Challenging Engineering Problems with Detailed Answers
2.1 Distillation column is used to distil a binary mixture with x,y,z as the more volatile mole fraction compositions and B(Bottoms), D(distillate),R(Reflux) and F(Feed) as molar flow rates. It is desired to control distillate composition y despite the disturbance in the feed flow rate F. All flow rates can be measured and manipulated except for F, which can only be measured. a) What are the input and the output variables ? (4) b) Sketch the schematic diagram of the system. (5) c) Use the schematic diagram to construct the Feedforward and feedback control methods. (11) QUESTION 2 2.1 Distillation column is used to distil a binary mixture with x,y,z as the more volatile mole fraction compositions and B(Bottoms), D(distillate), R(Reflux) and F(Feed) as molar flow rates. It is desired to control distillate composition y despite the disturbance in the feed flow rate F. All flow rates can be measured and manipulated except for F, which can only be measured. a) What are the input and the output variables? (4) b) Sketch the schematic diagram of the system. (5) c) Use the schematic diagram to construct the Feedforward and feedback control methods.
Answer the following triphasic problem:-There is a star-balanced three-phase load whose impedance per phase is 45 ohms at 52, fed at a line voltage of 2,300 Volts, 3 phases, 4 wires. Calculate phase voltage, line current, phase current, active power, reactive power, apparent power and power factor-There is a balanced three-phase load connected in delta, whose impedance per line is 38 ohms at 50, fed with a line voltage of 360 Volts, 3 phases, 50 hertz. Calculate phase voltage, line current, phase current; Active, reactive and apparent power
Problem I (30pts): Energies of Signals and Their Combinations Using the well-known unit-step function ull), two real-valued deterministic energy signals x(i) and (d) are constructed as follows, x(1) = u(1) - (1-10) and y(i)= u(1) - 2u(1-5)+ult -10), with their energies denoted by E, and E, respectively, 1. 6pts) Sketch the waveforms of signals x(i), y(i) and the product signal p., () x() y(i), with critical points clearly marked. 2. (6pts) Find the values for the followings, E,=? and 5 p.160dn = 5 x0) 360)dt = 2 3. (10pts) Find energies for the following two new signals constructed from linear combinations of x(1) and y(t), i.e. 2:() = x(t)+ y(t), and z.(1) = x(1)- y(t). That is, Ez =? and Ez = ? 4. (8pts) Find energies for the following two new signals constructed from linear combinations of the time-shifted versions of x(t) and y(t), i.e., (1) = x(1 +5)+ y(t +5), and 2(1) = x(t +5), y(t +5). That is, E = ? and E. = ?
1. (a) A logic circuit is designed for controlling the lift doors and they should close (Y) if:(i) the master switch (W) is on AND either(ii) a call (X) is received from any other floor, OR(iii) the doors (Y) have been open for more than 10 seconds, OR(iv) the selector push within the lift (Z) is pressed for another floor. Devise a logic circuit to meet these requirements.(8 marks) (b) Use logic circuit derived in part (a) and provide the 2-input NAND gate only implementation of theexpression. Show necessary steps.(c) Use K-map to simplify the following Canonical SOP expression.(,,,) = (,,,,,,,,,)
3. Design a low-pass filter to meet the following specifications: i) Pass-band from 0.1 Hz to 1 kHz ii) Attenuation: -12 dB (with respect to the pass-band) at 2 kHz iii) Pass-band gain: +6 dB iv) Available resistors: 5 k2 and 10 k2 only (PSpice) v) Available resistors: 1.5 k2 only (M2K) (Note: there are 5 available so you may use parallel or series combinations). Use a straight-line Bode plot approximation drawn on semi-log graph paper to initially design the filter and show your calculations, including the straight-line Bode plot. Note: in order to determine the value of C, you may try frequency scaling, ie: oon' = 2-1 ke= (n)/ (0,), and kr = 1/(RC) which will reduce the attenuation at the cutoff frequency to -3 dB, (see pages 588 and 589 of the text), however this may not be necessary to obtain the required roll-off/slope for the nth-order filter (ie: con= 1/(RC)). Hint: Based on your straight-line approximation, you should be able to determine the proper order of the filter (ie: 1st, 2nd, 3rd, etc.) and the cutoff frequency, on (20 pts) a) Using P-Spice, build the filter model using ideal op-amp(s), that do not require a DC bias, and run the simulation (AC Sweep) between 1 Hz and 100 kHz. Include (with date / time stamp) in your report a screen-shot of the circuit diagram as well as the Bode plot (semi-log plot). Be sure to change the default color of the Bode plot background from black to white and make sure that the trace is a dark color for legibility. Using the cursor, identify both the cutoff frequency (n) and the attenuation at 2 kHz. (60 pts)