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

Abstract

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 to perform the tracking controller design on the basis of a linear infinitedimensional 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 [1]. The governing equations of motion of the hysteresis and creep compensated cantilever are determined by means of the extended Hamilton's principle. This allows 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 parametrized in terms of a so-called flat output. In a second step, it is shown by numerical simulations that these parametrizations 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.

Experimental testing of spanwise morphing trailing edge concept

“…Among other applications, MFCs can be used to induce bending when bonded to a thin substrate, which has seen recent use in wing warping for Micro Air Vehicles [13], [14]. Still, challenges remain in compensating for hysteresis and creep in actuator design, which can be either approximately addressed through models or precisely addressed via closed loop control with an added sensor [15], [16].…”

Performance improvement of piezoelectric‐rubber by particle formation of linear aggregates

“…Piezoelectric materials, which have properties of converting a part of mechanical energy to electric energy and vice versa, are used as sensors and actuators. Recently, attention has been paid to them for their use as a vibration and noise reduction device and an energy conversion device . However, the piezoelectric‐ceramic which is used as standard piezoelectric material has the following problems.…”

Non-collocated feedback stabilization of a non-uniform Euler-Bernoulli beam with in-domain actuation

“…The power supply is provided by two high-voltage four-quadrant power amplifiers PA05039 of Trek Inc. 1 For the realization of the derived controller including the distributed-parameter observer a finite-dimensional approximation of (15), (16) is used by means of the Galerkin method. Here, the approach suggested in [3] is applied with the basis function chosen as the first 5 eigenmodes of a uniform cantilever beam.…”

“…In addition, the feedback control is validated by experimental results. Future work is dedicated to the combination of the dynamic feedback controller with the feedforward control presented in [3], [10] within the so-called two-degrees-of-freedom control concept, see, e.g, [11], in order to realize robust trajectory tracking control for the flexible cantilever beam.…”

“…Here, the indices c, p and tm indicate the contributions of the carrier layer, the patches and the tip mass, respectively. The equations of motion (2), (3) can be directly determined by means of Hamilton's principle as shown in [3] for a cantilever without tip mass.…”