Setpoint Servo Problem for Symmetric Affine System Practical Stabilization by PI Control

• Published in: Shisutemu Seigyo Jouhou Gakkai rombunshi Vol. 21; no. 8; pp. 253 - 259
• Main Authors: SHIMIZU, Kiyotaka, TAMURA, Kenichi
• Format: Journal Article
• Language: Japanese; English
• Published: THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE) 15.08.2008
• Subjects: four wheeled vehicle; manual reset quantity; nonholonomic system; PI control; symmetric affine system
• ISSN: 1342-5668; 2185-811X
• DOI: 10.5687/iscie.21.253

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 Kp, KI-, and in addition the so-called manual reset quantity m0. (Note that adjusting m0 is equivallent to adjusting an initial condition z0 of integrator z = e.) By the PI control with the manual reset m0 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 m0, 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.