MATERIALS SCIENCE AND ENGINEERING: INTRO
10th Edition
ISBN: 9781119571308
Author: Callister
Publisher: WILEY
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Chapter 5, Problem 1SSP
To determine
The drive-in diffusion time for aluminum diffusion in silicon.
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16.6. The transfer function of a process and measurement element connected in series is
given by
e-0.43
(2s + 1)²
(a) Sketch the open-loop Bode diagram (gain and phase) for a control system involving
this process and measurement lag.
(b) Specify the gain of a proportional controller to be used in this control system.
Determine (a) the input impedance and (b) the reflectedimpedance, both at terminals (a,b) in the circuit of Fig. P11.14.
16.7. (a) For the control system shown in Fig. P16-7, determine the transfer function C/U.
(b) For K-2 and to =1, find C(1.25) and the offset if U(t) = u(t), a unit step.
(c) Sketch the open-loop Bode diagram for K = 2 and tp = 1. For the upper part of the
diagram (AR versus ), show the asymptotic approximation. Include the transfer func-
tion for the controller in the open-loop Bode diagram.
(d) From the Bode diagram, what do you conclude about the stability of the closed-loop
system?
FIGURE P16-7
K(1+8)
Chapter 5 Solutions
MATERIALS SCIENCE AND ENGINEERING: INTRO
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- 11.4 Determine Vout in the circuit shown in Fig. P11.4.arrow_forward16.1. Calculate the value of gain K needed to produce continuous oscillations in the control system shown in Fig. P16-1 when (a) n is 2 (b) n is 3 Do not use a graph for this calculation. 2 R KE (2s+1)" FIGURE P16-1arrow_forwardFor the circuit in Fig. P11.1, determine (a) iL(t) and (b) theaverage power dissipated in RL.arrow_forward
- Example 16.1. Find a relation between relative stability (see below) and the phase margin for the control system of Fig. 16-7. A proportional controller is to be used. This block diagram corresponds to the stirred-tank heater system, for which the block diagram has been given in Fig. 12-17. The particular set of constants is T = Tm = 1 1 1 wC These are to be regarded as fixed, while the proportional gain Ke is to be varied to give a satisfactory phase margin. R- Ke U 1 s+1 1 C s+1arrow_forwardDesign a synchronous Up/Down counter to produce the following sequence (4 9 2,0,7,6,3,1,5) using T flip-flop. The counter should count up when Up/Down =1, and down when Up/Down = 0.arrow_forward16.2. (a) Plot the asymptotic Bode diagram B/E versus for the control system shown in Fig. P16-2. (b) The gain Ke is increased until the system oscillates continuously at a frequency of 3 rad/min. From this information, calculate the transportation lag parameter Td. R Ke 1 FIGURE P16-2 B 10s+1 s+1 e +1arrow_forward
- Solve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values X0=(000). - 2x16x2 x3 = -38 - -3x1 x2+7x3 = −34 -8x1 + x2 - 2x3 = -20arrow_forwardSolve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values Xº=(000). 3x12x2x3 = 4 - 2x1 x2 + 2x3 = 10 x13x24x3 = 4arrow_forwardEstimate the required air flow rate for the new activated sludge plant at Pea Ridge (Problems 23-223-723-10, and 23-13). The flow rate is 8,450 m³/day, the concentration of bCOD going into the system (So) is 137 mg/L, the concentration of bCOD leaving the system (S) is 16.3 mg/L, and the mass of cells produced per day (Pxvss) is 277.4 kg/d. Use the following assumptions to estimate the required air flow rate: . Clean water correction, a = 0.50 . Salinity correction, B = 0.95 Fouling factor = 0.9 Wastewater temperature = 12°C Atmospheric pressure = 101.325 kPa .Elevation 500 m . Depth of aerator = 5.6 m Operating DO 2.0 mg/L Percent oxygen leaving aeration tank - 19% ■ Manufacturer's SOTR = 535 kg/d Manufacturer's air flow rate at standard conditions 50 m³/d - aerator Express your answer with the units of m³/d and round to the nearest integer.arrow_forward
- Use Newton-Raphson method to solve the system x² - 2x-y+0.5= 0 x² + 4y² 4 = 0 - with the starting value (xo,yo) = (2,0.25) and two iteration number.arrow_forwardDetermine the required solids retention time (SRT) of a completely mixed activated sludge aeration tank for a conventional activated sludge system treating a design flow rate of 34,560 m³/d, where the effluent standards are 30.0 mg/L for BODs and 30.0 mg/L for total suspended solids (TSS). Assume that the BOD5 of the effluent TSS is 70% of the TSS concentration. Assume the BODs concentration leaving the primary clarifier is 128 mg/L that the MLVSS concentration (X₂) is 2,500 mg/L. Assume the following values for the growth constants: Ks 100 mg/L BODS ⚫ Hm - 2.5 d 1 kd = 0.050 d 1 Y = 0.50 mg VSS/mg BODs removed Express your answer in days and round to the nearest 0.1.arrow_forwardSolve the following systems using Gauss Seidal and Jacobi iteration methods for n=8 and initial values X0=(000). - 2x16x2 x3 = -38 - -3x1 x2+7x3 = −34 -8x1 + x2 - 2x3 = -20arrow_forward
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