6. Power and Control

Control Systems — Quiz

Test your understanding of control systems with 5 practice questions.

Practice Questions

Question 1

For a phase–lead compensator of the form $C(s)=\frac{Ts+1}{\alpha Ts+1}\,(0<\alpha<1),$ which expressions correctly give the maximum phase lead $\phi_{\max}$ and the frequency $\omega_m$ at which it occurs?

Question 2

In a unity‐feedback loop with open‐loop transfer $L(s)=\frac{8}{s(s+2)},$ the sensitivity function is $S(s)=\frac{1}{1+L(s)}\,. $ What is the magnitude $\bigl|S(j1)\bigr|\,$?

Question 3

For the open‐loop transfer function $G(s)=\frac{K}{s(s+1)(s+4)},$ how many asymptotes does its root locus have, at what angles (in degrees), and what is the centroid location?

Question 4

Which expression defines the complementary sensitivity function $T(s)$ in a unity‐feedback control system with loop transfer $L(s)$?

Question 5

Given a state‐space system $\dot x=\begin{pmatrix}0&1\\-10&-6\end{pmatrix}x+\begin{pmatrix}0\\1\end{pmatrix}u$, design state‐feedback $u=-Kx$ so the closed‐loop characteristic equation is $s^2+4s+8=0\,. $ What is $K=[k_1\;k_2]$?