Modelling approaches for active systems

To solve a wide range of vibration problems with the active structures technology, different simulation approaches for several models are needed. The selection of an appropriate modeling strategy is depending, amongst others, on the frequency range, the modal density and the control target. An active system consists of several components: the mechanical structure, at least one sensor and actuator, signal conditioning electronics and the controller. For each individual part of the active system the simulation approaches can be different. To integrate the several modeling approaches into an active system simulation and to ensure a highly efficient and accurate calculation, all sub models must harmonize. For this purpose, structural models considered in this article are modal state-space formulations for the lower frequency range and transfer function based models for the higher frequency range. The modal state-space formulations are derived from finite element models and/or experimental modal analyses. Consequently, the structure models which are based on transfer functions are directly derived from measurements. The transfer functions are identified with the Steiglitz-McBride iteration method. To convert them from the z-domain to the s-domain a least squares solution is implemented. An analytical approach is used to derive models of active interfaces. These models are transferred into impedance formulations. To couple mechanical and electrical sub-systems with the active materials, the concept of impedance modeling was successfully tested. The impedance models are enhanced by adapting them to adequate measurements. The controller design strongly depends on the frequency range and the number of modes to be controlled. To control systems with a small number of modes, techniques such as active damping or independent modal space control may be used, whereas in the case of systems with a large number of modes or with modes that are not well separated, other control concepts (e.g. adaptive controllers) are more convenient. If other elements (e.g. signal amplifiers or filters) in the signal paths have a significant influence on the transfer functions, they must be modeled as well by an adequate transfer function model. All the different models described above are implemented into one typical active system simulation. Afterwards, experiments will be performed to verify the simulations.