Practical Implementation Issues with a Full State Feedback Controller

In this video we investigate practical implementation issues that may arise when attempting to use a full state feedback controller on a real system. We illustrate and address control saturation as well as the inability to measure the full state of the system.
This video makes use of material developed in the previous videos so please watch these first before continuing with this lesson.
-‘Introduction to Full State Feedback Control’ (TBD)
In addition, some videos that may be helpful or relevant to the discussion at hand include:
-Modeling a DC Motor with Ordinary Differential Equations (TBD)
-Introduction to Linear State Estimation (TBD)
-Introduction to Linear State Estimation (TBD)
The Matlab/Simulink files associated with this video are located at:
-faculty.washington.edu/lum/Edu...
-faculty.washington.edu/lum/Edu...
Image of Voltaire By After Nicolas de Largillière - [1]; photographer: Erich Lessing, Public Domain, commons.wikimedia.org/w/index...

[@ChristopherLum]

In case it is helpful, here are all my Control Theory videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o. Please let me know what you think in the comments. Thanks for watching!

[@brianblasius]

Hello sir, Can you please share the link to the "Introduction to Linear State Estimation" video..

[@Gholdoian]

AE 511: The tracing of eigenvectors and eigenvalues to the states was very enlightening, I've never seen that perspective before and it definitely is insightful into developing a realistic K matrix.

[@ChristopherLum]

We'll take another look at this in AE512 in the context of aircraft systems, hopefully I'll see you there as well.

[@kenrickchan1165]

My controller was demanding kilovolts and driving up my electricity bill before this video helped me pick more reasonable poles.

[@everettkinyon7602]

Great to see some of the intuition behind choosing which poles to modify with full state feedback !

[@triskitman124]

Its great learning this after relying on PID for so long!

[@selamhendrix5252]

thank you for building on the previous topic with in depth explanations. It will be great to see how much better LQR is compared to this one which is easier to understand.

[@julianwoo1609]

It's nice to see the Matlab followup for this topic!

[@jacobcarroll3933]

Great lecture! This is an awesome explanation of the Full State Feedback.

[@mecrajib]

Thank you Sir! Learned a lot.

[@darylfishback-duran3580]

Great explanation and examples on obstacles when using full-state feedback control.

[@BonesBonesBonesBonesBones]

Amazing lecture! It's so helpful to see a quick physical example (something other than the inverted pendulum)

[@ChristopherLum]

Thanks for watching, I hope to see you at other videos.

[@sidraman6950]

Clear explanation on full state feedback. Very easy to follow

[@morganwalker940]

Very nice lecture! I really enjoyed the giant X's on the board for the poles and eigenvalues. They please me.

[@alecwicklund3311]

These lectures are so good that they cured my dog's arthritis. Thank u sir

[@ChristopherLum]

That is great to hear, I'm glad your dog is feeling better :). Thanks for watching!

[@andresfelipeluna7298]

Great lecture! Thank you very much for being so clear.

[@devinligman]

Really appreciate these videos!

[@kaisemuw7074]

AE 511. Great follow up to the previous lecture on how to actually use FSFB to meet realistic design constraints.

[@helenkuni9039]

Great video, very informative!

[@geraldocarvalhobritojunior4793]

Thanks for another excellent lecture! I enjoyed it very much!

[@ChristopherLum]

Glad you like it. There are other controls videos on the channel. Please feel free to check them out and let me know what you think. Thanks for watching!

[@MattAero]

AE511: great lecture. Definitely unsatisfying not to have a mapping of your “pole”(eigenvalue) placement to your actual state that you are affecting, so I’m quite interested in the next type of controller you mention at the end, LQRs.

[@marilynjasmer8365]

Good content on full state feedback

[@edwardsanchez2331]

great video on implementation of this controller

[@krystoflis7157]

The introduction to state estimation was great and highlights the limitation of a true full state feedback controller. Kalman filters are a powerful tool!

[@zhc3404]

hi Lis !where did you find the vidio about The introduction to state estimation ?case i can't find it

[@mohamedfarrag3869]

Yes, I am searching for this video nearly daily but I didn't find it ... Do you have any information where did it disappear ?

[@iKyle775]

Very clear explanation

[@zacharywilliams2436]

Interesting exploration of optimizing the performance of the controller while keeping the voltage the motor draws minimal.

[@jamesferrese2350]

Good info on a cool topic!

[@bartomiejwicher9374]

Great lecture!

[@hassanhumayoun2797]

can you post the link for the video -Introduction to Linear State Estimation (TBD)

[@spencergrayston1685]

Great video!

[@mrcjg42]

Yay, MATLAB! Thanks, Chris!

