Difference equation

Discussion in 'Programmer's Corner' started by zishan, Jan 28, 2011.

  1. zishan

    Thread Starter New Member

    Jan 28, 2011
    2
    0
    i have an example of difference equation
    y(n)-6y(n-1)+9ky(n-2)=19x(n)
    i want to find the step and the impulse responses for a k value that makes the system stable by using matlab
    Use MATLAB to find the output y(n) if x(n) = 2u(n) +5nu(n).
    i also want the block diagram for the system.
    please help me
     
  2. etuzuner

    Member

    Mar 21, 2009
    23
    0
    Zishan,

    A system is stable if the poles of closed-loop transfer function are located in the Left Hand Plane. Due to this information, first of all you need to find the transfer function which is easy to find for this system. You may begin with taking the Z-transform of the system. The calculation is very simple. y(z)-6z^-1y(z)... (you can do the rest) Then you will have an equation with 2 poles and 2 zeros. you can find those poles with the use of the equation mentioned in http://en.wikipedia.org/wiki/Quadratic_equation. Remember you can't have a value which rests in Right Hand Plane. I guess you can do the rest.

    Emre
     
  3. guitarguy12387

    Active Member

    Apr 10, 2008
    359
    12
    This isn't the case if you're doing z transforms. Z transform maps the Y axis of the S plane to the unit circle in the Z plane.

    So you actually want all poles to be inside the unit circle for stability.
     
  4. etuzuner

    Member

    Mar 21, 2009
    23
    0
    guitarguy12387,

    Thanks for the correction. I forgot to write "for stability", my bad.

    Emre
     
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