EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
7th Edition
ISBN: 9780100663657
Author: ULABY
Publisher: YUZU
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Textbook Question
Chapter 1.6, Problem 7E
Express the following complex functions in polar form:
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Q2. Figure Q2 shows a block diagram with an input of C(s) and an output R(s).
a)
C(s)
K₁
R(s)
K2
1 + 5s
1+2s
Figure Q2. Block diagram of control system.
Simply the block diagram to get the transfer function of the system C(s)/R(s).
b)
What is the order of the system?
c)
What is the gain of the system?
d) Determine the values of K₁ and K₂ to obtain a natural frequency w of
0.5 rad/s and damping ratio of 0.4.
e) What is the rise time and overshoot of the system with a unit step input?
Q4.
a) A purely derivative controller (i.e. with a zero at the origin only) is defined
by an improper transfer function. Considering its asymptotic behaviour,
explain why a purely derivative controller is difficult to implement in
practice. Relate your explanation to the potential limitations on system
performance.
b) Discuss the potential issues faced by a control system with a large cut-off
frequency. Relate your discussion to the implications on system
performance.
c)
The transfer function of a lag compensator is given by
2
KPID(S) = 2.2++0.2s
S
By using the asymptotic approximation technique:
(i) Obtain the standard form and corner frequency for each individual
component of KPID(S).
(ii) Clearly describe the asymptotic behaviour of each individual
component of KPID(S).
Module Code: EN2058
Q1. a) List the advantages and disadvantages of a closed loop system compared to
an open loop system.
b)
c)
What is the procedure for designing a control system for a bread toaster?
An RC circuit is given in Figure Q1. vi(t) and v(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
vo(t)
R₁ =R2 = 10 k
R3 = 100 kn C₁ = 100 μF
Figure Q1. RC circuit.
(iii) Assuming zero initial conditions, obtain the impulse and ramp responses
of the circuit from the step response derived in (ii). Sketching is not
needed.
Chapter 1 Solutions
EBK FUNDAMENTALS OF APPLIED ELECTROMAGN
Ch. 1.3 - Prob. 1CQCh. 1.3 - What is Coulombs law? State its properties.Ch. 1.3 - What are the two important properties of electric...Ch. 1.3 - What do the electrical permittivity and magnetic...Ch. 1.3 - What are the three branches and associated...Ch. 1.4 - How can you tell if a wave is traveling in the...Ch. 1.4 - Prob. 7CQCh. 1.4 - Why does a negative value of 0 signify a phase...Ch. 1.4 - Consider the red wave shown in Fig. E1.1. What is...Ch. 1.4 - The wave shown in red in Fig. E1.2 is given by...
Ch. 1.4 - The electric field of a traveling electromagnetic...Ch. 1.4 - Prob. 4ECh. 1.4 - The red wave shown in Fig. E1.5 is given by...Ch. 1.4 - An electromagnetic wave is propagating in the z...Ch. 1.5 - What are the three fundamental properties of EM...Ch. 1.5 - What is the range of frequencies covered by the...Ch. 1.5 - Prob. 11CQCh. 1.6 - Express the following complex functions in polar...Ch. 1.6 - Show that 2j=(1+j). (See EM.)Ch. 1.7 - Prob. 12CQCh. 1.7 - How is the phasor technique used when the forcing...Ch. 1.7 - A series RL circuit is connected to a voltage...Ch. 1.7 - A phasor voltage is given by V=j5V. Find (t).Ch. 1 - A 2 kHz sound wave traveling in the x direction in...Ch. 1 - For the pressure wave described in Example 1-1,...Ch. 1 - A harmonic wave traveling along a string is...Ch. 1 - A wave traveling along a string is given by...Ch. 1 - Two waves, y1(t) and y2(t), have identical...Ch. 1 - The height of an ocean wave is described by the...Ch. 1 - A wave traveling along a string in the +x...Ch. 1 - Two waves on a string are given by the following...Ch. 1 - Give expressions for y(x, t) for a sinusoidal wave...Ch. 1 - An oscillator that generates a sinusoidal wave on...Ch. 1 - Prob. 11PCh. 1 - Given two waves characterized by...Ch. 1 - The voltage of an electromagnetic wave traveling...Ch. 1 - A certain electromagnetic wave traveling in...Ch. 1 - Prob. 15PCh. 1 - Prob. 16PCh. 1 - Complex numbers z1 and z2 are given z1=3j2z2=4+j3...Ch. 1 - Complex numbers z1 and z2 are given by...Ch. 1 - If z=2+j4, determine the following quantities in...Ch. 1 - Find complex numbers t=z1+z2 and s=z1z2, both in...Ch. 1 - Complex numbers z1 and z2 are given by...Ch. 1 - If z=3j5, find the value of ln(z).Ch. 1 - If z = 3 j4. find the value of ez.Ch. 1 - Prob. 24PCh. 1 - A voltage source given by s(t)=25cos(2103t30)(V)...Ch. 1 - Find the phasors of the following time functions:...Ch. 1 - Find the instantaneous time sinusoidal functions...Ch. 1 - A series RLC circuit is connected to a generator...Ch. 1 - The voltage source of the circuit shown in Fig....
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