For the feedback control system shown in the figure, the process transfer function is G_p(s) = $${1 \over {s(s + 1)}},$$ and the amplification factor of the Power amplifier is K$$ \ge $$0. The design specifications required for the system, time constant is 1 sec and a damping ratio of 0.707.
(a) Find the desired location of the closed loop poles.
(b) Write down the requiredcharacteristic equation for the system. Hense determine the PD controller transfer function G_p(s) when K = 1.
(c) Sketch the root-locus for the system.

The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s) has no pole in the right half of s-plane, the number of roots of the system characteristic equation in the right half of s-plane is

The open-loop DC gain of a unity negative feedback system with closed-loop transfer function $${{s + 4} \over {{s^2} + 7s + 13}}$$ is

For the digital block shown in Figure. 2(a), the output Y=f(S₃,S₂,S₁,S₀) where S₃ is MSB and S₀ is LSB. Y is given in terms of minterms as $$Y\, = \,\sum m\left( {1,5,6,7,11,12,13,15} \right)$$ and its complements $$\overline Y \, = \,\sum m\left( {0,2,3,4,8,9,10,14} \right)$$.

(a) Enter the logical values in the given Karnaugh map [figure2(b)] for the output Y.
(b) Write down the expression for Y in sum-of products from using minimum number of terms.
(c) Draw the circuit for the digital logic boxes using four 2-input NAND gates only for each of the boxes.