P⋅SPR⋅D control and P⋅I⋅SPR⋅D control for affine nonlinear systems —Stabilization theory based on passivity—

Abstract

This paper is concerned with set-point sevo problems by PldrSPRldrD control and PldrIldrSPRldrD control of affine nonlinear system which is of multi input and multi output. PldrSPRldrD control consists of proportional (P) action + strict positive real (SPR) action + derivative (D) action. Such control can asymptotically stabilize the affine nonlinear system being passive. Stability analysis of PldrSPRldrD control and PldrIldrSPRldrD control is made, based on the passivity theory and LaSalle's invariance principle. The effectiveness of the proposed method is demonstrated by the simulation results for an elastic joint robot arm and TORA model.