Discuss the design requirements and the implications of

Question

Question 1

A second order system is under-damped with a damping ratio of 0.4 and a natural frequency of 10 Hz.

a) Transfer function

b) Time response when it is subjected to a unit step input

c) Percentage overshoot

d) Rise time, peak time, settling time

Question 2

Given an under-damped system with transfer function, Y₁(s) = 16/(s²+6s+16)*U(s) is subjected to a unit step input. Using MATLAB, investigate and discuss the following effects and plot the response obtained.

i. The effect of increasing the damping (ζ), on the Rise time (t_r), Peak time (t_p), Settling time (t_s) and maximum % overshoot, while keeping the natural frequency (ω_n), constant. Set D(s) = s² + bs +c, with b= 6,5,4,3 Discuss the design requirements and the implications of these parameters.