The complete Nyquist plot of the open-loop transfer function $G(s) H(s)$ of a feedback control system is shown in the figure.

If $G(s) H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is

A unity feedback system that uses proportional - integral (PI) control is shown in the figure.

The stability of the overall system is controlled by tuning the PI control parameters $K_p$ and $K_I$ The maximum value of $K_I$ that can be chosen so as to keep the overall system stable or, in the worst case, marginally - stable (rounded off to three decimal places) is $\_\_\_\_$

The block diagram of a feedback control system is shown in the figure.$$ \text { The transfer function } \frac{Y(s)}{X(s)} \text { of the system is } $$

The electrical system shown in the figure converts input source current $i_s(t)$ to output voltage $\theta_O(t)$.

Current $i_L(t)$ in the inductor and voltage $\vartheta_C(t)$ across the capacitor ate taken as the state variables, both assumed to be initially equal to Zero, i.e., $i_L(0)=0$ and $\vartheta_c(0)=0$. The system is