Excellent ! State-space and subsequently state variables are fascinating with ramifications towards linear and nonlinear system identification, and digital signal processing.
EXCELLENT and VERY CLEAR !!!! ... I am currently working on research utilizing state variables in modeling nonlinear systems for system identification and adaptive digital signal processing.
Wonderful! Thanks for providing such a clear description of key concepts in control theory, accessible to a broad audience with a minimum of undefined jargon.
Very clear and informative, thanks! What kind of monster writes a 5 backwards though?? (11:10) genuinely horrified... Great video though, control will be a breeze thanks to you :)
Very Nice. I have struggled with state space A and B matrix now for a while. Single input single output. I also have been struggling with multivariable as well. I am not sure how poles and zeros work into this understanding as well.
With a MIMO state space system, the relationship with the corresponding transfer function representation is a little more challenging. Specifically, a MIMO system can be represented by a single state space model, but requires multiple transfer function models, 1 for each input-output pair. For example, a system with 2 inputs and 3 output will require 6 transfer functions. Each of the transfer functions will have the same poles, which are equal to the eigenvalues of the A matrix. However, each transfer function may have different zeros. There are some conventions for speaking about the "zeros" of the state space model, things like transmission zeros, but this tends to be a more advanced topic.
+BANIYASAD In general, yes. The choice of output is a decision of the designer based on what is being controlled or analyzed. Ideally, you would be able to express your output as a function of the chosen state variables. If you can't, you may need to choose an alternate set of state variables. Recall, the choice of state variables is not unique.
+Rick Hill thank you so much for replying For equations as 2x1('' )+X1( ') +2(X1+ x2)=f(t) x2( ' )+ x2 -2(X1- x2)=0 and outputs X1, x( ' ' ) What state variables to find output equation that match to output values assigned?
If you had a MIMO system (multiple inputs and multiple outputs), the structure of the state-space representation is the same, it just changes the size of your B and C matrices. For example, if you have 3 inputs, then your B matrix would have 3 columns (and your input u would be a column vector).
It is simply an engineering decision (or is given to you). What output do you wish to control/analyze? That question determines what you choose y to be.
@@hillrickc thnx for ur answer Another question:ur example abt integer wht abt fractionel-order ?and why we choose the fractionel-order as a good result
