T.-S. TSAY 91
Table 2. Gain/phase margins, phase/gain cr ossover frequen-
cies and rise times.
Method GM
Hz
cp
PM
(deg.)
Hz
cg
Rise Time
(sec)
Optimization 9.05 50.03 69.35 8.13 0.0202
Adaptive Gain 9.19 49.73 69.35 8.13 0.0124
Figure 13. Time responses of position control system for
, and adaptive gain. K11K27.877
Table 3. Gain/phase margins, phase/gain crossover fre-
quencies and rise times.
Method GM
Hz
cp
PM
(deg.)
Hz
cg
Rise Time (sec)
Optimization 8.35 47.19 52.14 8.91 0.0513
Adaptive Gain 8.39 47.22 51.09 8.71 0.0334
se/gain crossover frequencies and rise times are given
also in Table 3. It gives controlled system using two
methods have same robustness while Figure 13 shows
the proposed method gives faster response.
4. Conclusions
The proposed adaptive piecewise linear controller has
been shown that provided controlled systems are refer-
ence input independent and both good performance and
fast response were obtained simultaneously. Three seg-
ments piecewise linear controller provided a switching
algorithm for low gain and high systems; i.e., low gain
for performance and high gain for response time. The
switching points were dependent on the command track-
ing errors. There are zero-damped ones used in Example
1 and 2 to get fast responses in large tracking error
phases.
Two servo control system examples were designed and
comparisons were made with famous on-line computing
and control methods and optimization method. They have
illustrated better performance and fast response of the
proposed method than those of other mentioned methods.
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