EBK MATLAB: AN INTRODUCTION WITH APPLIC
6th Edition
ISBN: 8220103113663
Author: GILAT
Publisher: YUZU
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Chapter 6, Problem 20P
A safe prime is a prime number that can be written in the form 2p +1 where p is also a prime number. For example, 47 is a safe prime since
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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 6 Solutions
EBK MATLAB: AN INTRODUCTION WITH APPLIC
Ch. 6 - Prob. 1PCh. 6 - Given: d=6e=4f=2 . Evaluate the following...Ch. 6 - Given: v=[-2 4 1 0 2 1 2] and w=[2 50 1 2 1 3]....Ch. 6 - Use the vectors v and w from Problem 3. Use...Ch. 6 - Evaluate the following expressions without using...Ch. 6 - Use loops to create a 46 matrix in which the value...Ch. 6 - Write a program that generates a vector with 30...Ch. 6 - Write a program that asks the user to input a...Ch. 6 - Write a program that asks the user to input a...Ch. 6 - The daily high temperature (°F) in New York City...
Ch. 6 - The Pascal triangle can be displayed as elements...Ch. 6 - Fibonacci numbers are the numbers in a sequence in...Ch. 6 - The reciprocal Fibonacci constant ?is defined by...Ch. 6 - The value of p can be estimated from:...Ch. 6 - The value of p can be estimated from the...Ch. 6 - Write a program that (a) generates a vector with...Ch. 6 - A vector is given by x= [9 -1.5 13.4 13.3 -2.1 4.6...Ch. 6 - The Pythagorean theorem states that a2+ b2= c2....Ch. 6 - Write a MATLAB program in a script file that finds...Ch. 6 - A safe prime is a prime number that can be written...Ch. 6 - Sexy primes are two prime numbers that the...Ch. 6 - A Mersenne prime is a prime number that is equal...Ch. 6 - A perfect number is a positive integer that is...Ch. 6 - A list of exam scores (S) (in percent out of 100%...Ch. 6 - The Taylor series expansion for axis:...Ch. 6 - Write a MATLAB program in a script file that finds...Ch. 6 - The following are formulas for calculating the...Ch. 6 - Body mass index (BMI) is a measure of obesity. In...Ch. 6 - Write a program in a script file that calculates...Ch. 6 - Write a program that determines the change given...Ch. 6 - The concentration of a drug in the body CPcan be...Ch. 6 - One numerical method for calculating the cubic...Ch. 6 - Write a program in a script file that converts a...Ch. 6 - In a one-dimensional random walk, the position x...Ch. 6 - The Sierpinski triangle can be implemented in...Ch. 6 - The roots of a cubic equation a3x3+a2x2+a1x+a0=0...Ch. 6 - The overall grade in a course is determined from...Ch. 6 - A Keith number is a number (integer) that appears...Ch. 6 - The following MATLAB commands create a sine-shaped...
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