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 _________.

A unity feedback control system is characterized by the open loop transfer function $$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$ The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below. If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is