EBK THE ANALYSIS AND DESIGN OF LINEAR C
8th Edition
ISBN: 9781119140320
Author: Toussaint
Publisher: VST
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Chapter 1, Problem 1.13P
The charge flowing through a device is
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c) An RC circuit is given in Figure Q1. vi(t) and vo (t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii) With a unit step change vi(t) applied to the circuit, derive and sketch the
time response of the circuit.
R₁ R2
v₁(t)
R3 C₁
v₁(t)
R₁ = R₂ = 10 k
R3
= 100 kn C₁ = 100 μF
Figure Q1. RC circuit.
c)
A RC circuit is given in Figure Q1.1. Vi(t) and Vo(t) are the input and output
voltages.
(i) Derive the transfer function of the circuit.
(ii)
With a unit step change of Vi(t) applied to the circuit, derive the time
response of the circuit.
C₁ C₂
Vi(t)
Vo(1)
R₁ C₂
R-25 k C=C2=50 µF
Figure Q1.1. RC circuit.
Answer 2 questions for 100 marks
Question 1: Process Design
[25 marks]
An incomplete process design of a flash drum distillation unit is presented in Figure 1. The
key variables to be controlled are flow rate, temperature, composition, pressure and liquid
level in the drum. Disturbances are observed in the feed temperature and composition.
Heat exchangers
Drum
Vapor
Liquid
Pump
Figure 1: Incomplete process design of a distillation unit
Answer the following questions briefly and in a qualitative fashion:
a) Determine which sensors and final elements are required so that the important
variables can be controlled. Sketch them in the figure using correct instrumentation
tags. Describe briefly what instruments you will use and where they should be
located. Reflect on the potential presence of a flow controller upstream of your
process design (not shown in the diagram). How would this affect the level controller in
the drum?
b)
[10 marks]
Describe briefly how you qualitatively determine the…
Chapter 1 Solutions
EBK THE ANALYSIS AND DESIGN OF LINEAR C
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Ch. 1 - A cell phone charger outputs 9.6 V and is...Ch. 1 - For 0t5s, the current through a device is...Ch. 1 - The charge flowing through a device is...Ch. 1 - The 12-V automobile battery in Figure P1-14 has an...Ch. 1 - The current through a device is zero for t0 and is...Ch. 1 - A string of holiday lights is protected by a 12A...Ch. 1 - When illuminated the relationship for a photocell...Ch. 1 - A new 6-V alkaline lantern battery delivers...Ch. 1 - The maximum current allowed by a device's power...Ch. 1 - Traffic lights are being converted from...Ch. 1 - Two electrical devices are connected as shown in...Ch. 1 - Figure P1-22 shows an electric circuit with a...Ch. 1 - Figure P1-22 shows an electric circuit with a...Ch. 1 - In Figure P1-24 the voltage v2 is 10 V and v4 is 5...Ch. 1 - For t0, the voltage across and power absorbed by a...Ch. 1 - Repeat Problem 1-22 using MATLAB to perform the...Ch. 1 - Using the passive sign convention, the voltage...Ch. 1 - Power Ratio (PR) in dB A stereo amplifier takes...Ch. 1 - AC to DC Converter A manufacturer's data sheet for...Ch. 1 - Charge-Storage Device A capacitor is a...Ch. 1 - Compute Data Sheet A manufacturer's data sheet for...Ch. 1 - Light Source Comparison A Today people have three...
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- Answer 2 questions for 100 marks Question 1: Process Design [25 marks] An incomplete process design of a flash drum distillation unit is presented in Figure 1. The key variables to be controlled are flow rate, temperature, composition, pressure and liquid level in the drum. Disturbances are observed in the feed temperature and composition. Heat exchangers Drum Vapor Liquid Pump Figure 1: Incomplete process design of a distillation unit Answer the following questions briefly and in a qualitative fashion: a) Determine which sensors and final elements are required so that the important variables can be controlled. Sketch them in the figure using correct instrumentation tags. Describe briefly what instruments you will use and where they should be located. Reflect on the potential presence of a flow controller upstream of your process design (not shown in the diagram). How would this affect the level controller in the drum? b) [10 marks] Describe briefly how you qualitatively determine the…arrow_forwardQuestion 2: Process Control [75 marks] As a process engineer, you are tasked to control the process shown in Figure 2. For biomedical engineers, the process could be interpreted as the injection of a solution of a medication compound A, with initial concentration CAO, into a human body, simplified as a Continuously Stirred Tank Reactor (CSTR). Therefore, your task is to analyse and model this process. The equipment consists of a mixing tank, mixing pipe and CSTR. F₁ Сло CA2 V₁ mixing pipe F4 CA4 F3 CA3 mixing tank Fs CAS Vs stirred-tank reactor Figure 2: Mixing and reaction processes Assumptions used for modelling are as follows: I. Both tanks are well mixed and have constant volume and temperature. II. All pipes are short and contribute negligible transportation delay, III. All flow rates are constant. All densities are constant and uniform throughout. IV. The first tank is a mixing tank. V. VI. The mixing pipe has no accumulation, and the concentration CA3 is constant The second tank…arrow_forwarda) Reflect on the assumptions and briefly explain their implications for your model. Do you agree with the assumptions? If not, briefly suggest improved assumptions. [6 marks] b) Derive a linear(ised) model (algebraic or differential equation) relating C'A2(t) to C'Ao(f). How do you define your system? What type of balance do you need to solve for this purpose? [12 marks] c) Derive a linear(ised) model (algebraic or differential equation) relating C'A4(t) to C'A2(f). Show your balance equation. [12 marks] d) Derive a linear(ised) model (algebraic or differential equation) relating C'A5(t) to C'A4(f). Show your balance equation. [12 marks] e) Combine the models in parts (a) to (c) into one equation relating C'A5 to C'Ao using Laplace transforms. [15 marks] f) Is the response (for example to step input) stable or unstable? Is the response periodic? Is the response damped? [6 marks] g) Carry out an inverse Laplace Transform for C'Ao(s) = A CAO/s (step function) to find C'A5(t) in the time…arrow_forward
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