16
Fuzzy Control
16.1
INTRODUCTION TO INTELLIGENT CONTROL
In the last two decades, a new approach to control has gained considerable attention.
This new approach is called intelligent control (to distinguish it from conventional or
traditional control) [1
15
Robust Control
15.1
INTRODUCTION
Control engineers are always aware that any design of a controller based on a xed
plant model (e.g., transfer function or state space) is very often unrealistic. This is
because there is always a nagging doubt about the
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625
part B q1 of Bm q1 while Eq. (14.4-16) should be valid, otherwise there is no
m
solution to the design problem.
It is necessary to establish conditions under which a solution for the polynomials R1 q1 and S q1 in Eq. (14.4-14), is gua
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613
In what follows, we seek to nd a control law uk, which drives the ltered
"
plant-model error ek d q1 ek d to zero. Using Eqs (14.3-21) and
(14.3-22), we have
q1 ek d q1 yk d q1 ym k d
b0 uk
q1 uk 1 Rq1 yk q1 ym k d
b0 uk hT u0 k
Robust Control
Figure 15.7
649
Checking robust stability with a multiplicative uncertainty, for Example 15.3.1.
15.3.2 Robust Stability with an Inverse Multiplicative Uncertainty
In this subsection a corresponding robust stability condition is derived for
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661
criterion, e.g., the Routh criterion. Applying the Routh criterion in the four
Kharitonovs polynomials, we obtain the following four Routh tables:
1.
2.
3.
4.
Polynomial p1 s:
1
s5
3
s4
4
s3
29=4
s2
s1 107=77
2
s0
7
9
7=3
2
0
Polyn
The Z-Transform
Figure B.3
709
The unit gate sequence g k k k1 k k2 .
Figure B.4 shows the graphical representation of rk k0 .
5 The Exponential Sequence
The exponential sequence is designated by gk and is dened as follows:
&k
a;
for k ! 0
gk
0;
for k <
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697
It is evident here that only rules 1, 2, 4, and 5 have a nonzero contribution, the
remainder playing no part in the nal decision. Furthermore, rule 1 is seen to be
dominant, while rule 2 has a signicant contribution. In contrast, rules 4
Fuzzy Control
Figure 16.13
685
Graphical forms of the rules 69 of Table 16.1.
Next, determine the value of sk , dened as follows:
1
n
o
sk min k1 ; k2 minf0:5; 0:2g 0:2
1
e
e
16:8-1
This completes the rst step, i.e., the determination of the sk . Note tha
System Identification
21.
601
E Walter. Identication of State Space Models. Berlin: Springer Verlag, 1982.
Articles
22.
23.
KJ Astrom, PE Eykhoff. System identicationa survey. Automatica 7:123162, 1971.
Special issue on identication and system parameter e