5. Dynamics and Control

Control Lab — Quiz

Test your understanding of control lab with 5 practice questions.

Practice Questions

Question 1

For a second-order underdamped system, the percent overshoot $M_p$ is given by $M_p= e^{-\zeta\pi/\sqrt{1-\zeta^2}}\times100\\%$. If a step response shows 10\\% overshoot, what is the approximate damping ratio $\zeta$?

Question 2

If the 2\\% settling time of a second-order system is measured as $T_s=1.2\,\mathrm{s}$ and the damping ratio is known to be $\zeta=0.5$, what is the natural frequency $\omega_n$ (in rad/s)? Use $T_s\approx4/(\zeta\omega_n)$.

Question 3

A data acquisition system advertises a total throughput of 12\,kS/s. If configured to scan 6 channels equally, what is the sampling period per channel?

Question 4

In a Bode plot for an open-loop system, the phase crosses $-180^\circ$ at 10\,Hz and the magnitude at that frequency is $-6\,$dB. What is the gain margin?

Question 5

Which performance metric is defined by the integral $\int_{0}^{T} t\,|e(t)|\,dt$ for evaluating control response?