A Conceptual Approach to Controllability and Observability | State Space, Part 3

Check out the other videos in the series: • State Space
Part 1 - The state space equations: • Introduction to State-...
Part 2 - Pole placement: • What is Pole Placement...
Part 4 - What Is LQR Optimal Control: • What Is Linear Quadrat...
This video helps you gain understanding of the concept of controllability and observability. Two important questions that come up in control systems engineering are: Is your system controllable? And is it observable? Assuming you have a good linear model of your system, you can answer both questions using some simple matrix operations and the A, B, and C matrices of your state-space model.
In this video, we’re going to approach the answers from a conceptual and intuitive direction.
References:
- Create, analyze, and use state-space representation for control design with MATLAB and Simulink: bit.ly/2HrtZQy
- Steve Brunton - Control Bootcamp: bit.ly/2HrWAFm
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[@BrianBDouglas]

Hey everyone, thanks for watching this video! If you have any questions or comments that you'd like me to see, please leave them under this comment so that I get notified and can respond. Cheers!

[@prashantajabe2693]

Make video on the how to interpret sensor data.

[@benallia8262]

exactly what i asked! thank you brian :D

[@gosayeweldemaryam2415]

Hi brian I'm from ethiopia. Your videos are exceptional. I'm truly satisfied. I thank you. My question is that can you do such videos on linear quadratic regulator (LQR)?

[@BrianBDouglas]

@@benallia8262 Glad to hear it!

[@BrianBDouglas]

@@gosayeweldemaryam2415 I'm finishing up a video on LQR right now! Should post next week.

[@kaipn9763]

You and Steve Brunton are 2 gems of control systems.!

[@ramisketcher2069]

Indeed! ;)

[@triagung2497]

I couldn't agree more!

[@turbotoblast4]

As true as it gets.

[@oldcowbb]

i just realize both of them are from Seattle

[@jagadishkumarmr1067]

I would say Katkim show and Christopher Lum(especially for aerospace) are can be added to the list..! Its just amazing that anyone can learn anything over the internet!

[@wiloberlies9598]

Really nice job Brian, you're right to be proud of this one...excellent explanation with well-chosen examples. Thank you for this!

[@victorthepaduani]

This deserves 100K+ views. Good job, Brian. Stay productive!

[@HerChip]

Such a practical example (the beam) at the end makes things so much more logic (unobservable modes) than I learned in class

[@shuvodev3708]

Thank you Brian

[@divyanshsati1116]

God bless you Brian, finally could understand the intuition behind all that math!

[@ashkabrawn]

Omg... I just came here after watching Steve's series !! Thanks for the pointers

[@thegent5167]

This is a fantastic explaination of the topic and gave me a better and clearer view of controllability and observability. Thanks a lot!

[@mpja]

This definitely helps the intuition. Good video!

[@patrickayivor2406]

Simple explanation with powerful examples

[@Daniboy370]

Probably the most useful video I happen to come across

[@johnfrobin]

Excellent video. Thank you.

[@spectra5024]

Your videos are art, thanks dude!

[@demisbooo743]

Great explanation! Thank you so much!

[@mukuljobra3972]

Hey! I have watched your lectures on your KZbin channel and it is good to see you here again on this MATLAB channel. Great explanation...nice work...Sir 😊

[@daouadiwalid5491]

That car driving example hits hard ... Brian shows that perfect examples could exists!

[@BrianBDouglas]

Thanks!

[@SteveJobzz]

I was looking for a brian douglas video on this topic and I was disappointed to not find any. This is a pleasant surprise!

[@blitz8229]

Thank you for this video!

[@pedrobenevenutovaladares9734]

Fantastic video !

[@dallasdominguez9501]

Another Brian Douglas Hood Classic👌

[@vivekmech1]

Hi Brian , awesome work! May I know which software you use for this illustrations? Thanks

[@shmoodiee6173]

Amazing stuff

[@hyperduality2838]

Controllability is dual to Observability Poles (eigenvalues) are dual to Zeroes The Initial value theorem IVT is dual to the Final value theorem FVT Stability is dual to instability Robustness is dual to performance Complex numbers are dual to real numbers In physics equivalence, similarity is also known as duality, so we have the the following duals (Jewels):- Energy is equivalent or dual to mass -- Einstein Gravitation is dual to acceleration --- Einstein Potential energy is dual to kinetic energy Space is dual to time -- Einstein Certainty is dual to uncertainty, the Heisenberg certainty/uncertainty principle Energy is literally duality. Energy is transported by the electromagnetic field in the form of photons or wave/particles, quantum duality. Energy is inherently dual. In physics everything is made out of energy hence duality. If energy is conserved and energy is duality then duality must be conserved! The conservation of duality is the fifth law of thermodynamics. Negative curvature is dual to positive curvature (Riemann, Gauss) Hyperbolic geometry is dual to elliptic, spherical geometry A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence) In mathematics: Integration is dual to differentiation Duality creates reality, all observers are inherently dual if they are made out of energy Genes are dual to memes Everything (all things) is/are dual to nothing.

