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(1) Fig. 4 is a block diagram of a linear feedback system. Obtain a signal flow graph for the system and hence calculate the overall gain C(s)/R(s) for the system. (a) The open-loop transfer funct10n of a unity feed-back control system is given by G(s)=(K/((s+2)(s+4)(s +6s+25)) By applying Routh-Hurwitz criterion determine (1) the range of k for which the closed-loop system Will be stable, (11) the values of k wh1ch Will cause sustained oscillation the closed-loop system What are the corresponding oscillation frequencies? (b) Asymptotic approximation of Bode magnitude plot of open-loop transfer fun chon, G(s), of asystem is given m F1g 5(b) Determine G(s) (c) Sketch the Nyquist plot for the control system whose loop transfer fun chon 1S g1ven by G(s)H(s)= 1/(s(1+02s)(1+005s)) Determine the gam margin and comment on the stab1hty of the system (a) The open-loop transfer fun chon of a unity feed-back control system 1S g1ven by G(s)= (k(s+4))/(s(s+l)) (b) Sketch the Root Locus plots and briefly explain qualitatively the improvements m system performance (stab1hty and steady state error) that are obtainable by introducing a compensating zero (s + 3) to the unity feedback system whose open -loop transfer function is G ( s) =k/( s(s+2)(s+6) ) (c) State and explain Masons' gam formula for Signal flow graphs F1g 4 shows block diagram of a Feedback Control system Obtain an expression for the closed loop transfer function of the system using Signal flow graph of the system 26 September 2014 18:26 New Section 1 Page 1

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(1) Fig. 4 is a block diagram of a linear feedback system. Obtain a signal flow graph for thesystem and hence calculate the overall gain C(s)/R(s) for the system.

(a) The open-loop transfer funct10n of a unity feed-back control system is given by

G(s)=(K/((s+2)(s+4)(s +6s+25))By applying Routh-Hurwitz criterion determine(1) the range of k for which the closed-loop system Will be stable,(11) the values of k wh1ch Will cause sustained oscillation the closed-loop systemWhat are the corresponding oscillation frequencies?

(b) Asymptotic approximation of Bode magnitude plot of open-loop transfer fun chon, G(s), of asystem is given m F1g 5(b) Determine G(s)

(c) Sketch the Nyquist plot for the control system whose loop transfer fun chon 1S g1ven by G(s)H(s)= 1/(s(1+02s)(1+005s))

Determine the gam margin and comment on the stab1hty of the system (a) The open-loop transfer fun chon of a unity feed-back control system 1S g1ven by G(s)= (k(s+4))/(s(s+l)) (b) Sketch the Root Locus plots and briefly explain qualitatively the improvements m system performance (stab1hty and steady state error) that are obtainable by introducing a compensating zero (s + 3) to the unity feedback system whose open -loop transfer function is G ( s) =k/( s(s+2)(s+6) ) (c) State and explain Masons' gam formula for Signal flow graphs F1g 4 shows block diagram ofa Feedback Control system Obtain an expression for the closed loop transfer function of thesystem using Signal flow graph of the system

26 September 201418:26

New Section 1 Page 1