Balancing and Attitude Control of Double and Triple Inverted Pendulums

Abstract

The design of robust computer control systems for balancing and attitude control of double and triple inverted pendulums is considered in this paper. For the double inverted pendulum, a DC motor mounted at the upper hinge is used to balance and control attitude of the upper link. For the triple inverted pendulum a DC motor mounted at the middle hinge is used to control the middle link, whereas proportional position control applied to a motor at the upper hinge is utilised to maintain the upper link in alignment with the middle link. In both cases the lower hinge is left free to rotate. The controller designs are based on linearised discrete-time models of the inverted pendulums. Each controller utilises state feedback implemented via reduced-order state observers. The relative stability properties of the control systems are evaluated using Nyquist plots of suitably defined functions. The controllers are designed using Matlab and implemented in a PC using C language. Experimental results showed satisfactory performance.