Solutions to Homework # 1

Chapter 1, problem 1

Chapter 1, problem2

Chapter 1, problem 3

Chapter 1, problem4

(in radians)

K

(in volt/radian)

Solutions to Homework # 2

Chapter 2, problem 2 c

Chapter 2, problem 5 b

Type the following MATLAB code in the Command window:

The output of pretty(f) and pretty(F) is:

Chapter 2, problem 6 a

Type the following MATLAB code in the Command window:

The output of pretty(G) is:

The output of pretty(g) is:

Chapter 2, problem 8 c

Chapter 2, problem 16 b

Chapter 2, problem 24

Chapter 2, problem 29

Solutions to Homework # 3

Chapter 3, problem 1

Chapter 3, problem 10 a

Chapter 3, problem 13 a

Program: 'a'

A=[0 1 3 0; 0 0 1 0;0 0 0 1; 7 9 2 3]; B=[0; 5; 8; 2]; C=[1 3 4 6]; D=0; statespace=ss(A, B, C, D) [num,den]=ss2tf(A, B, C, D); G=tf (num, den) 'b'

A=[3 1 0 4 2; 3 5 5 2 -1; 0 1 1 2 8; 7 6 3 4 0; 6 0 4 3 1]; B=[2; 7; 6; 5; 4];

C=[1 2 9 7 6]; D=0; statespace=ss(A, B, C, D) [num,den]=ss2tf(A, B, C, D); G = tf (num, den)

Computer response: a = x1 x2 x3 x4 x1 0 1 3 0 x2 0 0 1 0 x3 0 0 0 1

x4 7 9 2 3 b = u1 x1 0 x2 5 x3 8 x4 2 c = x1 x2 x3 x4 y1 1 3 4 6 d = u1 y1 0 Continuous-time model. Transfer function:

59 s^3 164 s^2 1621 s 260 ------------------------------- s^4 + 3 s^3 + 2 s^2 + 30 s + 7

Chapter 3, problem 18

l

Solutions to Homework # 4

Chapter 4, problem 6c

Chapter 4, problem 6d

Chapter 4, problem 27a

Chapter 4, problem 27b

Measuring the percent overshoot and settling time from the graph

%OS=(13.82 11.04) /11.03 = 25.3% ,

Chapter 4, problem 27c

Solutions to HW 5 : 5.14 , 6.12, 6.24, 6.29

Solutions to HW 6

7.12 a b, 7.17 a, 8.2, 8.3 a, 10.1