[@antonete125]

it’s very interesting the eigenvalues and eigen vectors analisys

[@adrianrevolotaipe3855]

Wao ,your explanation was amazing¡

[@abdallahmohamed9159]

great lecture

[@ivancordero5930]

Full state feedback is a great follow up from other control schemes

[@balasriramkodi7128]

hi christopher i didn't find below lecture video please keep the links -Modeling a DC Motor with Ordinary Differential Equations (TBD) -Introduction to Linear State Estimation (TBD) -Introduction to Linear State Estimation (TBD)

[@sifouad6945]

Me too 😢

[@cristianvalarezi7125]

I suggest you to put and indication (video time) where you start talking about the problem of measure all the system states in the description.... For the rest, it is a good explanation.

[@dhammartnawaghmare9081]

Thank you for providing such a wonderful series in an understandable format with implementations in Matlab. Sir, I am unable to find the link for 'Introduction to Linear State Estimation.' Please provide the link.

[@antonete125]

when you design an quadcopter controller, can you ignore the effects of the actuators, and choose Force and the three moments as inputs? or you must choose the four actuators commands as inputs. thanks in advance, your classes are amazing. greetings from spain.

[@omidhsd]

very very nice lecture

[@jimmiebruders2916]

great content

[@user-zp6zw3ot4o]

Deer professor, I really enjoy your videos! Can you provide the video link to the linear state estimation? Thanks a lot!

[@Bear_wonder]

this is a great video

[@ChristopherLum]

Thanks, I hope to have a follow up video on LQR control up in a few days.

[@nardiverbanac6714]

Dear Cristopher, have You already uploaded that video/lecture regarding linear state estimation? Unfortunately, I cannot find it...

[@lxzhang4911]

We are waiting for your videos of TBD

[@aakashdewangan7313]

thanks a lot

[@srikrishnang5106]

Where can i find your video on Modeling a DC Motor with Ordinary Differential Equations as you mentioned in 3:05 of the video.

[@nathanlipshutz3140]

AE511: Maybe you're going to get to this later in the video, but is there a way to set a "max" value of control authority, aka Vmax = 10 V or something, and solve for the poles associated with that max amount of control authority? Then you could solve for the FSFB gain matrix to get the best performance with that constraint in mind. I guess another consideration of FSFB is that probably in a lot of scenarios your initial conditions could be variable which could result in variable magnitude of control inputs.

[@ChristopherLum]

That is exactly the right question. This is what we will do next week with LQR control

[@hongkitchong71]

Hey guys -- to derive a state matrix, do we still need to go through lagrangian? I guess the Lagrangian helps us on deriving the transfer function, then we can use Matlab tf2ss to make it state space?

[@user-dz6vl5eq8v]

Dear Professor! We have end up our discussion here that if we can only measure shaft angle the appropriate full state control K matrice is [0.2099 0.0442 0.0031]. In other words, as you explained we are able to neglect control signals from current and speed. Now I am trying to understand the actual implementation of this controller. it seems that given this K vector we need to solve system equations find solution for U (control signal) which will be the function of measured X (angle). Is it correct?

[@jrcleeman]

what if i wanted to move the controller to a non-zero position? How would i go about simulating that?

[@justinhendrick3743]

When giving a list of poles to the `place` command, does the order matter? Say for example, a system has poles at -1 and -2 and our desired pole locations are at -2 and -3. Is there a difference between `place(A, B, [-2, -3])` and `place(A, B, [-3, -2])` ? I just ran the above example through matlab and got the same K matrix in both situations. But does there exist a system and desired pole locations such that `place(A, B, p) ~= place(A, B, fliplr(p))`?

[@andrewelstein3596]

Thanks!

[@ChristopherLum]

Hi Andrew, First let me say thank you for your generous support of the channel, it is very much appreciated! Do you have any particular interests in terms of videos or topics? I try to prioritize request made by interested parties as much as possible as I plan future videos. If you are interested, I interact personally with all Patreon members at www.patreon.com/christopherwlum. Given your interest in the topic, I'd love to have you as a Patron. In any event, I want to again say thank you for your contribution and for supporting the channel. I hope to hear from you at a future KZbin video or on Patreon! -Chris

[@fizi023]

@ChristopherLum Could you please share the link to the linear state estimation video?

[@nicolasgcavalcante]

How do I build an pole placement controller with non zero final states values, for a controller with non zero setpoints?

[@soofiyanatar9247]

How to set a motor for constant velocity instead of zero velocity using FSFB controller. Please help!

[@matthewjames7513]

Thanks for the video! When you used the place() MATLAB command you did it somewhat arbitrarily. Is there a way to determine them more optimally while applying constraints to control actuation? Thanks!

[@ChristopherLum]

Hi Matthew, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions you might have about any of the videos and have deeper discussions related these topics on Patreon. Thanks for watching! -Chris

[@kartikprakash4681]

I really enjoy your videos! Will the linear state estimation video be out soon!

