Recent questions tagged steady-state

​​​In the feedback control system shown in the figure below $G(s)=\frac{6}{s(s+1)(s+2)}$.$\text{R(s), Y(s)}$, and $\text{E(s)}$ are the Laplace transforms of $r(t), y(t)$...

A closed loop system is shown in the figure where $\mathrm{k}>0$ and $\alpha>0$. The steady state error due to a ramp input $\left(\mathrm{R}(\mathrm{s})=\alpha / \mathrm...

In given figure, the steady state output voltage corresponding to the input voltage $3+4 \sin 100 t \mathrm{~V}$ is$3+\frac{4}{\sqrt{2}} \sin \left(100 t-\frac{\pi}{4}\ri...

For the given circuit, which is in steady stateFind the frequency $\omega_{\mathrm{o}}$ at which the magnitude of the impedance across terminals $a, b$ reaches a maximum....

A unity feedback system has the plant transfer function $G_{p}(s)=\frac{1}{(s+1)(2 s+1)}$Determine the frequency at which the plant has a phase lag of $90^{\circ}$. An in...

A $\text{DC}$ voltage source is connected across a series $\text{R-L-C}$ circuit. Under steady-state conditions, the applied $\text{DC}$ voltage drops entirely across the...

The unit impulse response of a system is\[h(t)=e^{-t}, t \geq 0\]For this system, the steady-state value of the output for unit step input is equal to$-1$$0$$1$$\infty$

The time domain behavior of an $R L$ circuit is represented by\[ L \frac{d i}{d t}+R i=V_{o}\left(1+B e^{-R t / L} \sin t\right) u(t). \]For an initial current of $i(0)=\...

A unity negative feedback closed loop system has a plant with the transfer function $\text{G}(s)=\frac{1}{s^{2}+2 s+2}$ and a controller $\text{G}_{c}(s)$ in the feedforw...

The circuit shown below is driven by a sinusoidal input $\mathrm{v}_{\mathrm{i}}=\mathrm{V}_{\mathrm{P}} \cos (\mathrm{t} / \mathrm{RC})$. The steady state output $\text{...

Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically (where $t...

Two linear time-invariant systems with transfer functions$$G_{1}(s) = \frac{10}{s^{2}+s+1} \; \text{and} \; G_{2}(s) = \frac{10}{s^{2}+s\sqrt{10}+10}$$have unit step resp...

The block diagram of a closed-loop control system is shown in the figure. $R(s), Y(s),$ and $D(s)$ are the Laplace transforms of the time-domain signals $r(t), y(t),$ and...

In the circuit shown below, all the components are ideal and the input voltage is sinusoidal. The magnitude of the steady-state output $V_{o}$ ( rounded off to two decima...

Consider the following closed loop control systemwhere $G\left ( s \right )=\dfrac{1}{s\left ( s+1 \right )}$ and $C\left ( s \right )=K\dfrac{s+1}{s+3}$. If the steady s...

In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steady-state current $i(t)$, milliamperes (mA), is$\sin(1000\: t)+ \cos...

The diodes $D1$ and $D2$ in the figure are ideal and the capacitors are identical. The product $RC$ is very large compared to the time period of the ac voltage. Assuming ...

Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The...

The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current a...

The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/s...

In the circuit shown, the average value of the voltage $V_{ab}$ (in Volts) in steady state condition is ________.

In the circuit shown, the initial voltages across the capacitors $C_{1}$ and $C_{2}$ are $1\: V$ and $3\: V,$ respectively. The switch is closed at time $t = 0$. The tota...

The steady state output of the circuit shown in the figure is given by $y(t)=A(\omega) \sin (\omega t + \phi ( \omega))$. If the amplitude $\mid A (\omega ) \mid =0.25$, ...

The steady state error of the system shown in the figure for a unit step input is _________.

A continuous, linear time-invariant filter has an impulse response $h(t)$ described by $$h(t) = \begin{cases}3 & \text{for } 0 \leq t \leq 3 \\ 0 & \text{otherwise} \end{...