A Fuzzy-P controller of an active reaction force compensation (RFC) mechanism for a linear motor motion stage

Abstract

Residual vibration of system base due to high-speed motion of a stage may significantly reduce life span and productivity of the manufacturing equipment. Although a passive reaction force compensation (RFC) mechanism was developed to reduce residual vibration of a linear motor motion stage, the passive RFC mechanism should be redesigned according to variation of motion profiles. In this paper, we develop a fuzzy-P (proportional) controller of an active RFC mechanism to automatically tune the gain according to variation of motion profiles. First, frequency components of motion profiles for a linear motion stage are analyzed and performances of the passive RFC mechanism are approximately evaluated using a motion profile analysis. An active RFC mechanism with an additional control coil is introduced to overcome limitation of the passive RFC mechanism and a fuzzy rule is proposed to automatically tune the P controller of the active RFC mechanism according to variations of motion profiles. Simulations and experiments are performed to show effectiveness of the proposed fuzzy rule for tuning the P control gain of the active RFC mechanism. NOMENCLATURE a M = acceleration of mover c MT = damping of magnet track k MT = stiffness of magnet track k v = viscous friction of mover k P = gain of P control F f = thrust force for mover friction F fc = Column friction of mover F fs = Stribeck friction of mover F m = thrust force for mover motion F t = thrust or reaction force F tran = transmitted force m M = mass of mover m MT = mass of magnet track n = index of frequency component n s = Stribeck friction coefficient for exponential function n max = index of frequency component at peak acceleration of mover n MT = index of natural frequency of magnet track n' MT = output of defuzzification block T = period of motion profile T a = acceleration time T dw = dwell time T r = run time v s = Stribeck friction coefficient for velocity x MT = position of magnet track = velocity of magnet track = acceleration of magnet track ω = frequency ω MT = natural frequency of magnet track ω T = fandamental frequency of motion profile ζ = damping ratio θ n = phase of magnet track motion x · MT x ··

RTC (reaction torque compensated) induction motor and its open-loop control

“…A passive, Active and semi-active RFCs (reaction force compensation) to reduce the system vibration have been studied only for a linear motor motion stage [8][9][10][11]. Although the passive RFC mechanism is compact and costeffective, the passive RFC does not allow in situ modification of the dynamic characteristic of the RFC system.…”

“…Although the passive RFC mechanism is compact and costeffective, the passive RFC does not allow in situ modification of the dynamic characteristic of the RFC system. An active RFC mechanism using an additional coil can tune its dynamic characteristic and minimize the transmitted force against the motion profile variation [9]. In addition, a semiactive RFC can modify the damping of the RFC by adjusting the external resistor or open-close time ratio of an additional coil [9][10][11].…”

Reaction Force Compensator for High‐Speed Precision Stage of Laser Direct Imaging Process

“…Therefore, the reaction force applied to the granite has characteristics similar to that of the impulsive force. The force causes parasitic vibration and displacement error, which eventually result in unwanted error on the stage and workpiece [8][9][10]. Therefore, it is necessary to compensate for the reaction force to prevent the vibration and error on the granite and to increase the stability of the system with respect to operations at the high acceleration and deceleration speeds.…”