12.5: Robust Performance
- Page ID
- 47297
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The condition for good performance with plant uncertainty is a combination of the two conditions discussed in the previous sections. Graphically, the disk at the critical point, with radius \(|W_1|\), should not intersect the disk of radius \(|W_2 PC|\), centered on the nominal locus \(PC\). This is met if
\[ |W_1 S| + |W_2 T| \, < \, 1. \]
The robust performance requirement is related to the magnitude \(|PC|\) at different frequencies, as follows:
- At low frequency, \(|W_1 S| \simeq |W_1 / PC|\), since \(|PC|\) is large. This leads directly to the performance condition \(|PC| > |W_1|\) in this range.
- At high frequency, \(|W_2 T| \simeq |W_2 PC|\), since \(|PC|\) is small. We must therefore have \(|PC| < 1/|W_2|\), for robustness.
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