Hot questions in Control Systems
A system with the open loop transfer function $G(s)=\frac{K}{s(s+2)(s^2+2s+2)}$ is connected in a negative feedback configuration with a feedback gain of unity. For the closed loop system to be marginally stable, the value of $K$ is ______
asked Feb 12, 2017 in Control Systems by makhdoom ghaya (9.3k points)
negative-feedback
marginally-stable
The root locus of a unity feedback system is shown in the figure The closed loop transfer function of the system is $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)}$ $\frac{C(s)}{R(s)}=\frac{-K}{(s+1)(s+2)+K}$ $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)-K}$ $\frac{C(s)}{R(s)}=\frac{K}{(s+1)(s+2)+K}$
bode-plot
A single-input single-output feedback system has forward transfer function $G(s)$ and feedback transfer function $H(s)$. It is given that $|G(s)H(s)|< 1$ . Which of the following is true about the stability of the system? The system is always stable The ... are in left half of the s-plane It is not possible to say whether or not the system is stable from the information given
transfer-function
feed-back-system
The closed loop transfer function of a system is $T(s)=\frac{4}{s^2+0.4S+4}$ The steady state error due to unit step input is __________.
unit-step-function
closed-loop-system
The magnitude Bode plot of a network is shown in the figure The maximum phase angle $\phi _m$ and the corresponding gain $G_m$ respectively, are $-30^{\circ}$ and $1.73$ $dB$ $-30^{\circ}$ and $477$ $dB$ $+30^{\circ}$ and $4.77$ $dB$ $+30^{\circ}$ and $1.73$ $dB$
The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2 − j3)$. List all the poles and zeroes. Poles at $(2 \pm j3)$, no zeroes. Poles at $(\pm 2 − j3)$, one zero at origin. Poles at $(2 − j3)$, $(−2 + j3)$, zeroes at $(−2 − j3)$, $(2 + j3)$. Poles at $(2 \pm j3)$, zeroes at $(−2 \pm j3)$.
second-order-real-system
zeroes
The open loop poles of a third order unity feedback system are at $0, −1, −2$. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be $K$. Now suppose we introduce a zero in the open loop ... corresponds to a frequency less than $K$ It corresponds to a frequency $K$ Root locus of modified system never transits to unstable region
root-locus
unity-feedback-system
For the given system, it is desired that the system be stable. The minimum value of $\alpha$ for this condition is ____________. .
A discrete system is represented by the difference equation $\begin{bmatrix} X_1(k+1)\\ X_2(k+2) \end{bmatrix}=\begin{bmatrix} a & a-1\\ a+1 & a \end{bmatrix}\begin{bmatrix} X_1(k)\\X_2(k) \end{bmatrix}$ It has initial conditions $X_1(0)$ = $1$; $X_2(0)$ = $0$. The pole locations of the system for $a$ = $1$, are $1\pm j0$ $-1\pm j0$ $\pm 1+j0$ $0\pm j1$
stability-study
The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\dfrac{s+1}{5s^2+6s+2}$ $\dfrac{s+1}{s^2+6s+2}$ $\dfrac{s+1}{s^2+4s+2}$ $\dfrac{1}{5s^2+6s+2}$
asked Feb 12, 2017 in Control Systems by piyag476 (1.5k points)
The signal flow graph of a system is shown below. $U(s)$ is the input and $C(s)$ is the output. Assuming, $h_1=b_1$ and $h_0=b_0-b_1a_1$ , the input-output transfer function, $G(s)=\frac{C(s)}{U(s)}$ of the system is given by $G(s)=\frac{b_0s+b_1}{s^2+a_0s+a_1} \\ $ $G(s)=\frac{a_1s+a_0}{s^2+b_1s+b_0} \\ $ $G(s)=\frac{b_1s+b_0}{s^2+a_1s+a_0} \\$ $G(s)=\frac{a_0s+a1}{s^2+b_0s+b_1}$
In the figure shown, assume the op-amp to be ideal. Which of the alternatives gives the correct Bode plots for the transfer function $\dfrac{V_o(\omega )}{V_i(\omega )}?$
Consider an LTI system with transfer function $H(s)=\frac{1}{s(s+4)}$ If the input to the system is $cos(3t)$ and the steady state output is $Asin(3t+\alpha )$ , then the value of $A$ is $1/30$ $1/15$ $3/4$ $4/3$
linear-time-invariant-system
The operational amplifier shown in the figure is ideal. The input voltage (in Volt) is $V_{i} = 2 \sin(2\pi × 2000t)$. The amplitude of the output voltage $V_{0}$ (in Volt) is ________.
pid-controller
A Bode magnitude plot for the transfer function $G(s)$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant? $\frac{1000(s+10)}{s+1000}$ $\frac{10(s+10)}{s(s+1000)}$ $\frac{s+1000}{10s(s+10)}$ $\frac{s+1000}{10(s+10)}$
Consider the circuit shown in the figure. In this circuit $R=1 k\Omega$, and $C=1 \mu F$. The input voltage is sinusoidal with a frequency of $50$ Hz, represented as a phasor with magnitude $V_{i}$ and phase angle $0$ radian as shown in the figure. The output voltage is ... $0$ $\pi$ $\frac{\pi}{2}$ $-\frac{\pi}{2}$
feedback-system
The Bode plot of a transfer function $G(s)$ is shown in the figure below. The gain $\big(20 \log\mid G(s) \mid \big)$ is $32 dB$ and $-8 dB$ at $1$ rad/s and $10$ rad/s respectively. The phase is negative for all $\omega$. Then $G(s)$ is $\frac{39.8}{s} \\$ $\frac{39.8}{s^2} \\$ $\frac{32}{s} \\$ $\frac{32}{s^2}$
For the transfer function $G(s)=\frac{5(s+2)}{s(s+0.25)(s^2+4s+25)}$ The values of the constant gain term and the highest corner frequency of the Bode plot respectively are $3.2$ , $5.0$ $16.0$ , $4.0$ $3.2$ , $4.0$ $16.0$ , $5.0$
GATE2013-3
Assuming zero initial condition, the response $y(t)$ of the system given below to a unit step input $u(t)$ is? $u(t)$ $t\:u(t)$ $\dfrac{t^2}{2}u(t)$ $e^{-t}u(t)$
step-function
The open-loop transfer function of a dc motor is given as $\dfrac{\omega (s)}{V_a(s)}=\dfrac{10}{1+10s}$.When connected in feedback as shown below, the approximate value of $K_a$ 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 $1$ $5$ $10$ $100$