STUPIDSID
1(a)
Write short notes on open loop control systems and closed loop control systems. Discuss their advantages and disadvantages.
7 M
1(b)
Obtain system transfer function C(s)/R(s) using block diagram reduction
technique for the system shown in figure 1.
7 M
2(a)
Derive Correlation Between Transfer Functions and State-Space Equations.
4 M
Solved any one question from Q.2(b) & Q.2(c)
2(b)
Explain Mason's gain formula.
3 M
2(c)
Determine the state space model of the system shown in figure 2.
7 M
Solved any one question from Q.3 & Q.4
2(d)
Define transfer function.
Obtain the transfer
of the system defined by \[\begin{bmatrix}
\dot{x_1}\\
\dot{x_2}\\
\dot{x_3}
\end{bmatrix}=\begin{bmatrix}
-1 & 1 & 0\\
0 & -1 & 1\\
0 & 0 & -2
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2\\
x_3
\end{bmatrix}+\begin{bmatrix}
0\\
0\\
1
\end{bmatrix}u\ \ \ \ \ y=\begin{bmatrix}
1 & 0 & 0
\end{bmatrix}\begin{bmatrix}
x_1\\
x_2\\
x_3
\end{bmatrix}\]
7 M
3(a)
Define steady state error and derive the expressions for error constants K p , K v and K a corresponding to step, ramp and parabolic input respectively.
7 M
3(b)
Obtain the values of delay time t d , rise time t r , peak time t p , settling time t s
and peak overshoot M p for the given open loop transfer function of a unity feedback control system G(s)=16/s (s+6)
7 M
4(a)
Derive the expressions
Of Rise time, Peak time and Peak overshoot for the system having close loop transfer function \[T(s)=\dfrac{C(s)}{R(s)}=\dfrac{{\omega _{n}}^{2}}{s62+2\xi \omega _ns+{\omega _{n}}^{2}}.\]
7 M
Solved any one question from Q.5 & Q.6
4(b)
The open loop transfer function of a unity feedback system is given by \[G(s)=\dfrac{k}{s(1+Ts)}\] where k and T are constants. By what factor should the amplifier gain be reduced so that the peak overshoot of the system is reduced from 60% to 15% ?
7 M
5(a)
Using Routh's criterion check the stability of a system whose characteristic equation is given by s 6 +2s 5 +8s 4 +12s 3 +20s 2 +16s+16=0
7 M
5(b)
What is Root locus? Sketch the Root locus plot for the unity feedback system having \[G(s)=\dfrac{K}{s(s+1)(s+3)(s+4)}\]
7 M
6(a)
Determine range of k for system stability, for the given characteristic equation of Feedback control system s 4 +2s 3 +(4+k)s 2 +9s+25=0
7 M
Solved any one question from Q.7 & Q.8
6(b)
Sketch the Root locus plot for the unity feedback system having an open loop transfer function \[G(s)=\dfrac{K}{s(s+3)(s^2+2s+2)}\].
7 M
7(a)
State and explain compensator? Explain Phase-Lead compensator in detail.
7 M
7(b)
The feed forward transfer function of a close loop system is G(s)=1/s(s+1) and feedback transfer function is H(s) =1/(s+2).
(i) Draw the polar plot of G(s)H(s).
(ii) Find ? corresponding to \[\angle G(j\omega )H(j\omega )=180^{\circ}.\]
(iii) Find \[| G(j\omega )H(j\omega )|\] corresponding to frequency obtain in (ii).
(i) Draw the polar plot of G(s)H(s).
(ii) Find ? corresponding to \[\angle G(j\omega )H(j\omega )=180^{\circ}.\]
(iii) Find \[| G(j\omega )H(j\omega )|\] corresponding to frequency obtain in (ii).
7 M
8(a)
Draw the Nyquist plot for G(s)=1/s(s-1) and comment on system stability.
7 M
8(b)
Determine gain margin and phase margin using bode plot for the system having transfer function \[G(s)H(s)=\dfrac{1}{s(1+s)(1+0.1s)}\] and comment on stability.
7 M
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