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Homework Help: Control engineering problem

  1. Jul 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Hi, i have been trying to solve this equation for the past 2 hours but am not getting anywhere near the given answer. If any one can solve this it would be greatly appreciated!! Thank you.

    2. Relevant equations
    The answer is circled in red and was derived from the line above it. (picture attached)

    3. The attempt at a solution

    Attached Files:

  2. jcsd
  3. Jul 10, 2015 #2
    Looks like a simple matter to apply FOIL and simplity, with due care in execution.
  4. Jul 10, 2015 #3
    Thats what i did but unfortunately i keep getting different values.
  5. Jul 10, 2015 #4


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    Gold Member

    show us the steps you take
  6. Jul 10, 2015 #5
    I thought i could start with the easy part the denominator but then i don't know what to do with the Z's and end up as shown in picture, aaa my head hurts lol.

    Attached Files:

  7. Jul 10, 2015 #6


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    Gold Member

    just treat the z's like you would any other variable
  8. Jul 10, 2015 #7
    Am not getting anywhere with this tbh.. i think il leave this for now as i wasted too much time on it. Thanks for the help anyway.
  9. Jul 10, 2015 #8


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    Gold Member

    as was previously stated use foil...
    you should brush up on your algebra
  10. Jul 11, 2015 #9
    My advice would be to sign up for a Wolfram Alpha account.

    Its a great resource for helping with such problems.

    Enter your equation, and you will get a step-by-step solution.

    From there, you will be able to see how to do the algebra.
  11. Jul 11, 2015 #10


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    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Actually, you're not solving an equation. This is just simplifying the given form for the function.

    I suggest that you define some intermediate variables in order to simplify the look of this expression:
    Let: ##\ a=e^{-0.1}z^{-1}\ ##, ##\ b=e^{-0.2}z^{-1}\ ##, ##\ c=z^{-1}\ ##.
    Multiply the numerator & denominator by 2.​

    You get: ##\displaystyle \ \frac{(1-a)(1-b)-2(1-a)(1-c)-(1-c)(1-a)}{2(1-a)(1-b)} \ . ##

    Simplify that, then do the reverse substitution.
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