Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20$ dB/decade at least till $100$ rad/sec with the gain crossover frequency being $10$ rad/sec. The asymptotic Bode phase plot remains constant at $-90^{o}$ at least till $\omega = 10$ rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ________________ (rounded off to 2 decimal places).
Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of $G(s)$ are given in the table. The value of the gain $K_I$ ($>0$) for a $50^\circ$ phase margin is _____ (rounded off to 2 decimal places).
| $\omega$ in rad/sec | Magnitude in dB | Phase in degrees |
|---|---|---|
| 0.5 | −7 | −40 |
| 1.0 | −10 | −80 |
| 2.0 | −18 | −130 |
| 10.0 | −40 | −200 |
Simplified form of the Boolean function
$$ F(P, Q, R, S)=\bar{P} \bar{Q}+\bar{P} Q S+P \bar{Q} \bar{R} \bar{S}+P \bar{Q} R \bar{S} $$
is
In the circuit, the present value of $Z$ is $1$. Neglecting the delay in the combinatorial circuit, the values of $S$ and $Z$, respectively, after the application of the clock will be
