Question

Consider the inverted pendulum system presented in Fig. 1. The pivot of the pendulum is mounted on a cart, which can move in a horizontal direction. The pendulum can be kept balanced at a specific position by applying a horizontal force to drive the carriage. Assume that the pendulum mass, m, is concentrated ia at the end of the massless rod. The horizontal displacement of the pivot on the cart is x, the rotational angle of the pendulum is θ (measured from the y-axes and increasing from bottom to top), and the force driving the carriage is u. Assume that the friction coefficient of the cart is b. Based on this information, derive the dynamic system model equations for the inverted pendulum using the Euler-Lagrange approach mg IC 0 Figure 1: Inverted Pendulum System.

Answer 1

Toted force in X. direction mg Total ln e-direction ‘rte ranglah 2 mg D Usin Euler Larange coordi nate ax : u- b (M m dt 26a6 d. [mr..-md sinnn t m ] _ Emrx6-.my]최ne s) ces