Question 1 |
The damping ratio and undamped natural frequency of a closed loop system as
shown in the figure, are denoted as \zeta and
\omega _n, respectively. The values of \zeta and \omega _n are
\zeta =0.5 \text{ and }\omega _n=10 rad/s | |
\zeta =0.1 \text{ and }\omega _n=10 rad/s | |
\zeta =0.707 \text{ and }\omega _n=10 rad/s | |
\zeta =0.707 \text{ and }\omega _n=100 rad/s |
Question 1 Explanation:
Reduced the block diagram:
Transfer function,
\frac{C(s)}{R(s)}=\frac{100/(s(s+10))}{1+(100/s(s+10))}=\frac{100}{s^2+10s+100}
Standard form,
T.F.=\frac{\omega _n^2}{s^2+2\xi \omega _ns+\omega _n^2}
On comparison : \omega =\sqrt{100}=10rad/sec and 2\xi \omega _n=10
\Rightarrow \xi=\frac{10}{2 \times 10}=0.5
Transfer function,
\frac{C(s)}{R(s)}=\frac{100/(s(s+10))}{1+(100/s(s+10))}=\frac{100}{s^2+10s+100}
Standard form,
T.F.=\frac{\omega _n^2}{s^2+2\xi \omega _ns+\omega _n^2}
On comparison : \omega =\sqrt{100}=10rad/sec and 2\xi \omega _n=10
\Rightarrow \xi=\frac{10}{2 \times 10}=0.5
Question 2 |
In the given figure, plant G_{P}\left ( s \right )=\dfrac{2.2}{\left ( 1+0.1s \right )\left ( 1+0.4s \right )\left ( 1+1.2s \right )} and compensator G_{C}\left ( s \right )=K\left [ \dfrac{1+T_{1}s}{1+T_{2}s} \right ]. The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is _____________.
(Round off to 2 decimal places.)
(Round off to 2 decimal places.)
12.25 | |
14.12 | |
9.54 | |
6.22 |
Question 2 Explanation:
\begin{aligned} e_{s s} &=\lim _{s \rightarrow 0}\left[\frac{s R}{1+G_{C} G_{p}}-\frac{s D G_{p}}{1+G_{C} G_{P}}\right] \\ R(s) &=0 ; D(s)=\frac{1}{s} \\ \therefore \qquad\qquad e_{s s}&=\frac{2.2}{1+2.2 K}=0.1 \\ \therefore \qquad\qquad K_{\min }&=9.54 \end{aligned}
Question 3 |
Consider a closed-loop system as shown. G_{P}\left ( s \right )=\dfrac{14.4}{s\left ( 1+0.1s \right )} is the plant transfer function and G_{c}(S)=1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is ___________________ \text{rad/s}. (Round off to 2 decimal places.)
10.9 | |
4.62 | |
12.02 | |
8.05 |
Question 3 Explanation:
\begin{aligned} q(s)&=s^{2}+10 s+144=0 \\ \omega_{n}&=12 ; \xi=\frac{5}{12} \\ \omega_{d}&=\omega_{n} \sqrt{1-\xi^{2}} \\ \quad&=12 \sqrt{\frac{119}{144}}=10.90 \end{aligned}
Question 4 |
Consider a negative unity feedback system with the forward path transfer function \frac{s^2+s+1}{s^3+2s^2+2s+K}, where K is a positive real number. The value of K for which the system
will have some of its poles on the imaginary axis is ________ .
9 | |
8 | |
7 | |
6 |
Question 4 Explanation:
CE is
1+G(s)H(s)=0
\Rightarrow \, 1+\frac{s^{2}+s+1}{s^{3}+2s^{2}+2s+k}=0
\Rightarrow \, s^{3}+3s^{2}+3s+(1+K)=0
R.H. criteria:
9 - (1 + K) = 0
\Rightarrow \, \, K=8
1+G(s)H(s)=0
\Rightarrow \, 1+\frac{s^{2}+s+1}{s^{3}+2s^{2}+2s+k}=0
\Rightarrow \, s^{3}+3s^{2}+3s+(1+K)=0
R.H. criteria:
9 - (1 + K) = 0
\Rightarrow \, \, K=8
Question 5 |
Which of the following option is correct for the system shown below?
4^{th} order and stable | |
3^{rd} order and stable | |
4^{th} order and unstable | |
3^{rd} order and unstable |
Question 5 Explanation:
\begin{aligned}
1+\frac{20}{s^{2}(s+1)(s+20)}&=0\\ (s^{3}+s^{2})(s+20)+20&=0\\ s^{4}+20s^{3}+s^{3}+20s^{2}+20&=0\\ s^{4}+21s^{3}+20s^{2}+20&=0
\end{aligned}
Given system is fourth order system and unstable.
stablity status: since it has one missing term of 's' thus undoubtedly given transfer function is unstable.
Given system is fourth order system and unstable.
stablity status: since it has one missing term of 's' thus undoubtedly given transfer function is unstable.
There are 5 questions to complete.