State variable control 29: Observer design, Part 1

This video is part of the module Control Systems 344 at Stellenbosch University, South Africa. The first term of the module covers continuous state variable control and and second term covers digital classical control.
Most of the material in this module is based on the textbook "Digital Control and State Variable Methods" (4th edition) by M. Gopal.

[@faisaltariq_artist]

Wow! never seen it explained so clearly. Thank you Sir!

[@shimaalcarrim7949]

Thanks

[@demisbooo743]

Great! Thank you 🙏

[@adelsalam9735]

thank you so much sir

[@marcelozortea]

Hi there, nice video but I have a question. In engineering we see that "there is no free lunch", all of changes that we do in a system have a consequence. In pole placement method, when we choose the poles of our system we can not move the poles to where we want because we can overload the actuador. However, in observer design I cannot see the price that we pay to move the observer poles, in observer design the objective is to have the poles in the LHP too much far than jw axis that we can, right? why not to move the poles to -1e+99999 for example?

[@cornevandaalen1862]

Good question! The answer is one that we do not cover in this module, but it is easy enough to see: the faster you make the observer poles, the larger the observer gain will be. Now if there is any noise in the measured output (which there always is in practical systems), this noise will be amplified by the observer gain, influencing the state estimates. A larger observer gain therefore means noisier state estimates. There is actually a "sweet spot" for which the state estimates are the best ("best" means closest to the actual states on average) -- this is the optimal estimator, or Kalman filter.

[@marcelozortea]

​@@cornevandaalen1862 wow, thank you !! I was with this doubt for a long while. I started to study about control recently, so could you recommend me some bibliography about how to design this? I have took a look in Gopal pdf, however at internet I did not find the whole book, the documents whose I found are missing some pages and are wrote as "hidden page".

[@cornevandaalen1862]

@@marcelozortea "Feedback Control of Dynamic Systems" by Franklin, Powell and Emami-Naeini is a nice introduction to control systems.

[@marcelozortea]

@@cornevandaalen1862 could you share the book with me? [e-mail]

[@dz7056]

Is this leunberger observer?

[@metehandeniz6741]

sir i have a question. Lets say there are 4 states. One of them is not observable. Then what should be the size of matrix C and matrix Y.

[@cornevandaalen1862]

I do not quite understand your question: We usually do not try to construct observers for systems that are not observable. The dimensions of the system matrices are also not influenced or determined by observability. Do you rather mean: "One of them is not observed"? If you clarify your question, I could try to answer it.

[@metehandeniz6741]

@@cornevandaalen1862 yes i mean "one of them is not observed". Btw i understood :)