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The preceding article draws attention to the advantage of using complex conjugate poles and zeros in servo compensator circuits.
English (United States)
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Phase Lag Compensator Circuit
The preceding article draws attention to the advantage of using complex
conjugate poles and zeros in servo compensator circuits.
The above figure shows a phase-lag circuit following the same
principles. The relationships between the component values are given
by the following equations.
C'=C(1) + C(3)
and R'=R(1)R(3)/(R(1) + R(3))
the relationships are
C(2)/C'=2a the square root of (C(2)R(2)/(C'R'))cos Theta-1
C'R'=1/Omega(0) the square root of (1/a.C'R'))cos theta-1
R(3)=R'/(2(1-a)cos Theta) the square root of (C(2)R(2)/(C'R'))
where a is the ratio of the radius on which the poles lie to the
radius on which the zeros lie, which in this case will be less than 1. Omega(0) and Theta have the same meaning as in the phase-lead
circuit, and the amplifier gain is again assumed to be infinite.
Referring to equation (3), tolerance problems can be avoided by choosing the
ratio C(2)R(2)/(C'R') high enough to ensure that 2a the square root of
(C(2)R(2)/(C'R'))cos Theta is reasonably large compared with 1.
One can regard this circuit as a type of low-pass filter in which, as frequency
increases, the gain falls to a finite value instead of zero. Were this acceptable,
the circuit has the advantage over a conventional low-pass filter of lower phase-
lag in the pass band.
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