Final Value Theorem and Steady State Error

Подписаться 292 тыс.

Просмотров 322 тыс.

50% 1

Get the map of control theory: www.redbubble.com/shop/ap/550...
Download eBook on the fundamentals of control theory (in progress): engineeringmedia.com
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.
Don't forget to subscribe! I'm on Twitter @BrianBDouglas!
If you have any questions on it leave them in the comment section below or on Twitter and I'll try my best to answer them.
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!

Опубликовано:

6 апр 2013

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 190

@BrianBDouglas 11 лет назад

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 RU-vid 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!

@rohlay00 4 года назад

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!!

@youcefyahiaoui2644 10 лет назад

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!

@mohamedebrahim4977 3 года назад

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

@Pyrohawk 3 года назад

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.

@BrianBDouglas 11 лет назад

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.

@GalaxianExplosionGS 10 лет назад

You're awesome!, I have learned a lot from you, rather than one of my "teachers". Thank you for your videos man.

@JetNmyFuture 7 лет назад

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!

@BrianBDouglas 11 лет назад

Thanks for the comment. I'll be address Nyquist after the lead/lag videos ... so hopefully in 4 or 5 weeks.

@pacrat90 8 лет назад

I searched RU-vid for the topic and hoped that I would find one of your videos, and there it was. Thanks for the great lectures!

@BrianBDouglas 11 лет назад

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!

@Thewowhahahawow 5 лет назад

Damn, this is gold. Beautiful and concise, you make learning a lot faster and easier!

@alishahabi6274 7 лет назад

Very Nice Brian! I really enjoy you the way you explain the concepts. Thank you. Keep up the awesome videos!

@BrianBDouglas 11 лет назад

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.

@chenming6940 9 лет назад

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!

@widdalightsout 10 лет назад

You are amazing.. Please don't ever stop teaching :)

@isagumus1 5 лет назад

The best explanation ever so far ! Appreciated

@BrianBDouglas 11 лет назад

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.

@doktoren99 9 лет назад

You are very good, my man!

@ahmedkhaledmohamedmohamed746 5 лет назад

Best one I heard teaching control really Thank You

@hanans7527 8 лет назад

YOU MADE EVERYTHING EASIER. THANKS DUDE!

@mrjohn6021 6 лет назад

you're such a king man, I have a professor who graduated from MIT but you still explain way better!!

@BrianBDouglas 11 лет назад

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!

@BrianBDouglas 11 лет назад

@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!

@wilerjrxd 8 лет назад

Great lecture! Congrats! :)

@markkerollos 11 лет назад

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?

@hanbiniwa 7 лет назад

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!

@kevinklose 8 лет назад

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 :$

@pieceworth 5 лет назад

Thank you, Mr Douglas. You save my life

@Hypnodr0ne 7 лет назад

Very descriptive and helpful. Thank you!

@yejinlee9721 8 лет назад

Thanks you for your correct explains on FVT &Steady State Error ,wich is so informative to understand control engineering easily.

@jessstuart7495 5 лет назад

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).

@markkerollos 11 лет назад

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.

@mannykrish1 10 лет назад

iam nothing in control systems without brian douglas .thanks to you and you are my lovely gift.

@lolitahaze6470 9 лет назад

That is so clear and awesome! Great video

@dandyremix2360 6 лет назад

Simple and to the point. Thank you sir.

@mandeadd 3 года назад

You the real MVP during this time of online classes man.

@BrianBDouglas 11 лет назад

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.

@frankcollins6580 2 года назад

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.

@timothdev 9 лет назад

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 !

@mdnafiskhan9336 11 лет назад

Thanks for providing us with great lectures for free

@AJDification 6 лет назад

Exam in 3 hours, cheers dude that was super helpful :)

@pimpingbuss 11 лет назад

WOW! man I love your videos! please keep up with your good work! wish we had a prof at the university like you!

@BrianBDouglas 11 лет назад

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.

@imahugeman 5 лет назад

This is exceptional. Thank you so much!

@sashamuller9743 4 года назад

you make control theory fun to learn thank you

@deanmillard9853 5 лет назад

these lectures are gospel, better teaching than the lecturers I pay tuition for.

@mdasrafulkabir3659 9 лет назад

What will happen of steady state error if there is any disturbance function add at system. what will be formula or procedure?

@OliverFoote 3 года назад

I think you're about to save my life. Thank you

@phillipmaser132 4 года назад

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?

@zoen2862 6 лет назад

You've just saved my bacon for my 1st assignment doing my masters degree... thank you so much!

@joshuapatterson5095 7 лет назад

Mate!!!! Absolutely love your videos!!!! You're like the Sal Khan of Control Systems :-)

@switchology_io 11 лет назад

Your Videos really help my understanding! Thank's a lot! Are you going to do some vids on state space representation?

@javoncook2441 7 лет назад

That was fire!! Great job!!

@OzzzyKane 7 лет назад

thank you so much for making these.!!!

@BrianBDouglas 11 лет назад

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.

