Question: Consider the inverted pendulum mounted to a motor. The motor and load are assumed to have no friction damping. The pendulum to be balanced is

Consider the inverted pendulum mounted to a motor. The motor and load are assumed to have no friction damping. The pendulum to be balanced is attached to the horizontal shaft of a servomotor. The servomotor carries a tachogenerator, so that a velocity signal is available, but there is no position signal. When the motor is unpowered, the pendulum will hang vertically downward and, if slightly disturbed, will perform oscillations. If lifted to the top of its arc, the pendulum is unstable in that position. Devise a feedback compensator Gc (s) using only the velocity signal from the tachometer.

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