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The output response, ?(?) of a feedback control system is given by: ?(?) = (? /...

The output response, ?(?) of a feedback control system is given by:
?(?) = (? / ?+? ) [?−?^−(?+?)?], where ? is a constant.
Determine:
a) The value of ?(3), taking ?=5. Give your answer accurate to 2d.p.


b) The inverse function ?−1(?), where ? is a constant.

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Answer #1

a)   

  when k=5

  

  

  correcting to 2 d.p,

    

b)   

Let

    

taking log on both sides,

  

  

where k is a constant and

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