Final Value Theorem and Steady State Error
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- Опубліковано 6 кві 2013
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The Final Value Theorem is a way we can determine what value the time domain function approaches at infinity but from the S-domain transfer function. This is very helpful when we're trying to find out what the steady state error is for our control system, or to easily identify how to change the controller to erase or minimize the steady state error.
Two proofs of the Final Value Theoerm:
www.ee.kth.se/~tn/.../Basic.../Initial_and_Final_Value_Theorems_uk.pdf
renyi.ece.iastate.edu/zhengdao/initial-value-theorem.pdf
Errata:
7:55 I wrote "If all poles are in LHP then type 1 and FV=0" and it should be "If all poles are in the LHP then type 0 and FV=0"
11:53 I left the 's' off the final value theorem equation. It should be the limit as s approaches 0 of 's' times the transfer function.
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I will be loading a new video each week and welcome suggestions for new topics. Please leave a comment or question below and I will do my best to address it. Thanks for watching!
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Longer than I had originally thought :) From crafting the idea and the flow of the lecture, to drawing (or recording video in some cases), to editing/voice over, and posting to UA-cam usually takes me about 10 hours per video spread out over 3 days. And since I also work a full-time job that is why I can only do one video a week. But I really enjoy making them and I've been getting a lot of great responses from people like you so it's easy to continue. Thanks for the comment!
Mate, you are an absolute legend. I'm a second year student studying robotic engineering and you have saved my arse! Seriously. You have made this boring subject (because of how it's taught) really interesting and given me a great intuitive understanding of it. This will have a huge impact for my degree (as control is used in many subjects). Thank you!!
Just ingenious teaching. Brian, you really raised the bar for making control topic not only interesting but enjoyable to watch. Your teaching style needs to be considered as a standard way of teaching as you optimally drive the points home. Kudos!
Man it is from 7 years and it really benefits me now in 2020 , so i would like to thank you for your efforts and keep up the good work
Every time I encounter a new topic in my controls theory curriculum and I see you've made a video about it, I let out a sigh of relief and smile. I hope you're aware of how impressive and useful these tutorials are.
You're awesome!, I have learned a lot from you, rather than one of my "teachers". Thank you for your videos man.
I now feel like I have a chance of actually learning this topic to the point where I can use it in a practical way. I love your style and presentations. About every 5 minutes, I have a moment where I say "Ooooohhhhhh, yeah, got it now......"
Thank you for sharing! fantastic!
I searched UA-cam for the topic and hoped that I would find one of your videos, and there it was. Thanks for the great lectures!
Damn, this is gold. Beautiful and concise, you make learning a lot faster and easier!
Very Nice Brian! I really enjoy you the way you explain the concepts. Thank you. Keep up the awesome videos!
Hi Henning, that is a great list, thanks for the suggestions! I have a plan for the next few videos already but I'm adding these topics to the list for sure. I really like the first topic ... sort of a survey of popular control methods. I'll work on something. I appreciate your comment, thanks again.
I would love to continue this series on through modern control. I have some ideas and concepts I want to finish up in classical control first before moving on so it might be 4-5 months still before I get to topics like state space. But it'll come eventually!
The best explanation ever so far ! Appreciated
You know what? Our department's PhD qualifier exam contained the problem that I found answer in your video!! The type number and its impact on the performance of the system. I didn't have much time to review control theory to prepare for the exam, but I did watched lots of your videos. I only saw type number once in your video and I still remembered that in yesterday's exam. Thank you!! I will recommend all my friends to watch your control video as important preparation for qualifier!
Thanks for the comment. I'll be address Nyquist after the lead/lag videos ... so hopefully in 4 or 5 weeks.
You are amazing.. Please don't ever stop teaching :)
you're such a king man, I have a professor who graduated from MIT but you still explain way better!!
Best one I heard teaching control
really Thank You
YOU MADE EVERYTHING EASIER. THANKS DUDE!
Thanks you for your correct explains on FVT &Steady State Error ,wich is so informative to understand control engineering easily.
You are very good, my man!
with modern software's ability to solve differential equations easily, process control can be taught almost entirely in the time domain. Laplace is hanging on only because its engrained in process control texts. Excellent teaching! Perhaps you could do a series for understanding process control within t.
Very descriptive and helpful. Thank you!
Great lecture! Congrats! :)
Simple and to the point.
Thank you sir.
