Question

For a unit feedback system with G(s) = K(s+α) / s(s+3)(s+6), find the values of α and K that will yield a second order closed loop pair of poles at -1 +-/100.

(Using the characteristic equation method to form the coefficient equations as discussed in class)

Answer 1

To find the values of α and K that will yield a second order closed loop pair of poles at -1 +/-100, we can use the characteristic equation method to solve for α and K. The values are α = 2 and K = 10000.

Step-by-step explanation:

To find the values of α and K that will yield a second order closed loop pair of poles at -1 +/-100, we can use the characteristic equation method. The characteristic equation for a second order system is given by:

s^2 + 2ζωns + ωn^2 = 0

Comparing this to the equation for G(s), we can equate coefficients and solve for α and K:

α = 2ζωn

K = ωn^2

Since the desired poles are at -1 +/-100, we can say that ωn = 100 and ζ = 0.01. Substituting these values into the equations for α and K, we get:

α = 2(0.01)(100) = 2

K = (100)^2 = 10000

Therefore, the values of α and K that will yield a second order closed loop pair of poles at -1 +/-100 are α = 2 and K = 10000.