The type of transient you get in a second-order system depends on the location of the poles of the system. The transfer function of the second-order system is

and let the input be x(t) = u(t).

(a) Let the coefficients of the denominator of H(s) be b₁ = 5, b₀ = 6, find the response y(t). Use MATLAB to verify the response and to plot it.

(b) Suppose then that the denominator coefficients of H(s) are changed to b₁ = 2 and b₀ = 6, find the response y(t). Use MATLAB to verify the response and to plot it.

(c) Explain your results above by relating your responses to the location of the poles of H(s).

Transcribed Image Text:

Y (s) H(s) = X(s) ? + b,s + bo %3|