That is so clear and awesome! Great video
Thank you, Mr Douglas. You save my life
I have been getting Nyquist requests non stop recently! I'll definitely cover that topic but unfortunately it won't be before your final. Good luck and hopefully you'll still find the videos helpful after your class.
iam nothing in control systems without brian douglas .thanks to you and you are my lovely gift.
You the real MVP during this time of online classes man.
Thanks for providing us with great lectures for free
I had that "aha" moment (following details closely, but then feeling like all of a sudden thrown above to the sky for a bird's eyes view) at: "We can find final value of output, but who cares?" -> leading into steady state error as the meaningful measurement of system performance... That seems really obvious now, but somehow completely missed it while reading a textbook. Thanks for kindling the intuition Brian!
Wow that's a lot of work. From a viewer's point of view though, it definitely pays off. I'm currently doing controls as a subject and it's probably the most interesting subject. Keep up the good work, and hopefully you get some sponsorship or something for your vids to push you forward.
The system type comes from characteristics of the error function in a closed-loop control system. Some of the first applications of control system design were motor controls.
Type 0 System: The error can go to zero. (motor position control).
Type 1 System: The first derivative of the error can go to zero (motor speed control, but not position).
Type 2 System: The second derivative of the error can go to zero (motor acceleration control, but not velocity or position).
WOW! man I love your videos! please keep up with your good work! wish we had a prof at the university like you!
you make control theory fun to learn thank you
Hi Abu, I'll continue to touch on system ID in my Control System Lab videos which I'm trying to put out every other week. But in the lecture series I think I need to address so of the other topics first before hand which is why I've switched topics so abruptly.
Exam in 3 hours, cheers dude that was super helpful :)
This is exceptional. Thank you so much!
Brian your videos are ridiculously good. You somehow manage to teach what would be more than 1 hour of lecture time in less than 15 minutes and yet I get more out of these than any lecture.
Out of curiosity, how long does each one of these take you to produce?
thank you so much for making these.!!!
HI Aaron, if you divide by 's' and replace 's' with zero you are finding the final value of the function to an impulse input. You have to multiply the transfer function by 's' to find the final value to a step response. So for a step response the multiply by 's' and the divide by 's' cancel and you're left with the original transfer function where you set 's' to zero. Then you get 10/5 which is 2. I'm betting the book was solving the final value to a step input.
That was fire!! Great job!!
these lectures are gospel, better teaching than the lecturers I pay tuition for.
Mate!!!! Absolutely love your videos!!!! You're like the Sal Khan of Control Systems :-)
Andy, I don't follow any particular book when creating these lectures so I can't recommend one single book to use to follow along with. However, my all time favorite controls book is "Control Theory" by JR Leigh. If you're looking for a book that explains the topics in straightforward language this is the book. It's not heavy on math but if you're looking for more depth the reference section will point to other books. Also, you can read a lot of it for free on google books so that's great too!
Thank you. Your video helped alot!
You're amazing.
Thank you so much!
your videos are sick bro...thanks
You are special! Thanks Brian!
Great video Brian. Helped alot! thanks!:)
i cant just thank......
Some day i will teach someone something valuable like this ..........
Just saying thanks is not the best way to be grateful, it should come from the heart and that becomes action.........
i ll for sure do something valuable for nothing.....just like you do !
This is just amazing!
You should be an axual teacher. So many hard to grasp topics in one playlist, explained nicely and cleanly while my teacher didn't manage to do the same in half a year of lectures
@younesshah, where would the 2 come from? If we were integrating in the time domain then there would be some coefficient, but we are integrating in the S-domain. In the S-domain integration is just 1/s. So to integrate an impulse function (1 in the S-domain) once would be 1*1/s = 1/s or a step. Then just keep multiplying by 1/s to get higher orders, 1/s^2 for ramp and 1/s^3 for parabolic.
By the way, congrats on taking your last exam for your degree! I'm sure it feels great to be done!
So helpful!! Greetings from LiU Sweden =)
So THATS WHAT THOSE SYSTEM TYPES ARE?!?! thanks man took me way too long trying to figure something so simple out.
I think you're about to save my life. Thank you
You've just saved my bacon for my 1st assignment doing my masters degree... thank you so much!
Hi vibhu, a zero in a transfer function is just an 's' in the numerator which corresponds to a derivative. However, you have to be careful because adding a derivative term to your plant G(s) won't actually help solve this tracking problem in the feedback system. That's because the system transfer function is U/(1+G) and so there's no way to actually ONLY add a zero to this closed loop transfer function by ONLY changing G. At least one way to get around this is by adding a feed forward path.