[@ChristopherLum]

Thanks, unfortunately I've got a backlog of other higher priority videos so this probably won't be up for a while. I've got a lot of other videos on control theory that I hope you'll enjoy, thanks for watching!

[@BalajiSankar]

Am unable to find the introduction to linear state estimation video in your list. Could you please post a link?

[@ahungryflyer]

AE511: This video made me eager to dive into LQR, since you point out that most "real life" systems are not as clear cut with regards to the pole-state coupling we see in the DC motor example. In practice with something like a consumer quadcopter, would we see regulators like FSFB and LQR used for stability augmentation?

[@ChristopherLum]

There are several codebases that you can inspect if you are curious. The ArduCopter firmware is popular and it does indeed use some of these ideas (as well as PID controllers).

[@mattschierholtz2554]

How are the eigenvectors of system different from the pole locations?

[@gustavoexel5569]

What happened to the DC motor modelling video? I can't seem to find it.

[@aakashdewangan7313]

sir, state estimator video is NOT here on youtube. could you please post the link of it?

[@lxzhang4911]

The eigenvector analysis is impressive. Could you maybe dive into this topic? As you've mentioned, the eigenvalues are actually not exactly the poles. What is the relationship between them?

[@ChristopherLum]

Ix, great to hear from your again. I will try to work on a video to explain this in greater detail. I hope it will be up later in the fall.

[@gitarplayer13]

Thanks professor. Would moving the pole in the last example to somewhere less than the pole at -4.77 (instead of to -2) be a bad idea, since this would make the other pole dominant and affect the system dynamics?

[@ChristopherLum]

I don't think so. We'll see in the very next video how there are better ways to move the poles than trying to change specific eigenvalues. Perhaps let's defer this question for a week and hopefully the next video will answer this.

[@tonnirvana]

Hello sir, thanks for the great video.... And also as motioned in comments below, I also couldn't find "Introduction to Linear State Estimation"... :(

[@ChristopherLum]

Hi, thanks for the kind words. Sorry about the estimation video, I'm actually in the process of making that video right now. I hope to have it up on the channel soon. Thanks for supporting the channel!

[@lucksilva16]

Dear professor, where can I find the video regarding the modelling of the dc motor? I can't find it in your channel. Thanks in advance and great lectures!

[@ChristopherLum]

Thanks for watching. I'm currently working on this video. I hope to have it up in a few weeks. If you are subscribed to the channel hopefully you'll see if when it goes live thanks!

[@lucksilva16]

That's great to hear. I'll be looking forward to it. Keep it up with the great work!

[@alanlee4326]

AE511-great presentation! I am confused about the last part where we set the K = [0.21 0.04 0.003] in the sense that I don't see how it solves the inability to measure the full state of the system issue. Since we can't measure x2 and x3, then the feedback only consist of x1. Thereby, no matter what values k2 and k3 is, the input will end up being u=k1x1?

[@ChristopherLum]

Alan, you bring up an excellent point. The key here is that k2 and k3 are small relative to k1. Therefore, if we simply neglect x2 and x3 (since we cannot measure them) and only use the control law you mention of u = k1*x1, then this is hopefully not too much of an approximation of the true, FSFB control law of u = k1*x1 + k2*x2 + k3*x3 (since k2 and k3 are small).

[@surjasekharchakraborty210]

@@ChristopherLum Sir, Thank you for the lecture. Do you have any reference for this approximation? If I want to go for a publication whether it is okay to put this concept straight away or do I need to give some reference? Looking forward for your answer. Thank you Sir.

[@ChristopherLum]

@@surjasekharchakraborty210 Feel free to use as you see fit, thanks for watching.

[@cansuyldrm7616]

Where is the linear state estimation video ?

[@ranganajayasanka5000]

Where is the state estimation video?

[@shuyangan3892]

great

[@quincyjones3839]

Can you provide a link to the previous video you mention of Introduction to "Full State Feedback Control"?

[@ChristopherLum]

Hi Quincy, thanks for watching. This video is going to be up in the next 2 weeks or so. If you subscribe and turn on notifications you'll get a message when it goes live. Thanks for watching.

[@quincyjones3839]

​@@ChristopherLum Already sub'ed! Great videos. I'll be on the lookout. Thank you.

[@ChristopherLum]

@@quincyjones3839, in case you are still interested, this video is now up at kzbin.info/www/bejne/Z6usepaPm9Voh6M.

[@nivethavadamalraj9895]

link for previous lecture about full state feedback control???

[@ChristopherLum]

in case you are still interested, this video is now up at kzbin.info/www/bejne/Z6usepaPm9Voh6M.

[@yanben]

Made lab easy!