Calculating zeroes of functions arising in various control system problems

The paper considers three separate special cases of functions for which the zeroes are determined graphically. First, the spring constant of a structural member is replaced by a complex number to allow for hysteresis losses during vibration. The corresponding characteristic function has non-conjugate zeroes which are useful in calculating frequency response, but have no meaning for transient response. Secondly, vibration acting along the input axis of a pendulous accelerometer causing displacement of the proof mass; an in-Phase cross vibration will cause a rectified torque. The real part of the compliance function is needed; knowing the zeroes is useful but not necessary in evaluating the integral over the frequency range by use of residues. Third, sampled-data systems have z transforms which often involve the sum of reciprocals of vectors. Finding real values of zeroes is simplified because only magnitudes need be considered; some graphical techniques can simplify the general vector problem. For each of the above problems alternate methods of calculation can be used; those presented are most apt to be of value to those engineers who are used to working with zeroes and poles. This paper will be published by the AIEE.