Section A
Q1.
(a) An LTI system has the property that an u(n) → n an u(n) Considering the system as causal and stable, find the frequency response H(ω) of the system. Also, determine the difference equation that relates the input x(n) and the output y(n). Consider a unity feedback system with open-loop transfer function given as
(b)
G(s) = ((s-2)(s-4))/((s + 20)(s-3)(s2 + s + 1)) Sketch the root locus diagram for G(s) and show that G(s) cannot be stabilized by a stable controller. The electromagnet shown in the figure below is used to lift a sheet of steel. The |c| coil has 400 turns and a resistance of ohms. The reluctance of the magnetic material is negligible. The magnetic core has a square cross- section o
f cm by cm. When the sheet of steel is fitted to the electromagnet, air gaps, each of length g = 1 mm, separate them. An average force of 550 newtons is required to lift the sheet of steel. Considering the fact that the same r.m.s. current is required to produce the same average torque when the supply is DC or 50 Hz AC, find the ratio of the two supply voltages (i.e., AC voltage r.m.s. value to DC voltage) to lift the sheet : 12 ∑k=19+1 R = 5 \Omega q = 1 mm
(d) GO circuit of single-phase transmission line is composed of three solid conductors of radius 1.2 cm. The return circuit is composed of two solid conductors of radius 2 cm. The conductors layout is as shown in the figure below. Find the inductance per km of the complete line : a -10m Conductor X Conductor Y SGSE-T-ELE/71 2
