SPACE-TIME SPECTRAL ELEMENT METHOD FOR OPTIMAL SLEWING OF A FLEXIBLE BEAM

A new computational approach to modelling and control of a flexible be am is proposed. The structural modelling and the control design proble ms are formulated in a unified mathematical framework that allows simu ltaneous structural and control design iterations that result in an op timal overall system performance. The method employs the space-time sp ectral elements for simultaneous space and time discretizations of a T imoshenko beam model. Dimensionless equations of motion are derived us ing Hamilton's principle of variable action and an integral formulatio n in the framework of space-time spectral elements is introduced. An o ptimal control problem formulated for the continuum model is transform ed by the space-time spectral element formulation into an optimization problem in a finite-dimensional parameter space. Dynamic programming is then used to obtain both open and closed loop control laws. A simul ation study shows good performance of the control law applied to the n ominal model. It is also demonstrated that proper discretization yield s performance robustness of the system with respect to modal truncatio n.