Optimal Actuator Placement and Static Load Compensation for Euler-Bernoulli Beams with Spatially Distributed Inputs ?

摘要

Adaptive structures in civil engineering are based on active structural elements. In this paper, an active beam element is considered with potentially multiple fluidic inputs spatially distributed over the beam’s length. It is modeled by a one-dimensional beam equation. The inputs are realized as torque inputs, where the torque is proportional to the pressure of the fluid. A method to calculate the optimal input values analytically depending on a given static load case is presented in the first part of the paper. In the second part, by generalizing the static load using a sufficient number of discrete loads evenly distributed along the beam, optimal actuator positions can be calculated for a given number of actuators. The cost function is based on extending the idea of the Gramian compensability matrix to systems governed by spatially distributed ordinary differential equations. Since the number of actuators can be a design variable, this yields a Pareto front supporting the user in selecting an appropriate number. A fluidic actuator serves as example to illustrate the potential of the proposed placement algorithm.