Modeling, simulation and control of a twin-inverted pendulum on a moving cart

Abstract

In this paper, a mathematical model of a twin-inverted pendulum on a moving cart has been derived. This is done using the Lagrange–Euler method and, hence, a highly nonlinear mathematical model is resulted from this derivation. These nonlinear and unstable dynamics are written in a simple matrix form. For this challenging system, we use two types of efficient control approaches to treat the control problem of the twin inverted pendulum, namely, linear quadratic regulator (LQR) and nonlinear model predictive control (NMPC). Simulations with several scenarios are also presented to demonstrate the control performances and the model validity.