Machining, Measurement, and Control Laboratory

A Numerical Optimization Approach to Frequency-domain Loop-shaping Design of a Fixed-structure Controller
(Design of an Anti-Vibration Filter for a Feed Drive System)

Soichi Ibaraki (Kyoto University)
Takuya Tanaka (Kyoto University)
Atsushi Matsubara (Kyoto University)
Yoshiaki Kakino (Kyoto University)

This paper presents a tuning methodology of a fixed-structure feedback controller based on the frequency-domain loop shaping technique. Although the present methodology requires to solve a nonconvex optimization problem, it offers quite a practical way to tune a feedback controller such that the closed-loop system exhibits the desired control performance. As an application example, the tuning of a linear feedback controller is demonstrated for a feed drive system driven by a linear motor. In order to suppress the structural vibration of lower frequency, one must tune the controller by taking into explicit consideration its phase dynamics, as well as its gain dynamics. The loop-shaping design based on the proposed formulation is quite effective in practice in such a case.
Key Words:   numerical optimization, anti-vibration filter, frequency-domain loop-shaping, structural vibration, NC machine tools, linear motor.