2008 Volume 44 Issue 7 Pages 575-582
This paper is concerned with P·SPR·D control of affine nonlinear system and the Lagrangean system 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 affine nonlinear system being of multi input and multi output. Further a set-point servo problem (a set-point tracking control) for the Lagrangean system is also solved by the P·SPR·D control. Stability analysis of P·SPR·D control is made, based on the passivity theory and LaSalle's invariance principle. P·SPR·D control is applied to an inverted pendulum. 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 it at the upright position. The effectiveness of the proposed method is demonstrated by the simulation results.
