P·SPR·D control for affine nonlinear system and robot manipulators -Stability analysis based on K-Y-P property and LaSalle’s invariance principle-

Abstract

This paper is concerned with P·SPR·D control of affine nonlinear system and robot manipulators which are passive systems. P·SPR·D control consists of proportional(P) action + strict positive real(SPR) action + derivative(D) action. Such control can asymptotically stabilize the affine nonlinear system being of multi input and multi output. Stability analysis of the P·SPR·D control is made, based on the passivity theory and LaSalle¿s invariance principle. The L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -gain disturbance attenuation problem is also investigated. Further a set-point servo problem (set-point tracking control) for the robot manipulator is also solved by the P·SPR·D control. The effectiveness of the proposed method is demonstrated by the simulation results for a two-link manipulator.