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Consider the inverted pendulum system shown below. The inverted pendulum is mounted on top of a motor driven cart. The pendulum and cart have two degrees of freedom in plane together, i.e x and θ. It is desired to keep the pendulum upright in the presence of disturbances, such as unexpected force applied on the cart. The slanted pendulum can be brought back to the vertical position by applying a control force u applied to the cart. Once the pendulum is stable at the vertical position, it is desired to bring the cart back to the reference position (x-0) esin θ im cos θ ng 0

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