Modeling of servo dynamic stiffness for multiple-periodic repetitive learning control system

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Abstract
Servo dynamic stiffness is a pivotal index in characterizing the rejecting performance for the exogenous periodic disturbances of the repetitive learning control system. In this paper, the mathematical modeling of the servo dynamic stiffness for the well-designed repetitive learning control system with multiple-periodic signals is studied by the frequency analysis method. To analysis the complex form of the servo dynamic stiffness, the magnitudes of the direct (real part) and quadrature (imaginary part) servo dynamic stiffness at harmonics of the disturbance are discussed based on the parameters of the repetitive learning controller. An illustrated example of the two linear servomotors with the mechanical coupling is given in this study. Computer simulation are presented to illustrate the effect of the proposed measurement method of the servo dynamic stiffness for the multiple-periodic repetitive learning control system. The proposed servo dynamic stiffness modeling can be used to accurate design the parameters of the repetitive learning control system, such that the batter control performance of the repetitive learning control system at most of the harmonics of the multi-periodic input signal can be achieved.

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