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As shown in Figure 3, at frequency 10 and 100 Hz, the maximum tracking errors using proposed design approach are 0.022 and 0.129, respectively; however, the maximum tracking errors using design approach based on BRL are 0.032 and 0.173, respectively.
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Figure 4 The variation curves of the maximum tracking error of (pmb{x_{d}^{(2)}(i)}).
Figures 3 and 4 show the variation curves of the maximum tracking error.
Figure 7 is the curve chart describing the variation of the maximum tracking error with iteration numbers.
Numerically, in the twentieth iteration, the absolute values of the maximum tracking error are (1.9185times10^{-8}) and (1.5564times10^{-9}).
In sinusoidal profile cutting the maximum tracking error was reduced by 83% and the average magnitude of the error was reduced by 63%.
In sharp corner cutting the DSFD reduced the maximum tracking error by 38% and the average magnitude of the error by 39%.
With the increase number of iterations, the state tracking error can converge to zero. Figure 3 The variation curves of the maximum tracking error of (pmb{x_{d}^{(1)}(i)}).
where W p ( s ) is user-defined weighting function to impose the requirements for the tracking bandwidth and maximum tracking error limitation, and the state-space realization form of W p is as follow, x ?
The improved controller with the learning control element reduced the maximum tracking error to 1.62 μm in the sinusoidal reference motion at a frequency of 20 Hz and an amplitude of 10 mm.
Likewise, the maximum tracking error reduces by 71%, from 13.7% (using industry-standard integral control) to 3.9% (using RC with hysteresis compensation), underscoring the benefits of RC with hysteresis compensation.
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