Control System Analysis

he system has a damped oscillatory response due to complex poles. Step Response: Shows oscillations that gradually die out and settle to a

The numerator and denominator are defined, and the transfer function model is created using tf(num, den). The code then plots the step response to show how the system reacts to a sudden change in input. The response is damped and oscillatory, indicating the presence of complex poles.

The system poles are located at s=−2±j4.58s = -2 \pm j4.58s=−2±j4.58, which lie in the left-half of the s-plane, confirming that the system is stable. The natural frequency of the system is ωn=5\omega_n = 5ωn​=5 rad/s, and the damping ratio is ζ=0.4\zeta = 0.4ζ=0.4, showing that the system is underdamped.

Finally, the Bode plot is used to study the system’s frequency response, illustrating how the gain and phase vary with frequency.