The asymptotic magnitude Bode plot of a minimum phase system is shown in the figure. The transfer function of the system is $$(s) = {{k{{(s + z)}^a}} \over {{s^b}{{(s + p)}^c}}}$$, where $$k,z,p,z,b$$ and $$c$$ are positive constants. The value of $$(a + b + c)$$ is ___________ (rounded off to the nearest integer)

The figure below shows the Bode magnitude and phase plots of a stable transfer function

$$G(s) = {{{n_0}} \over {{s^3} + {d_2}{s^2} + {d_1}s + {d_0}}}$$.

Consider the negative unity feedback configuration with gain k in the feedforward path. The closed loop is stable for k < k₀. The maximum value of k₀ is ______.

For a unity feedback control system with the forward path transfer function

$$G(s) = {K \over {s\left( {s + 2} \right)}}$$

The peak resonant magnitude M_r of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.

The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then the closed loop system (having unity gain feedback) is