@BrianBDouglas 11 лет назад

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.

@Contarius9 10 лет назад

You're amazing. Thank you so much!

@randomandspontaneous 11 лет назад

Great video Brian. Helped alot! thanks!:)

@stereodrive 5 лет назад

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 ?

@R0kmyS0X 8 лет назад

Thank you. Your video helped alot!

@LKodiak 6 лет назад

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

@sarvariabhinav 7 лет назад

your videos are sick bro...thanks

@yash_jivrajani 8 лет назад

The best way to learn control systems!!

@aleksandaryanarov7141 10 лет назад

Awesome! And how can I calculate the gain of a system to reach a SSe of 0.2?

@fisfisarenskanal 4 года назад

So helpful!! Greetings from LiU Sweden =)

@aregayohannes9973 2 года назад

You are special! Thanks Brian!

@arjenwassenaar9963 4 года назад

This is just amazing!

@OmarSiddiqi__ 9 лет назад

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!

@DrunkinHulk 6 лет назад

Such a great Video, However I am still stuck. @11:53 you missed an S but didn't specify where the S would go making the equation useless am me stuck. I have to do a unit step and then a unit ramp and I found the unit step somewhere else. I'm hoping to reverse that and find the S so I can do the ramp. Otherwise great video and I learned a lot. Thanks

@vijayn2443 10 лет назад

Thanks a lot...this was helpful

@deepaksree6 6 лет назад

can you do a video on how to handle errrors in nonunity feedback system?

@thewayoftheroll6358 Год назад

Can you go into further detail about the end when you design G(s) on the bottom? I'm lost there

@lazio20roe 11 лет назад

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.

@vishnunarayanv526 11 лет назад

In order for the system to respond to a constantly accelerating input, we change the system type by adding a POLE at the origin, so that an extra s comes in the numerator and the error term goes to zero for s =0, right? Towards the end of the lecture, it was told to be a zero. We add a pole so that the transfer function itself helps in integrating the input thus making the output to accelerate as fast as input??

@SuperVaibha 11 лет назад

Hi brian could you please elaborate on how to add a zero in a transfer function?

@himym910 9 лет назад

Thank you sir from Waterloo University, Canada !

@smiwabiva6657 8 лет назад

I find this very very relaxing. This is music to my ears

@fidelischimombe2800 11 лет назад

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

@sajjankumarhello 9 лет назад

Hey Brian! If we have a pole on Origin along with pole on Imaginary axis, can we still apply the Final Value theorem ? what will be the system type ? and Thanks for you videos.

@magedelsharkawy1366 9 лет назад

sajjan kumar you cannot apply Final Value Theorem to a system if it has 1 pole on the imaginary axis or the RHP. Even if you have 1 pole in the LHP you still cannot apply FVT.

@sivonparansun 7 лет назад

I am interested in getting a copy of your book! whats the best way to do that

@lazio20roe 11 лет назад

do you have another video with a Ess example with numbers? thanks again

@BrianBDouglas 11 лет назад

If I ever see you in real life than I shall take you up on your offer!

@adrianrevolotaipe3855 4 года назад

what i great videos , all this serie of videos will help me a lot in the unversity ........

@TheBirdMan 9 лет назад

Today I understood what FVT is really ! In my full course I didn't knew what this really means lolz :D

@davidfof13 11 лет назад

Excellent. Brian can you do a video on Nyquist analysis, Nyquist diagram and Nyquist criterion? I want to understand the whole thing. Cheers if you can

@13shamas 3 года назад

In ess do you just take the plant into equation or the whole system ( controller, sensor)

@JackST95 8 лет назад

Brilliant Video

@MexterO123 9 лет назад

So the final value of a system changes depending on the input since depending on the input you could change the system type? correct?

@v4nGu4rD666 11 лет назад

hey Brian, can you please do a video on dynamic error series as well? Thanks in advance

@alessandrotrujillo2605 5 лет назад

What would happen if not only we get roots on the y axis but also on the right hand side? Would it be oscillatory? or would it go to infinity? Thanks in advance

@geethapallati7252 6 лет назад

Is final value and steady state error are same in every case

@benjaminjohannesson2095 8 лет назад

When taking the limit to obtain the steady state error would it be s * (U(s)/(1+G(s))?

@prashantsharma3134 8 лет назад

Thanks Brian... Can you also explain "DC Gain" of a system. Is DC gain and Final Value/Steady state value are same??

@malharjajoo7393 8 лет назад

+Prashant Sharma - I think its the same for a step input

@xMrJanuaryx 7 лет назад

I have a question. What if I add a disturbance to the last system and I want to find the steady state error. Is it going to be the superposition of e(s)/u(s) + e(s)/d(s) where d(s) is my disturbance?

@gypsycathunter 10 лет назад

You are my friend. Keep telling me facts.

@MrKlein96 8 лет назад

are type 2 systems always unstable?

@alexanderali2971 5 лет назад

great video thank you so much

@lazybites7286 Год назад

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.