Frequency Domain Analysis
Figure 8.55
361
(contd.)
!
!
!
!
Gs
1
GsF s
1
G s
H s
H s
1 GsF s
F s 1 GsF s
F s 1 G s
F s
From the above relation we conclude that when F s 6 1, we can directly apply
the results of the present section for H s, as long as, ins
Classical Control Design Methods
Figure 9.33
397
The transient response method. (a) Experimental step response; (b) detailed
step response.
general form shown in Figure 9.33b. In this case, we introduce the parameters
td delay time and tr rise time. Aimin
Classical Control Design Methods
385
where Kp , Ki , and Kd are the proportional, integral, and derivative gains, respectively. PID controllers are also expressed as follows:
!
Kp
1
K
G c s K p 1
Td s ;
where
Ti
and
Td d
Ti s
Ki
Kp
9:6-1b
where Kp is t
Classical Control Design Methods
373
In the frequency domain the specications are given on the basis of the
Nyquist, Bode, or Nichols diagrams of the transfer function Gc sGs and they
mainly refer to the gain and phase margins and to the bandwidth. In the
Classical Control Design Methods
409
already explained in Remark 9.4.1 of Sec. 9.4. To satisfy the specication for a phase
margin of 408, the phase of the controller transfer function
G j !
c
1 j !aT
1 j !T
should be 228.
Remark 9.7.1
Using the relation
Classical Control Design Methods
421
For Eq. (9.10-13) to be valid for every "R1 , the function X s, where
^
^
^
X s U GR GGU GGU GR
must satisfy the following condition:
2 j1
J
X s"R1 ds 0
2 j j 1
9:10-14
9:10-15
We assume that the control signal ut is
State-Space Design Methods
W
!
1
0
0
;
1
469
!
3
^
a
;
2
a
0
0
!
and therefore
u
1
2
!
^
W T R 1 1 a a
3
2
!
Introducing the value of u into g, F, and H yields
!
!
3
3 1
36
;
H
;
F
g
1
2 0
12
1
0
!
(c) Let pc s s 1s 2s 3 s3 6s2 11s 6 be the desired char
State-Space Design Methods
445
Figure 10.5 Block diagram of the closed-loop system in Example 10.3.3. (a) Block diagram
of the position control system; (b) simplied block diagram for Lf 0:5, Rf 2, Jm 1,
Bm 1, and Km Kf Ia 2.
lar position y m of the motor