Inversed pendulum with slugged flywheel oscillation control system synthesis method

The problem of a well-known system control consisting of the inversed pendulum with the fixed suspension point is considered. At that, an electric motor with a flywheel is fastened on the pendulum. The motor spindle has a rigid coupling with the flywheel. Its rotation could clamp the pendulum in position. The rotative moment developed by the electric motor is applied both to its rotor (i.e. to flywheel) and to its stator (i.e. to pendulum). The pendulum should be moved to the top instable position, and stabilized in this position — to obtain autooscillations with the specified amplitude and frequency. A new control law for the inversed pendulum to provide stability in top position is synthesized. The control law is based on the energy invariants of the system.