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# Servo Compensator Circuit Using Complex Conjugate Poles and Zeros

IP.com Disclosure Number: IPCOM000045328D
Original Publication Date: 1983-Mar-01
Included in the Prior Art Database: 2005-Feb-06
Document File: 2 page(s) / 44K

IBM

Taub, DM: AUTHOR

## Abstract

If the poles and zeros of servo compensator circuits are not confined to the negative real axis, i.e., if complex conjugate poles and zeros are allowed, more-flexible control of the overall characteristic can be obtained.

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Servo Compensator Circuit Using Complex Conjugate Poles and Zeros

If the poles and zeros of servo compensator circuits are not confined to the negative real axis, i.e., if complex conjugate poles and zeros are allowed, more- flexible control of the overall characteristic can be obtained.

Phase-lead and phase-lag compensator circuits for servos are generally implemented as passive resistor/capacitor circuits, which implies that the poles and zeros of their transfer function lie on the negative real axis of the s-plane. A property of these circuits is that the phase shift varies only slowly with frequency, so that the designer has less control over the overall phase characteristic than is sometimes wished.

A greater degree of control can be obtained by using complex conjugate poles and zeros, placing them on straight lines through the origin, the lines being angled with respect to the real axis, as shown in Fig. 1. The example shown represents a phase-lead circuit. The phase and gain of this circuit change more rapidly with frequency than in the more general case, and there is the added advantage that for a given peak phase lead, the ratio of high-frequency to low-frequency gain is lower. The transfer function to be implemented is: G(s)=(s-z(1))(s-z(2))/((s-p(1))(s-p(2))) where z(1) and z(2) are the positions of the zeros and p(1) and p(2) the positions of the poles. Referring to Fig. 1, this can be written as G(s)=(s/2/ + (2O mega (0)/the square root of a.cos Thet...