黒田 雅治

Recent research on fractional order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional order LQR control to a current-controlled attractive-force type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force type magnetic levitation system expressed as an integer-order system is extended to a fractional order system expressed using fractional order derivatives. Then target value tracking control of levitated objects is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional order LQR controller is designed for the extended system. For state-feedback control such as fractional order servo LQR control, which requires information of all states, a fractional order state-observer is configured to estimate fractional order states. Simulation results demonstrate that fractional order servo LQR control can achieve equilibrium point stabilization and enable target-value tracking. Finally, to verify the fractional order servo LQR control effectiveness, experiments using the designed fractional order servo LQR control law are done with comparison to conventional integer-order servo LQR control.

<p>In this paper, we propose a null-space compensation control for linear first-order systems with redundant two input channels. In the input redundant systems, control input vector generally has null-space component of the plant parameter vector. The null-space component does not contribute to the generation of the control force which drives the plant state. If a control input that does not include the null-space component can be generated, efficient control is achieved from the viewpoint of minimizing the norm of the control input. In the proposed method, an adaptive control method is used to design a control system that compensates for the null-space component, even if the plant parameter vector is unknown. The effectiveness is shown by numerical examples.</p>

本研究ではマイクロカンチレバーに振動を付与して加工を行う方法に注目し，実験により加工時のマイクロカンチレバーの振動現象を明らかにすることを目的とした．加工の実現に向けて試料とマイクロカンチレバーの距離に応じたダイナミクスを把握するために，強制加振状態でのフォースカーブ（動的フォースカーブ）を計測した．この結果から，マイクロカンチレバーの振動形態を（a）引力タッピング，（b）斥力タッピング，（c）押しつけこすり，（d）引きこみこすりと分類した．また，マイクロカンチレバーを強制加振した状態で加工実験を行い，加工を行うには押しつけこすり状態が有用であることを切削くずの多さから指摘した．