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The elastic vibration of the flexible manipulator is the key problem to be solved before its effective application. The mobile flexible manipulator system (MFMS), under variable load conditions, is taken as the research object. Based on Lagrange’s principle and the singular perturbation theory, the two-timescale subsystems dynamic models of the MFMS are constructed to set up the system payment function and the Hamiltonian function which correspond to the subsystems states and errors. Then, with the minimization of the system Hamiltonian function, the synchronization optimization of the designed two-timescale optimal observer (TSOO) and the designed optimal state feedback controller is realized, under the premise of the system stability which is verified by the Lyapunov stability criterion. Furthermore, with the contradiction between the control rapidity and the accuracy of the optimal state feedback controller considered, by combining the input shaping technology, the master-slave composite controller for the elastic vibration of the MFMS is constructed. Finally, simulation results verify the validity of the designed TSOO and the master-slave composite controller.

Master-Slave Composite Vibration Control of a Mobile Flexible Manipulator via Synchronization Optimization of Observation and Feedback