Constrained H ∞ Control Application to Inverted Pendulum with Control Moment Gyroscope

This paper presents the dynamics and control of a gyroscopic inverted pendulum where the stabilization of the inverted pendulum is achieved by control torque generated by gyroscopic precession momentum. Two flywheels rotating in opposite directions at the same speed are considered. The control strategy is proposed to stabilize the inverted pendulum at the upwarp unstable equilibrium position and to maintain the gimbal angle as small as possible. Such a problem is formulated as a constrained H ∞ disturbance attenuation problem and then transformed into a solving of Linear Matrix Inequalities (LMIs). The effectiveness of the H ∞ state-feedback controller is illustrated through simulation. It is shown that the state-feedback control strategy effectively stabilizes the inverted pendulum.