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    <pre style="white-space:pre-line"><code>Frequency-Response Compensation Design                                           427

FIGURE 11.2 Polar plots: (a) lag compensator; (b) lead compensator; (c) lag-lead
compensator.

Solving for the angle fc yields

    fc  Â¼  tanÃ€1                      oT  Ã€  tanÃ€1  oaT    Â¼  tanÃ€1  oT Ã€ oaT    Ã°11:3Ãž
                                                                     1 Ã¾ o2aT 2

or

    T2  Ã¾    aÃ€1                          T  Ã¾   1   Â¼  0                        Ã°11:4Ãž
           oa tan fc                            o2a

where a &gt; 1 for the lag compensator and a &lt; 1 for the lead compensator.
In the design procedures shown in later sections, a frequency o is specified at
which a particular value of fc is desired. For the selected values of a, fc, and o,

Copyright Â© 2003 Marcel Dekker, Inc.</code></pre>
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