LQR control on linear model of flexible inverted pendulum

Abstract

Most kinds of robots in researches are in solid structures. In these models, Euler-Lagrange method is easily used to obtain dynamic equations for simulation and obtaining controllers. But, actually, there is always flexibility - even very small or remarkable - in all kinds of robots. This research solves a problem in modelling a complex robot with a flexible link-flexible inverted pendulum- by presenting a method to simplify that robot. Thence, controller and simulation of controlling model can be tested. The flexible inverted pendulum is a distributed parameter system which is developed from cart and pole system, a robot with all solid links. An investigation of applying LQR control on this model is examined. In simulation, approximated dynamic equations are presented. The knowledge of the structure of the model leads to designing a linear LQR controller. Genetic algorithm is successfully utilized to optimize the controller. After a survey in a simulation, a hardware platform is presented and tested. In an experiment, LQR is proven to work well and suit theoretical points.