Control of a flexible beam actuated by macro-fiber composite patches: I. Modeling and feedforward trajectory control

摘要

This paper considers a systematic approach for motion planning and feedforward control design for a flexible cantilever actuated by piezoelectric macro-fiber composite (MFC) patches. For accurate feedforward tracking control, special attention has to be paid to the inherent nonlinear hysteresis and creep behavior of these actuators. In order to account for these effects an appropriate compensator is applied which allows us to perform the tracking controller design on the basis of a linear infinite-dimensional model. A detailed analysis of the nonlinear actuator behavior as well as the compensator design and the overall experimental validation is presented in the companion paper (Schr?ck et al 2011 Smart Mater. Struct. 20 015016). The governing equations of motion of the hysteresis and creep compensated cantilever are determined by means of the extended Hamilton's principle. This allows us to consider the influence of the bonded patch actuators on the mechanical properties of the underlying beam structure in a straightforward manner and results in a model with spatially varying system parameters. For the solution of the motion planning and feedforward control problem a flatness-based methodology is proposed. In a first step, the infinite-dimensional system of the MFC-actuated flexible cantilever is approximated by a finite-dimensional model, where all system variables, i.e. the states, input and output, can be parameterized in terms of a so-called flat output. In a second step, it is shown by numerical simulations that these parameterizations converge with increasing system order of the finite-dimensional model such that the feedforward control input can be directly calculated in order to realize prescribed output trajectories.