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​it's  an upside down pendulum so it cannot stay balanced on its own. It will simply fall over. Then how do we balance it? We need to know the direction in which the pendulum is falling, how much the pendulum has tilted and the speed with which it is falling, then We combine all these inputs and generate a signal which drives its cart in the direction in which it is falling and keeps the pendulum balanced.

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the pendulum mathematical model done by hand calculations depend on mechanics and control theory concepts . then State feed back controller designed with C code algorithm and Matlab.