The inverted pendulum is a classical control problem, which involves developing a system to balance a pendulum. For visualization purposes, this is similar to trying to balance a broomstick on a finger. There are three main subsystems that compose this design including the mechanical system, the feedback network which includes sensors and a method to read them, and a controller and its interface to the mechanical system. The system model, state space representation and controller design is described, the model is converted into state space form, and is used to design a controller using the Linear Quadratic Regulator (LQR) cost equation. The final system results in a cart that could balance a pendulum for a limited amount of time. This was due to many imperfections in the mechanical system and the inability to model the dynamics of these imperfections along with the calculation limitations of the Atmel Mega32.
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