The paper is aimed at presenting, in the sense of analyzing and comparison, some aspects of modeling, simulation and control of piezoelectric flexible smart structures from the vibration suppression point of view. Taking into account the necessity of a good model development for the purpose of the structure simulation and model-based control design, two approaches are considered: finite element (FEM) method based methodology and system identification approach. The finite element analysis includes modal analysis of the structures with piezoelectric active elements (actuators and sensors) together with the active elements dynamics. Resulting dynamic model of the structure is represented in the form of equations of motion, which after appropriate transformations and modal reduction lead to a state-space model convenient for the controller design. As an alternative, the subspace based system identification is proposed, which in case of the real structure availability, provides a model of the structure from the input-output measured data. Controller design for the purpose of vibration suppression is model based. Optimal LQ tracking and direct model reference adaptive control laws are considered. Uncontrolled and controlled behavior of structures is investigated and the comparison of the proposed control laws and their efficiency verification is performed through the examples.
The objective of the paper is to present an overall design methodology based on the finite element method (FEM), where the focus is on the relation between the controller design and the multi-physics structure, consisting of the passive base structure, the actuators, the sensors and also the control electronics. First, it is shown how such an overall virtual computer model can be generated and applied to design smart structures and to study the behavior of the structures under different operating conditions taking into account also disturbances, model uncertainties, etc. As a reference example a smart plate structure is used to discuss different design versions and controller approaches in detail. Then two industrial applications are briefly mentioned, where our approach was used to design the structures based on an overall virtual computer model.