Modeling and simulation of rotary-rotary planer inverted pendulum

Abstract

There exist different mechanical structures of inverted pendulum system. This paper presents mathematical modeling of rotary-rotary-planer inverted pendulum system (R-R-P inverted pendulum system), which is a highly nonlinear unstable system. In this planer inverted pendulum configuration, the pendulum is attached to its rotary-rotary actuating base with a pin joint. This configuration of planer inverted pendulum is taken into account, as the configuration can best describe the balancing of broomstick in one's hand, by considering the shoulder and elbow as revolute joints and such configuration will also help in the study of underactuated robotic systems. The dynamical equation of R-R-P inverted pendulum is derived by using Lagrangian equation of motion. To validate the mathematical model, simulation of nonlinear mathematical model of the system is performed via MATLAB Simulink.