. If the sum of the phases by all the poles and zero do not add up to -180 degrees, it does not necessary means that the controller will not do the job. It might be even better because you took, unintentionally, a design point which has a more strict requirements. It could be also worse than you have expected. The angle and magnitude criterion in the root locus method is a tool to get to the required specifications for a controller, but we all know it is sometimes necessary to tune the controller (gain, zero and or pole location). I also do that in the videos, because it is always first time right.
You're welcome! The PI pole and zero are relatively close to each other in order to make the negative phase contribution of the PI controller small. For example: if the PI controller is at s = 0 and the PI zero is at s = 2 , it could be that the PI phase contribution is too negative, so you need to redo the calculations for the PD-controlled system or need to add more positive phase because of too much negative phase by the PI controller. Is this explanation helpful for you?
If you start with the design of the PD controller part first and then add the PI controller part, then the required adjustment in the gain of the final PID controller is very small compared to the gain of the PD controller. However, this is only true if the pole and zero of the PI controller is close to each other and far away from the dominant closed-loop poles.
Благодарю Вас за очень полезный урок! Скажите пожалуйста , если передаточная функция имеет ноль и два комплексных полюса, будет работать этот метод, можно будет им пользоваться? Спасибо за ответ
Thanks for your message. The root locus method uses the dominant closed-loop poles to estimate the performance of the closed-loop system with all the poles and zeros. The location of the dominant closed-loop poles are used as the design point to calculate the required controller parameters.
Thanks for your message! If the poles or zeros are complex, you can also determine the phase contribution for each pole and zero. You basically draw a line connecting the pole or zero with the design point (dominant pole). Using geometry, you can determine what the angle of that line is with respect to the positive real axis. See for more details Chapter 6 in Modern Control Engineering, Katsuhiko Ogata, 5th Edition
@@DiegoMartinez-sr9rm It really depends on the available power of your system. For low power applications, it might be not possible to realize the gains. Try to realize the transfer functions using op-amp circuit to see what is really possible using low power electronics.
If the poles are complex, you can still calculate the magnitude and phase contribution as given in this video. Just use geometry from the complex poles towards the design point to determine the magnitude and phase.
Thank you! I ended up getting a first order step response but I am supposed to get a Mp of 10% , ts2% of 1.5s with zero steady state error. Any idea of what could have gone wrong?
@@aleceaolivier2111 The response is determined by the closed-loop poles and zeros of the open-loop system and the controller (if there is any). The formulas for the overshoot and settling time assumes that you have a second-order system with only poles (thus no zeros). If you have a zero or higher-order system, then the formulas might get you the correct results.
@@aleceaolivier2111 It depends on the specifications. If you need a zero steady-state error for step input, then you will need integral control if the system without the controller does not have a pole at s = 0.
COMPLETE List: Root Locus Design Method - Controller Design: ua-cam.com/play/PLuUNUe8EVqlnY2zKWnx-6nyc6CqyPApDD.html
when you put Zpi = 0.5 angle criterion at 14:20 does not satisfy. We have found PHI of (Zpd) = 83, since total of PHI of (Zpi) + PHI of (Zpd) = 226, PHI of (Zpi) = 143. And we know that Zpi is between 0 and -1 so we should find tan(180 - 143) = 6/x (x is the bottom edge of triangle) from this equation we get x = 7.96 so Zpi = 0.04. I dont understand why you put Zpi = 0.5 directly. Can you please explain where am i wrong? thanks for the great videos.
Thank you for your video!!!
It's really helpful ^^
Thanks for your message. Great to hear it helped you out. See my channel for more examples on root locus design and other topics.
Thank you very excellently
You are welcome :)
Thank you for your helpful video and the step-by-step guide. I have a question. When I calculate my PI controller, using the angle criterion, the angle came out to be larger than 180 degree, what should I do in such an occasion? My plant has 2 complex poles.
Thanks for your message and you are welcome! I am glad you liked the video.
About your questions about the phase criterion in the root locus method. If the sum of the phases by all the poles and zero do not add up to -180 degrees, it does not necessary means that the controller will not do the job. It might be even better because you took, unintentionally, a design point which has a more strict requirements. It could be also worse than you have expected.
