Question 5.13: A Cart–Inverted-Pendulum System Consider the mechanical syst...
A Cart-Inverted-Pendulum System
Consider the mechanical system shown in Figure 5.79, in which a uniform rod of mass M and length L is pivoted on a cart of mass m. An external force f is applied to the cart. Assume that the pendulum is constrained to move in a vertical plane, and the cart moves without slipping along a horizontal line. Denote the displacement of the cart as x and the angular displacement of the pendulum as \theta.
a. Draw the necessary free-body diagram and kinematic diagram, and derive the nonlinear equations of motion.
b. Linearize the equations of motion for small angular motions, and determine the state-space form with x and \theta as the outputs.
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