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Balancing a reaction wheel pendulum with PM synchronous motor actuation

The reaction wheel pendulum is an underactuated electromechanical system consisting of a pendulum with an un-driven rotation axis at one end and a motor-driven wheel at the other end. Current flow in the motor induces a torque on the wheel and a corresponding reaction torque on the pendulum. This type of system has been studied by various researchers over the past decade, but in every case under the assumption that a brush-commutated permanent-magnet dc motor actuates the system. The purpose of this paper is to extend prior work by actuating the system instead with a brushless three-phase permanent-magnet synchronous ac motor. A systematic approach to modeling and control is pursued for the problem of balancing at the inverted equilibrium. Both state-feedback and output-feedback controllers are designed on the basis of a reduced-order model, and the designs are compared through simulation and analysis. Linear quadratic optimization is used to obtain both regulator and estimator gains, and a loop transfer recovery procedure is used so that the loop gain of the output-feedback design approximates that of the state-feedback design.