P·SPR·D control of passive nonlinear systems and inverted pendulum

Author

Shimizu, Kiyotaka

Author_Institution

Fac. of Syst. Design Eng., Keio Univ., Yokohama, Japan

fYear

2010

fDate

8-10 Sept. 2010

Firstpage

608

Lastpage

614

Abstract

This paper is concerned with P·SPR·D control of affine nonlinear systems and Lagrangian systems which are passive system. P·SPR·D control consists of proportional(P) action + strict positive real(SPR) action + derivative(D) action. Such control can asymptotically stabilize the passive nonlinear systems with multi-input and multi-output. Stability analysis of P·SPR·D control is made based on the passivity theory and LaSalle´s invariance principle. The P·SPR·D control is applied to an inverted pendulum problem. We swing up the pendulum by the Direct Graient Descent Control at the first stage, and then switch to the P·SPR·D control in order to stabilize (balance) it at the upright attitude. The effectiveness of the proposed method is demonstrated by the simulation results.

Keywords

asymptotic stability; gradient methods; nonlinear systems; pendulums; three-term control; LaSalle invariance principle; Lagrangian systems; P·SPR·D control; affine nonlinear systems; asymptotically stability; derivative action; direct gradient descent control; inverted pendulum; passive nonlinear systems; passivity theory; proportional action; strict positive real action; Equations; Manuals; Mathematical model; Nonlinear systems; Servomotors; Stability analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Applications (CCA), 2010 IEEE International Conference on

Conference_Location

Yokohama

Print_ISBN

978-1-4244-5362-7

Electronic_ISBN

978-1-4244-5363-4

Type

conf

DOI

10.1109/CCA.2010.5611267

Filename

5611267