1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

State Space Representation

  1. Sep 26, 2013 #1
    1. The problem statement, all variables and given/known data

    A first-order dynamic system is represented by the differential equation,

    [tex]5\frac{dx(t)}{dt} + x(t) = u(t).[/tex]

    Find the corresponding transfer function and state space reprsentation.

    2. Relevant equations



    3. The attempt at a solution

    Putting the equation in the Laplace domain yields,

    [tex]5sX(s) + X(s) = U(s)[/tex]

    [tex]\Rightarrow G(s) = \frac{X(s)}{U(s)} = \frac{1}{1+5s}[/tex]

    For the state space equations,

    [tex]\frac{dx(t)}{dt} = -0.2x(t) + 0.2u(t)[/tex]

    The answer they provide is,

    [tex]\frac{dx(t)}{dt} = -0.2x(t) + 0.5u(t), \quad y(t) = 0.4x(t)[/tex]

    How did they 0.5u(t) and how did they know that y(t) = 0.4x(t)?

    Thanks again!
     
  2. jcsd
  3. Sep 29, 2013 #2
    Bump, can someone please clarify this for me?
     
  4. Sep 29, 2013 #3

    gneill

    User Avatar

    Staff: Mentor

    Hi jeques. I don't know if I can help to clarify your problem. The definition of the first-order system made no mention of y(t), so it's a mystery to me where it came from at the end! Is there something missing from the problem statement that might tie-in with y(t)?
     
  5. Sep 29, 2013 #4
    Here's the question. (see attached)
     

    Attached Files:

    • SSQ.JPG
      SSQ.JPG
      File size:
      25.1 KB
      Views:
      149
  6. Sep 30, 2013 #5

    gneill

    User Avatar

    Staff: Mentor

    Hmm. Nope, that doesn't help me :frown: The transfer function bit is clear enough, but I don't "get" the introduction of the y(t) stuff. I'll see if I can find someone who recognizes the problem type.
     
  7. Sep 30, 2013 #6

    gneill

    User Avatar

    Staff: Mentor

    Upon reflection and discussion with another Homework Helper, it occurred to me that the problem would make more sense to me if the variable used in the dynamic system differential equation was y rather than x.

    Is it possible that we should take the given system D.E. to represent the form of the equation describing the system rather than an equation of the state variables?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: State Space Representation
Loading...