[@ashkabrawn]

Did you just cover Heisenberg in more ways than he himself pictured.. 😉😅

[@hyperduality2838]

@@ashkabrawn Dark energy is dual to dark matter! Thesis is dual to anti-thesis -- the generalized or time independent Hegelian dialectic. Hegel's cat: Alive (thesis, being) is dual to not alive (anti-thesis, non being) -- Schrodinger's cat. Immanuel Kant: Synthetic a priori knowledge, all knowledge is dual. Philosophy, physics, mathematics, control theory all lead to duality! "Philosophy is dead" -- Stephen Hawking. It looks like Mr Hawking got this one wrong! No philosophy = no duality.

[@ashkabrawn]

@@hyperduality2838 what is the duality for universe, biverse and multiverse ?

[@hyperduality2838]

@@ashkabrawn The future is dual to the past. Many worlds (possibilities) or the multiverse would be the future and the one world or universe (reality) is the past. The present or the 'now' is therefore the duality or the biverse. The future meets or intersects the past in the present via duality! Noumenal (before measurement, a priori) is dual to phenomenal (after measurement, a posteriori). Deduction (rational) is dual to induction (empirical) -- Immanuel Kant. Positive is dual to negative. Duality converts possible worlds into the real world or probability = 1. Time is dual:- My absolute time is your relative time and your absolute time is my relative time. Absolute time (Galileo) is dual to relative time (Einstein).

[@ravikiran4495]

so ying and yang

[@abdelz1617]

Great video!

[@yinarodriguez6672]

Nice to find Brian here!

[@qamarkilani551]

Hi Brian Many Thanks for your great videos , do you have notes/slides that can be shared in pdf format ?

[@learningexploring5717]

Thank you for sharing :)

[@thelegendkilleragab]

Hello Brian, can you please make a lecture about stabilizability and detectability? those are very confusing terms. Thank you

[@manerlind]

Это просто превосходно!

[@jairguilhermecertorio6362]

Your definition of controllability is actually reachability, in continuous systems they are equivalent but for discrete systems they are not. To be reachable the system must be able to go from your initial state to any other state, to be controllable the system must be able to go from any initial state to zero. In discrete systems it is easy to see that a A = [0 0; 0 0] would be controllable (gets to zero from any point in one sampling without depending on B), but it would only be reachable if B = [1 0; 0 1] (individually control each state). Great video nonetheless.

[@PlayboyHZ]

Would have been nice of some demonstrations in matlab/simulink, just like part 2

[@zeeshangla]

Hey! good Job Sir, Hello All.... Is there any specialized Power system course using SIMULINK

[@blessoneasovarghese9834]

Could you please tell me why will C-matrix be zero when states are not measurable. Also what could be the output y in the examples of train and car? What role do output y and C-matrix play in observability, conceptually?

[@tushermyth]

wow!

[@MarcusViniciusMO]

Using reconstructed velocity, by position diferentiation, and these same positions as output can bring more information to estimate other states?

[@eatctitox]

Love your videos! Can you please explain why is the D matrix usually regarded as zero in college courses?

[@samchan5251]

To my understanding. D matrix is the direct feed through term, the input will change your measurement (y) directly, not through the system evolution (Ax). And this type of system is rare (never see and cannot think of one). Note that if D is non-zero, the transfer function will not be strictly proper. Another reason maybe, because the maths is the same with or without D being zero, college courses usually design to be easy to understand and illustrate the key concept.

[@samchan5251]

Just something came up in my mind. If you are discretizating a continuous time system, it is likely that the resulting discrete system (Ad,Bd, Cd,Dd) Dd is non-zero. I think there is a paper talks about discretization will introduce something call "sampling zeros". Even the continuous model is strictly proper, the discretized system will not be.

[@hyperduality2838]

Correction to my earlier mistake:- A white hole (big bang, divergence) is dual to an infinite mass black hole (convergence) Dark energy is literally hyperbolic geometry or negative curvature Positive is dual to the negative.

[@vineetverma6645]

When we judge people from outside based on their color or financial status, we are observing only a handful of states, and thus we end up fooling ourselves

[@achmadfatoni2555]

Bnhihhhh