Euler-Lagrange Based Dynamic Model of Double Rotary Inverted Pendulum

Double Rotary inverted pendulum (DRIP) is an important member of nonlinear, unstable, non-minimum phase, and under-actuated mechanical systems. The DRIP is known widely as experimental setup for testing different kind of control algorithms. This paper, described a development of nonlinear dynamical equations of the DRIP system using Euler-Lagrange methods. Euler-Lagrange methods does not requisite complicated and tedious formulation since DRIP is not large multi-body system. The linear model and state space representation was also presented. The Simulink model of DRIP was developed based on the derived equations. Simulation study was carried out and the results indicated that, the DRIP system is inherently nonlinear and unstable. It is realized that the difficulties and limitations in the previous dynamic equation of DRIP proposed in literature are eliminated. Euler-Lagrange methods can be regarded as an alternative method for finding the dynamic model of the systems.