Thanks a lot...this was helpful
The best way to learn control systems!!
What I'm confused about is that I read in multiple sources that a type 2 system achieves perfect tracking of a ramp input... what does that mean? I can see how a type 1 achieves perfect tracking of a step input, but not the type two for ramp :$
Brilliant Video
really good video thx!
what i great videos , all this serie of videos will help me a lot in the unversity ........
''The impulse response of an integrator will be the integral of the impulse''
Can you elaborate more? How the integral of the impulse became a step function?
I know it's a simple question, but it's not exactly clear for at the moment.
By the way, you are explanation is just excellent!
First I would like to thank you very much for your effort for producing this videos in such a amazing quality. It helps me really much during my studies!
I have a little question, I'm apparently bad in mathematics. Around minute 9:00 you start to explain how the final value can be calculated for the different system types. My question is when I have the transfer function 1 / (s² + s) , do I have to factorize it , or can I just simple put all the s's to 0 and get my answer as 1 / (0 ²+ 0 ) = 1. In the following example for a system with a step input, we are using lim s ->0 s * 1/s * 1 / ( s² + s). Because I can short out the s * 1/s all left is the TF from the previous example 1 / (s² + s) (System 1) but now it equals infinity? Shouldn't it equal = 1 as well ?
9 years on youre helping me with my biomed engineering classes xd
thanks a lot..it really helped
Brian, you are on top of this. Great learning from you. I have a control problem I want to share and find a way for matlab to solve and find the coefficients and two sensor system and one output. Do you have or use fmincon in mathlab?
Your Videos really help my understanding! Thank's a lot! Are you going to do some vids on state space representation?
great video thank you so much
Thank you sir from Waterloo University, Canada !
I find this very very relaxing. This is music to my ears
Thanks SO much!
so helpful thanks
You are perfect man ! :)
You are my friend. Keep telling me facts.
I liked your video Brian, i failed to understand this concept for three weeks, but you made me understand. I am working on a project whereby i am making videos for high school kidz in my country Zimbabwe, what tools do you use. I have bought a bamboo tablet, and i am using smoothdraw, and a screen capture, but i can't write anything meaning ful on my bamboo tablet
Hello Fidelis, I posted a video showing how I make a control system video lust last week. I explain there which hardware and software I use. You should be able to create a very similar style video using the tablet and the software you mention. As for the drawing it took me about a week of practice to learn how to write on the tablet! It's not like writing on paper. I kept writing up at an angle or just really sloppy. Just stay with it and you'll get it. Good luck with your project.
your videos are amazing, my lecturers should be ashamed, they make this content seem impossible to understand, you make it seem fairly easy. Thank you so much, i dont know if you get anything back from this, in that case you are truly selfless. In my eyes selflessness is the most important and most often neglected human trait.
Great Video! However, I'm wondering if you made a video to explain what one could do to analyze the SS error of a system with poles in the right half plane - or is that even possible? Thanks!
like something like this Question:
a) Plot this Nyquist diagram:
GH(s)= 50 / s(s+2)(s+4)
b) Investigate the stability of the system based on Nyquist diagram.
c) Use Routh-Hurwitz stability criterion to validate the stability
Thank you sooo much!
Super sir. awesome
What will happen of steady state error if there is any disturbance function add at system. what will be formula or procedure?
Its so hard for me, ah damn , thanks Mr 👍
THANK YOU!
Thank you sir..
great vid
This is perfect
Basically, the feed forward path would predict how to change the output so that it could follow an accelerating input and then the feedback path would attempt to reduce the error to zero. In this case the error would come from the differences between the feed forward model and the real system. Unless you're familiar with what I just said already I don't think this explanation will help you much :( I'll address feed forward in the future and hopefully it'll clear things up then.
thank u man!
Awesome!
This dude is a saint
this is awsome
How do you find the final value if there is a single pole on the RHS? Example the transfer function is 3 / (s^2+2s-3) and we have to find the final value of system with a step input.
You are amazing
Can you go into further detail about the end when you design G(s) on the bottom? I'm lost there
In ess do you just take the plant into equation or the whole system ( controller, sensor)
Today I understood what FVT is really ! In my full course I didn't knew what this really means lolz :D