114 A. M. Puhwein and M. J. Hochrainer “transfer system”, which transmits the simulated forces or movements to the physical model. It typically uses actuators with robust and high-precision control, which also limit the possible frequency and amplitude range of the RTHT experiment. The transfer system and its control directly influence the quality and even the stability of the entire setup, see. e.g. [2–5]. Since dynamic properties are often unknown, different control schemes have been proposed, e.g. phase shift [6],[7] and inverse compensation [8],[9], adaptive control with actuator identification [10]-[13], or AI based approaches [14]. Another way to reduce the adverse effects of the transfer system is the restriction to repeatable processes. To reduce inaccuracies due to coupling errors, the entire experiment can be repeated while adapting the transfer system control until the required accuracy is achieved, see e.g. [15]. If the experiment is focused on quasi-stationary periodic processes, iterative learning control (ILC) or repetitive control (RC) [16]-[19] can be applied successfully. ILC used in this project works very accurately and robustly, does not require prior knowledge of the dynamics of physical model and transfer system, dead times are perfectly compensated and it has proven to operate reliably for quasi-stationary processes. In RTHT the focus is generally on the physical model, but the simulation model plays an equally important role as it must represent all relevant components that are not tested experimentally. In recent years the development of virtual models is well supported by high end simulation tool which have developed significantly. Today several reliable tool chains are commercially available that automatically convert the simulation model into the required representation for the real-time application. To study nonlinear dynamic absorption, the physical oscillator used in this work is of Duffing type, see Fig 1a). The nonlinear restoring forces result from the interaction of a strong base magnet with a small magnet attached to the absorber mass, see Fig 1b). For the host structure, it is assumed that it can also be represented as a Duffing type SDOF oscillator, see again Fig 1a). According to the RTHT methodology, host structure and absorber are separated, the absorber is tested physically, whereas the host structure (virtual model, simulated model) is simulated in real time. a) b) Fig. 1 a) Model of the coupled system b) laboratory setup of test bench The simulated host structure can be regarded as “digital twin” of the real structure which can be configured easily in a wide parameter range. Any dynamics or nonlinearity can be implemented, as long as the motion can be calculated in real time. Therefore, the selection of nonlinear host structure parameters which reflect a proper physical system is crucial. For the dynamic absorber, in the contrary, it is rather difficult to develop a setup with adjustable dynamic parameters. For oscillators of Duffing type this can be achieved either by geometric or material nonlinearities or the application of magnetic interaction. The latter approach is quite convenient, because permanent magnets are commercially available in any size and shape. It has been demonstrated in [20], that a duffing type absorber can be obtained by adding repelling or attracting magnets to the mass of a linear oscillator. Since magnetic interaction forces depend on the magnetic field strength, it is convenient to attach a small light magnet onto the moving mass while providing a strong magnetic field by a much larger permanent magnet which is rigidly attached to the base. Furthermore, almost linear damping can be added to the oscillator by inserting an aluminum plate close to the moving magnet. It creates eddy current damping effects which are proportional to the relative velocity of the magnet with respect to the damping plate. By changing the distance between moving magnet and plate the almost linear viscous damping can be adjusted.
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