## 1 Introduction
Interest in adaptive control was renewed in the 1990s. Taking into account the stability framework introduced in the 70s [15] and the robustness framework established in the 80s [16], hundreds of successful approaches with applications for engineering were developed [17]. The different algorithms used can be classified into two general categories: feedback and feedforward active vibration control. The feedforward method is implemented in active control applications owing to its self-adjustment ability to adapt to dynamically varying structures; however, these control systems typically rely on a large number of error sensors and actuators, i.e., [18] and they have several other limits. Adaptive feedback control enables to track changes in the plant dynamics. In this paper, the approach known as a indirect adaptive pole placement controller with feedback loop is considered. The technique is based on the recursive estimation of the unknown system model, and then synthesizes the control law by implementing the pole placement procedure. The main assumption of the pole placement technique involves solving the Diophantine equation for a closed-loop system. The high complexity of this problem involves performing many calculations and using IT solutions instead of classical methods. The number of calculations strongly depends on the order of the controller. In the paper [19], instead of performing calculations online, the symbolic formulas for controller parameter estimation, which included only simple mathematical operations, such as multiplication and addition, were applied. This solution works well if the 4 th-order ARX model (AutoRegressive with eXogenous input model) of the system has enough fidelity; however, for complex objects, modeled with the higher-order polynomials, the resulting symbolic formulas must be strongly optimized and reduced. The aim of this paper is to investigate an approach for the reduction of vibrations of a thin circular plate for which an adaptive feedback control algorithm, appropriately selected for the range of its resonance frequencies, was applied. The dynamic behaviour of the considered plate, the lightly damped structures subjected to low-frequency excitation, is mostly determined by their resonances. The first three resonant frequencies of the plate have the greatest impact on vibrations, they are in the range (0-400 Hz). With this assumption the response of the structure is controlled by a small number of modes [20]. The limitations of the method are largely dependent on the computer hardware and A/D and D/A measurement cards used. In order to correctly identify the object, the signals should be sampled more often than it results from the Nyquist-Shannon theorem. A sufficiently short sample time should be selected, which may cause difficulties in performing all complex calculations of the adaptive algorithm in case of more broadband vibration control. The algorithm contains procedures for the automatic change of the controller settings, based on the object model, determined and updated during the process by means of online parametric identification. This means that the active vibration reduction system can automatically adjust to changing operating conditions. The control algorithm was coded in a PC PowerDAQ device with a real-time operating system, equipped with a data acquisition card working with the xPC Target platform [21]. The results of experimental tests confirm the possibility of using the proposed solution to reduce the vibration of plates.