Stabilization and disturbance attenuation control of the gyroscopic inverted pendulum

In this study, a control moment gyroscope is used as an actuator to stabilize the inverted pendulum. A control strategy is proposed to stabilize the inverted pendulum at the upright unstable equilibrium point 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 solving linear matrix inequalities. The performance of the proposed controller is evaluated through simulation for linear and nonlinear cases. It is shown that the proposed state-feedback control strategy effectively stabilizes the inverted pendulum.