tailieunhanh - Magnetic Bearings Theory and Applications Part 5

Tham khảo tài liệu 'magnetic bearings theory and applications part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Magnetic levitation technique for active vibration control 49 The control current of zero-power controller is given by s 1 s Pd Pvs X s 24 s Pz where Pz integral feedback in the minor current loop. From Eqs. 22 to 24 it can be written as X s s Pz d0 25 W s s3 b0Pv Pz ss b0Pd b0PvPz a0 s a0Pz I s s sPv Pd PvPz d0 26 W s s 3 b0 Pv Pz s s b0 Pd b0 PvPz a00 s a0 Pz To estimate the stiffness for direct disturbance the direct disturbance W s on the isolation table is considered to be stepwise that is W s F F0 constant . 27 s The steady displacement of the suspension from Eqs. 25 and 27 is given by lim x t lim sX s F0 F . 28 t w s 0 a0 ks The negative sign in the right-hand side illustrates that the new equilibrium position is in the direction opposite to the applied force. It means that the system realizes negative stiffness. Assume that stiffness of any suspension is denoted by k. The stiffness of the zeropower controlled magnetic suspension is therefore negative and given by k -ks. 29 Realization of Zero-Power From Eqs. 26 and 27 lim i t lim si s 0. 30 t w s 0 It indicates that control current all the time converges to zero in the zero-power control system for any load. 50 Magnetic Bearings Theory and Applications Stiffness Adjustment The stiffness realized by zero-power control is constant as shown in Eq. 29 . However it is necessary to adjust the stiffness of the magnetic levitation system in many applications such as vibration isolation systems. There are two approaches to adjust stiffness of the zeropower control system. The first one is by adding a minor displacement feedback to the zeropower control current and the other one is by adding a proportional feedback in the minor current feedback loop Ishino et al. 2009 . In this research stiffness adjustment capability of zero-power control is realized by the first approach. Figure 4 shows the block diagram of the modified zero-power controller that is capable to adjust stiffness. The control current of the

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