Flatness-based feedforward control design for flexible structures

This contribution presents a solution to the feedforward tracking control problem for flexible beam structures. The design methodology is based on the modal analysis of the structural dynamics to determine an inverse system representation by parameterizing modal states and system input in terms of a parameterizing function and its time-derivatives. Convergence of the resulting parameterizations is thereby directly related to the problem of motion planning. In addition, the analytical feedforward control design approach is adapted to incorporate finite-element methods, which makes this approach especially suitable for the control of structures with complex geometry, boundary conditions or spatially varying material properties. Simulation results for a clamped-free Timoshenko beam with piezoelectric actuation are presented, where it is desired to drive the beam tip from zero deflection to a given desired stationary deflection within a finite-time interval