Mathematical Modeling, Motion Planning and Control of Elastic Structures with Piezoelectric Elements
The objective of this work is the development of a motion planning and tracking control approach for elastic structures. Motivated by the morphing wing concept of the field of aerospace engineering a so-called “smart wingsail” defines the center of the presented research. The motion planning and tracking control approach has to achieve different rest-to-rest motions of the wingsail’s transversal displacement. The design of the mechanical structure as well as the control concept of the wingsail relies on the results of proof of concept studies. For this purpose, different systems of interconnected bending beams are considered which emulates parts of the wingsail. The development of the model based control approaches requires an accurate system description. The modeling itself is done by an analytic energy based approach for the beams’ systems, where for the wingsail the finite elements method is used due to the risen complexity of the curved structure. To achieve a precise description of the governing dynamics different parameter identification concepts are discussed and applied. This leads to a precise but rather complex system description which covers the measured behavior of the experimental setups. Considering the objective of a real time capable control approach the complexity has to be reduced without a significant loss of accuracy. For this purpose different model order reduction techniques are discussed and applied. The resulting systems models are the bases of the control designs. Two different control concepts are presented and evaluated. At first the two-degrees-of-freedom control approach is introduced which combines a flatness-based feedforward control approach with a feedback controller. On the other hand, the so-called model predictive control approach is presented which is based on the solution of an optimization problem. Both concepts are evaluated by numeric analyses and by experiments.