Vibration and robust control of symmetric flexible systems

The use of symmetry in the vibration analysis and control of symmetric flexible systems is investigated. For a symmetric flexible system with actuators/sensors being symmetrically allocated, an internal and external decoupling control scheme is developed to simplify the controller design. The whole flexible system can be separated into two uncoupled subsystems under the decoupling scheme, and the control algorithm for each subsystem can be designed and implemented independently. Consider the case of a direct output feedback based controller design with actuators and sensors collocated. Two robustness properties of this controller, i.e., full-order closed-loop stability and reliable control, are exploited. For demonstrative purposes, the optimal modal space approach is adopted for controller design of each subsystem and to illustrate the advantages of the decoupling control scheme. Simulation results of the control of a uniform simply supported beam are given to show the effectiveness of this proposed scheme.