Transfer Function Analysis: Zeros, Poles, Initial & Final Values of X(s) = 808/[s*(s^2+2s+101)]

To find the initial value of the transfer function, we need to take the limit as s approaches infinity:

lim(s->∞) X(s) = lim(s->∞) 808/[s*(s^2+2s+101)] = 0

Therefore, the initial value of the transfer function is 0.

To find the final value of the transfer function, we set s=0:

X(s=0) = 808/[0*(0^2+2*0+101)] = undefined

Since the final value of the transfer function is undefined, we can conclude that the system has no finite steady state.

To find the poles of the system, we need to solve the denominator of the transfer function for s:

s^2+2s+101 = 0

Using the quadratic formula, we get:

s = (-2 ± sqrt(2^2 - 41101))/21 s = (-2 ± sqrt(-404))/2 s = -1 ± jsqrt(101)

Therefore, the system has two complex conjugate poles at s = -1 + jsqrt(101) and s = -1 - jsqrt(101).

To find the zeros of the system, we set the numerator of the transfer function equal to zero:

808 = 0

Since there are no solutions to this equation, we can conclude that the system has no zeros.