The angle and magnitude criterion in the root locus method is a tool to get to the required specifications for a controller, but we all know it is sometimes necessary to tune the controller (gain, zero and or pole location). I also do that in the videos, because it is always first time right.
Thanks for video
Can you explain me the reason that why we should put zero of PI controller nearby the pole of itself? in step3
You're welcome!
The PI pole and zero are relatively close to each other in order to make the negative phase contribution of the PI controller small.
For example: if the PI controller is at s = 0 and the PI zero is at s = 2 , it could be that the PI phase contribution is too negative, so you need to redo the calculations for the PD-controlled system or need to add more positive phase because of too much negative phase by the PI controller.
Is this explanation helpful for you?
@@CANEDUX I understand!
thanks for replying fast it was very helpful video for me
@@이동훈-g6p5n Glad to know!
When we combine the PI control with the PD, we don't need to readjust the gain of the controller?
If you start with the design of the PD controller part first and then add the PI controller part, then the required adjustment in the gain of the final PID controller is very small compared to the gain of the PD controller. However, this is only true if the pole and zero of the PI controller is close to each other and far away from the dominant closed-loop poles.
@@CANEDUX got it, thank u ☺️
@@DiegoMartinez-sr9rm Great 👍 You are welcome!
Благодарю Вас за очень полезный урок!
Скажите пожалуйста , если передаточная функция имеет ноль и два комплексных полюса, будет работать этот метод, можно будет им пользоваться?
Спасибо за ответ
Thanks for your message.
The root locus method uses the dominant closed-loop poles to estimate the performance of the closed-loop system with all the poles and zeros. The location of the dominant closed-loop poles are used as the design point to calculate the required controller parameters.
Sir, what if the closed loop pole is above real axis (eg. -4+1j, -4-j) , how to calculate the angle with dominant pole?
Thanks for your message! If the poles or zeros are complex, you can also determine the phase contribution for each pole and zero. You basically draw a line connecting the pole or zero with the design point (dominant pole). Using geometry, you can determine what the angle of that line is with respect to the positive real axis.
See for more details Chapter 6 in Modern Control Engineering, Katsuhiko Ogata, 5th Edition
After step 2, when you get the PD controller the gains would be Kd = 11 and Kp = 11*8.73?
That is correct.
@@CANEDUX just curiosity and understanding it's just an example, but in a real life system that would be a huge derivative gain right?
@@DiegoMartinez-sr9rm It really depends on the available power of your system. For low power applications, it might be not possible to realize the gains. Try to realize the transfer functions using op-amp circuit to see what is really possible using low power electronics.
@@CANEDUX nice nice, reeeeaaaally interesting
@@DiegoMartinez-sr9rm Good luck 👍
Sir please can you tell what does the blue circle indicates in the root locus plot
A circle indicates a zero, a cross indicates a pole.
Thank you sir for the reply, but i was asking the large blue circle in the time 27.40
Time 27.40 of the video
@@sweta7667 That is the shape of the root locus plot. This depends on the location of the poles and zeros. Try this also in MATLAB.
Hi sir, what happens if your open loop poles are not on the real axis being complex conjugates?
If the poles are complex, you can still calculate the magnitude and phase contribution as given in this video. Just use geometry from the complex poles towards the design point to determine the magnitude and phase.
Thank you! I ended up getting a first order step response but I am supposed to get a Mp of 10% , ts2% of 1.5s with zero steady state error. Any idea of what could have gone wrong?
Should I rather them try a PI controller than a PID?
@@aleceaolivier2111 The response is determined by the closed-loop poles and zeros of the open-loop system and the controller (if there is any). The formulas for the overshoot and settling time assumes that you have a second-order system with only poles (thus no zeros). If you have a zero or higher-order system, then the formulas might get you the correct results.
@@aleceaolivier2111 It depends on the specifications. If you need a zero steady-state error for step input, then you will need integral control if the system without the controller does not have a pole at s = 0.
can you please show the simulation steps in MATLAB ? please
Do you mean the MATLAB code?
@@CANEDUX yes
you talk like cr7
Is that a compliment?
cristiano is the best player in the world so YES it's a compliment :) @@CANEDUX
my bad for late reply btw 😂
@@sirtodip5272 Thanks!😉