Title :
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
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;
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
DOI :
10.1109/CCA.2010.5611267
