The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in the 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

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The signal flow graph of a system is shown below. U(s) is the input and C(s) is the output.Assuming, h1=b1 and ho=b0−b1a1, the input- output transfer function, G(s)=C(s)U(s) of the system is given by

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Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is

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In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system ?

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The open-loop transfer function of a dc motor is given as ω(s)Va(s)=101+10s. When connected in feedback as shown below, the approximate value of Ka that will reduce the time constant of the closed loop system by one hundred times as compared to that of the open-loop system is

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For a system with the transfer function: H(s)=3(s−2)s3+4s2−2s+1the matrix A in the state space form ˙x=Ax+Bu is equal to

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The loop transfer function of a negative feedback system is given byG(s)H(s)=Ks(s+2)(s+6),where k>0. The value of K at the breakaway point of the root locus for the above system (rounded of to one decimal place) is5

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A second order control system has the settling time of 5 seconds (for ± 2) tolerance ) and the peak time of 2 seconds. The locations of poles in the s-plane are

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The frequency responseG(s)=1/[s(s+1)(s+2)] plotted in the complex G(jω) plane (for 0<ω<∞) is

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The loop transfer function of a feedback control system is given by,G(s)H(s)=K(s+6)s(s+4)The range of value of K for underdamped system will be

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A unity feedback system has an open loop transfer function, G(s)=Ks2. Its root locus plot will be

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The asymptotic Bode phase plot of G(s)=k(s+0.1)(s+10)(s+p1), with k and p1 both positive , is shown below.The value of p1 is1

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A second-order real system has the following properties:(a) The damping ratio ξ=0.5 and undamped natural frequency ωn=10rad/s.(b) The steady state value of the output to a unit step input is 1.02.The transfer function of the system is

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Consider a linear system whose state space representation is ˙x(t)=Ax(t).If the initial state vector of the system is x(0)=[1−2],then the system response is x(t)=[e−2t−2e−2t]. If the initial state vector of the system changes to x(0)=[1−1], then the system response becomes x(t)=[e−t−e−t].The eigen-value and eigen-vector pairs (λi,vi) for the system are

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The root locus of the systemG(s)H(s)=Ks(s+2)(s+3)has the break-away point located at

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