Question

A unity feedback closed-loop system contains an open-loop transfer function G(S) = s / (s + S). A factor D(S) = ks + 1 is cascaded with G(S). Find the value of K necessary to provide a critically damped closed-loop system.

a. K = 0.5
b. K = 1
c. K = 2
d. K = 3

Answer 1

The value of K necessary to provide a critically damped closed-loop system is K = 2 (option C).

Step-by-step explanation:

To achieve a critically damped closed-loop system in a unity feedback closed-loop system with an open-loop transfer function G(S) = s / (s + S), a factor D(S) = ks + 1 should be cascaded with G(S). In order for the system to be critically damped, the damping coefficient should be equal to the square root of the product of the spring constant and the mass coefficient divided by twice the mass coefficient. In this case, k = 2 because the damping coefficient in the factor D(S) is 2. Therefore, the value of K necessary to provide a critically damped closed-loop system is K = 2 (option C).