Differential game-based distributed vibration control for gyroelastic beam using control moment gyroscopes

To suppress the vibration of gyroelastic beams – a class of flexible structures integrated with control moment gyroscopes (CMGs) – a differential-game-based vibration suppression scheme is proposed in this paper. Collocated pairs of CMGs and angular rate sensors are used as distributed actuators/sensors mounted along the gyroelastic beam. Firstly, a precise model incorporating the dynamics of the CMGs and their interactions with the flexible gyroelastic beam is established using the finite element method under a cantilever boundary condition, which isolates elastic vibration modes for focused control evaluation. The gyroelastic beam's dimensionless stiffness and frequency ratios are selected to be comparable to those of representative deployable space truss elements reported in the literature, ensuring relevance to space applications. Secondly, a differential-game-based controller is proposed based on a non-zero-sum differential game strategy, in which each CMG is regarded as an independent player. The controller uses angular rates at actuator locations as input and outputs the gimbal angular rates of CMGs. To yield a Nash equilibrium solution, the coupled Hamilton–Jacobi equations are resolved by leveraging a policy iteration algorithm. Finally, numerical simulations are conducted in four different cases to verify the effectiveness and feasibility of the proposed method. The simulation results and comparative analyses demonstrate that the designed controller can achieve vibration suppression of gyroelastic beams with multiple actuators at a high collaborative level.