List of practice Questions

A controller \( D(s) \) of the form \( (1 + K_D s) \) is to be designed for the plant \[ G(s) = \frac{1000\sqrt{2}}{s(s+10)^2} \] as shown in the figure. The value of \( K_D \) that yields a phase margin of \(45^\circ\) at the gain cross-over frequency of 10 rad/sec is __________ (round off to one decimal place). 

Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ___________ (round off to the nearest integer).

Using shunt capacitors, the power factor of a 3-phase, 4 kV induction motor (drawing 390 kVA at 0.77 pf lag) is to be corrected to 0.85 pf lag. The line current of the capacitor bank, in A, is __________ (round off to one decimal place). 

Consider the state-space model 
\[ \dot{\mathbf{x}}(t) = A \mathbf{x}(t) + B r(t), \quad y(t) = C \mathbf{x}(t) \]
where \( \mathbf{x}(t) \), \( r(t) \), and \( y(t) \) are the state, input, and output, respectively. The matrices \( A \), \( B \), and \( C \) are given below:
\[ A = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}, \quad B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, \quad C = \begin{bmatrix} 1 & 0 \end{bmatrix} \]
The sum of the magnitudes of the poles is __________ (round off to the nearest integer).

An ideal low pass filter has frequency response given by \[ H(j\omega) = \begin{cases} 1, & |\omega| \leq 200\pi \\ 0, & \text{otherwise} \end{cases} \] Let \( h(t) \) be its time domain representation. Then h(0) = _________ (round off to the nearest integer).

The steady state capacitor current of a conventional DC-DC buck converter, working in CCM, is shown in one switching cycle. If the input voltage is \( 30~{V} \), the value of the inductor used, in mH, is __________ (round off to one decimal place)

In the Wheatstone bridge shown below, the sensitivity of the bridge in terms of change in balancing voltage \( E \) for unit change in the resistance \( R \), in V/Ω, is __________ (round off to two decimal places). 

In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a \(2\,\Omega\) resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: \( V_{{Source}} = 200\,{V}, \quad V_R = 9\,{V}, \quad V_{{Load}} = 199\,{V}. \) Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, in W, is __________ (round off to one decimal place).