1 (a)
Define rise time.
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1 (b)
Define gain margin and phase margin.
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1 (c)
What are the difficulties encountered in applying Routh stability criterion?
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1 (d)
Find out response of give system for a unit step I/P.
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2 (a)
Obtain the transfer function of the mechanical system shown in Fig. 11A (i).
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2 (b)
Draw a signal flow graph for the system shown in fig 11a (ii) and hence obtain the transfer function using Mason's gain formula.
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3 (a)
Derive the expression for step response of second-order under damped system.
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3 (b)
Find the impulse response of the second order system whose transfer function \( G(s) = \dfrac {9}{(s^2 + 4s+ 9)} \)
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4 (a)
A unity feedback system is characterized by an open loop transfer function \( G(s) = \dfrac {K} {s(s+10)}. \) Determine the gain K so that the system will have a damping ratio of 0.5. For this values of K determine settling time peak over shoot and time to peak over shoot for a unit step input.
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4 (b)
An unity feedback system is given as \( G(s) = \dfrac {1} {s(s+1)}. \) The input to the system is described by r(t)=4+6t+2t2. Find the generalized error coefficients and the steady state error.
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5 (a)
Sketch the Bedplate showing the magnitude in dB and phase angle in degree as a function of log frequency for the transfer function given by \( G(s) = \dfrac {10} {s(1+0.5s) (1+0.1s)} \) and hence determine the gain margin and the phase margin of the system.
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5 (b)
Sketch the root locus for n unity feedback system with open loop transfer function \( G(s) = \dfrac {K}{s(s^2 + 8s + 32)}. \)
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6 (a)
Using Routh Hurwitz criterion for the unity feedback system with open loop transfer function \( G(s) = \dfrac {K}{s(s+1) (s+2) (s+5)} \) find
i) the range of k for stability
ii) the value of k for marginally stable
iii) the actual location of the closed loop poles when the system is marginally stable.
i) the range of k for stability
ii) the value of k for marginally stable
iii) the actual location of the closed loop poles when the system is marginally stable.
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6 (b)
Explain controllably and observably.
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