fact0ry said:well, first you have get a proper transfer function. You do that by dividing the numerator to the denominator to find the direct part of the sistem (d) : Y(s) = d*u(s). So in your case that would be 1/2.
Now you have a proper transfer function (a first degree polynomial on a second degree polynomial). Now there are two well-known forms of the state space:
If your proper h(s) = n(s)/d(s),
where n(s) = s^n+ a1*s^(n-1) +...+an
d(s) = c1*s^(n-1)+...+cn
standard reachability form:
Ar =
[ -a1 -a2 ... -an
1 0 ... 0
0 1 ... 0
...
0 0 .. 1 0 ]
br= [1 0 ...0]'
cr=[c1 ... Cn]
(also ar1 = the rows upside down ; br1=[0...1]; cr1=[cn...c1] )
standard observability form:
Ao =
[ -a1 1 0 ... 0
-a2 0 1 ... 0
-a3 0 0 ... 0
....
-an 0 0 ... 0 ]
co= [1 ... 0]
bo= [c1...cn]
(also there is an equivalent ). If you need that i'll write it.
And of course there is d, which is 1/2 for your h(s).
berkeman said:Thread moved from EE to Homework Help forums.
Welcome to the PF, guys. Homework and coursework questions need to be posted here in the Homework Help forums, and when you post a HH question, you need to use the HH Template that is provided, and show us your work so that we can provide tutorial assistance.
And fact0ry, on homework/coursework questions like this (it may not have been obvious to you, since it was posted incorrectly in the EE forum), we are not allowed to do the original poster's (OP's) work for them. You can offer hints and point out mistakes in the OP's work, but the OP needs to do the bulk of the work.
The process of converting a transfer function to state space involves several steps. First, the transfer function must be written in polynomial form. Then, the state vector must be defined, along with the state equations. Finally, the output equation must be written in terms of the state variables.
Yes, any transfer function can be converted to state space. However, some transfer functions may have an infinite number of state space representations, so it is important to choose the most appropriate one for your specific application.
Converting a transfer function to state space can provide a more intuitive understanding of the system dynamics. It also allows for easier implementation of control algorithms and analysis using modern control theory techniques.
One limitation is that the state space representation may not accurately capture all the dynamics of a system, especially if the system is nonlinear. In addition, the state space representation can become very large and complex for systems with many inputs and outputs.
Yes, there are many online tutorials and textbooks available that provide step-by-step instructions and examples for converting transfer functions to state space. Some popular resources include "Modern Control Systems" by Richard C. Dorf and Robert H. Bishop, and "Control Systems Engineering" by Norman S. Nise.