5. Dynamics and Control

Control Systems — Quiz

Test your understanding of control systems with 5 practice questions.

Practice Questions

Question 1

For the characteristic equation $s^4 + 3s^3 + 2s^2 + s + K = 0$, what range of $K$ ensures all roots lie in the left-half $s$-plane (closed-loop stability)?

Question 2

In the Ziegler–Nichols open-loop (process reaction curve) tuning method, a process has a dead time $L=2\,\mathrm{s}$ and time constant $T=10\,\mathrm{s}$. What proportional gain $K_p$ is recommended?

Question 3

On the root locus of $G(s)=\frac{K}{s(s+4)(s+6)}$, the real-axis breakaway point satisfies $\sum\frac{1}{s-p_i}=0$. Which approximate value of $s$ corresponds to the breakaway?

Question 4

For the open-loop transfer $G(s)=\dfrac{10}{s(s+5)}$ in a unity-feedback system, what is the gain margin?

Question 5

A lead compensator has transfer $C(s)=K\frac{\tau s+1}{\alpha\tau s+1}\,(0<\alpha<1)$. If the maximum phase lead required is $\phi_m=45^\circ$, what is the value of $\alpha$?