対称アフィンシステムの設定点サーボ問題 : PI制御による実用安定化 Setpoint Servo Problem for Symmetric Affine System : Practical Stabilization by PI Control
This paper is concerned with control of nonholonomic systems. As is well known, symmetric affine system is unable to control with continuous time invariant state feedback control. In this paper we apply PI Control to a setpoint servo problem for the symmetric affine system. PI control posesses two adjustable parameters <I>K<SUB>p</SUB>, K<SUB>I</SUB></I>-, and in addition the so-called manual reset quantity <I>m</I><SUB>0</SUB>. (Note that adjusting <I>m</I><SUB>0</SUB> is equivallent to adjusting an initial condition z<SUB>0</SUB> of integrator z = e.) By the PI control with the manual reset <I>m</I><SUB>0</SUB> appropriately chosen, not only controllable part of symmetric affine system is asymptotically stabilized but also uncontrollable part can be made to converge to the desired point. Applying the PI control with <I>m</I><SUB>0</SUB>, we can control the symmetric affine system without transforming into the "chained form". We confirmed the effectiveness of the proposed method by the simulation results for various plants like a two-wheeled vehicle and a four-wheeled vehicle, a flying robot, etc.
システム制御情報学会論文誌 21(8), 253-259, 2008-08-15