CHAPTER 5
5.1
CONCEPTS OF STABILITY AND THE ROUTH
STABILITY CRITERION
(a) All the elements in the first column of the Routh array are +ve.
Therefore, all the roots are in the left-half plane.
(b) Two sign changes are found in the first column of the Routh
CHAPTER 6
6.1
THE PERFORMANCE OF FEEDBACK SYSTEMS
(a) Refer Section 6.3 for the derivation
(b) The characteristic equation is
s2 + 10s + 100 = s2 + 2zwn s + w 2 = 0
n
(i) wn = 10 rad/sec; z = 0.5; wd = w n 1 - z 2 = 8.66 rad/sec
(ii) tr =
p
p - cos -1 z
=
CHAPTER 7
7.1
COMPENSATOR DESIGN USING ROOT LOCUS
PLOTS
(a) sA = 2 ; fA = 60, 180, 300 ; intersection with jw-axis at
j5.042; angle of departure fp from 1 + j4 = 40.
(b) sA = 1.25 ; fA = 45, 135, 225, 315 ; intersection with jw-axis at
j1. 1; angle of d
CHAPTER 8
8.1
THE NYQUIST STABILITY CRITERION
AND STABILITY MARGINS
(a) Revisiting Example 8.1 will be helpful.
(i) 1 0
(ii) 0 180
(iv)
t 1t 2
- 90
t1 + t 2
(b) Revisiting Example 8.2 will be helpful.
(i) t j
(ii) 0 180
(c) Revisiting Example 8.3 will b
CHAPTER 9
9.1
9.2
9.3
9.4
FEEDBACK SYSTEM PERFORMANCE
BASED ON THE FREQUENCY
RESPONSE
For derivation of the result, refer Section 9.3; Eqn. (9.9).
For derivation of the result, refer Section 9.3; Eqn. (9.18).
For derivation of the result, refer Section 9.
CHAPTER 10
COMPENSATOR DESIGN USING
BODE PLOTS
10.1 (a) From the Bode plot of G(jw)H(jw), we find that GM = 6 dB and
FM = 17
(b) Now the gain and phase of the compensator with Kc = 1 are added to
the Bode plot. From the new Bode plot we find that the gain
CHAPTER 11
11.1 (a)
(b)
HARDWARE AND SOFTWARE
IMPLEMENTATION OF COMMON
COMPENSATORS
E( s)
RD
TD s
=
=
; a = R/RD ; TD = RD CD
Y ( s)
R + 1 / CD s
aTD s + 1
E( s)
R
K (T s + 1)
=
= c D
R1 + R2 / (1 + sR2 C)
aTD s + 1
Y ( s)
Kc =
R
R1
;a=
; TD = R2C
R1 + R2