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

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:

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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!

[kaipn]

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

[HerChip]

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

[victorthepaduani]

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

[wiloberlies]

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

[divyanshsati]

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

[daouadiwalid]

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

[Daniboy]

Probably the most useful video I happen to come across

[thegent]

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

[patrickayivor]

Simple explanation with powerful examples

[hyperduality]

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.

[pravinpalve]

why this video does not have million likes?

[mpja]

This definitely helps the intuition. Good video!

[mukuljobra]

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

[AhmedMagdy-xbbl]

Man you are awesome.
Thank you very much.

[jairguilhermecertorio]

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.

[vivekmech]

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

[eatctitox]

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

[thelegendkilleragab]

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