Question

Copy of For the process described by the exact transfer function G(s) = 5(s+2)/{(11s+1)(3s+1)(2s+1)(0.5s+1)} Use Taylor series expansion method to find an approximate first-order-plus-time-delay transfer function model of the form Ke-θs/(τs+1) and determine the values of

a. ___________

b. ___________

c. ___________

Answer 1

Given:

The transfer fuction given in the question is

  

On denominator we have to retain gratest time constant othe than this we have to approximate with time delay using taylor series:

0.5s+1= e(0.5s )

1/(3s+1) = e(-3s)

   1/(2s+1) = e(-2s)

1/(0.5s+1) = e(-0.5s)

puttin all these in above equation we gets

  

equating the above equation with the equation given in question we get:

K = 10

So the constants are find out from the taylor series.