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Modeling a Gantry Crane

Obtaining a mathematical model for the system is always the first step in designing the controller. The model for the system used has only two decrees of freedom. This lends itself to use the Lagrangian approach to derive the equations of motion.

Lagrange's Equation

Potential Energy (V)

Kinetic Energy (T)

Lagrangian Equation (T-V)

Generalized Coordinate "x"

Generalized Coordinate "θ"

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