Stability
241
jytj C2 , for t 2 0; 1, where C2 is a nite constant. If for all possible bounded
inputs the corresponding outputs of the system are also bounded, then the system is
said to be BIBO stabl
The Root Locus Method
2 1
;
nm
0; 1; . . . ; jn mj 1
The root locus for K
following angles:
2
;
nm
277
7:3-12
0 approaches asymptotically the straight lines having the
0; 1; . . . ; jn mj 1
7:
Stability
265
4p12 1
p11 3p12 2p22 0
2p12 6p22 1
The above equations give the following matrix
!
51
44
P 1 1
4
4
If we apply the Sylvesters criterion (Sec. 2.12), it follows that the matrix P is posit
Stability
Figure 6.3
253
Block diagram of the automatic depth control system of a submarine.
approximated by a second-order transfer function. The depth of the submarine is
measured by a depth sensor
The Root Locus Method
Figure 7.8
289
The root locus of the supersonic airplane closed-loop system.
Example 7.3.4
Consider the closed-loop control system which controls the thickness of metal sheets,
s
Frequency Domain Analysis
Figure 8.44
349
The weighting function W u lncoth juj=2.
relation G j ! 0 F j ! 908, the phase margin is about 908. To obtain a more
desired (smaller) value for the phase mar
Frequency Domain Analysis
Figure 8.32
337
The block diagram of the automatic thickness control system.
the closed-loop system is stable. The controller transfer function Gc s is specied as
follows:
(a
Frequency Domain Analysis
325
itate the construction of the Nyquist diagram of H s we divide the Nyquist path N
into four segments and construct the Nyquist diagram for each of the corresponding
four
Frequency Domain Analysis
313
Figure 8.8
(a) Amplitude M and (b) output yt curves of two different systems which show
the relation between Tr and bandwidth BW.
Figure 8.9 (a) The amplitude M and (b) t