Q2. Consider the control system whose open-loop transfer function is: G(s) K s (s² +4.8s + 12.6) Check the range of gain (K), for the stability of this system by using the bode diagram?

A controller is designed so that the nominal closed-loop transfer function has bandwidth 1.9 rad/s and rolls off with -40dB/dec at high frequencies. If the model has multiplicative uncertainty above 10.7 rad/s, what is the maximum uncertainty gain in dB that can be tolerated according to the Small Gain Theorem?

Consider a system with a stable loop transfer function L(s). If the gain|L(iω)| is less than 1 (0 dB) whenever the phase ∠L(iω) crosses −180◦, then the closed-loop system is stable. Answer ture or fasle with explanation.  If the Nyquist plot of the loop gain L(s) encircles −1, then the closed-loop system is unstable.  Answer ture or fasle with explanation.

The bode plot of the open loop transfer function of a quadratic system is shown above. If the settling time of the closed loop system is 4 seconds, calculate the undamped natural frequency of the system, the damping ratio, the highest amplitude value of the frequency response of the closed loop system and at which input frequency it occurs. Attention!!!: Use the numbers as three decimals during the design phases. Solution: Belonging to the closed-loop transfer function Damping rate = [ ? ] Undamped natural frequency = [ ? ] rad/s The highest amplitude value of the frequency response [ ? ] and [ ? ] occurs at the rad/sec input frequency.