## 1 Introduction  
The control of the low frequency vibration of plates is a longstanding and growing problem which should be considered while both designing and using equipment. Such vibrating surfaces have significant applications in manufacturing, infrastructure engineering, and consumer products. Mechanical vibrations degrade the quality of the products and the fabrication process rate, and they create noise in the surrounding area. As soon as the performance of IT solutions, especially advances in digital signal processing (DSP), presented the opportunity to use more advanced control algorithms, the idea of active vibration control (AVC) became the most popular alternative to passive techniques [1, 2]. The main aim of active control systems designed for flexible planar structures is to cancel their vibrations and related acoustic radiation as much as possible. Many classical strategies can be used for active vibration control--for example, classical approaches using proportional-integral-derivative controllers (PID), pole placement design, linear quadratic Gaussian (LQG) and the optimal control algorithm (LQR), which have also been applied by the authors [3, 4, 5, 6]. The LQR, and LQG algorithms are used for active vibration control of smart flexible plates in recent years, i.e., [7, 8].The major disadvantage of such approach is the fact that they require an exact mathematical model of the structure. Finding such a mathematical model is an art in itself and often involves several approximations and simplifying assumptions, therefore, often not closely match the real system. However, recently the LQR control strategy was applied in combination with maximising the energy transformation from actuator to structure [9, 10]. More recently, to improve active vibration control performance of structures, a hybrid Fuzzy-PID and intelligent PID controllers optimized by artificial bee colony algorithm (PID-ABC) have been proposed [11]. An overview of the available works from recent years shows that the Positive Position Feedback (PPF) together with MFC elements is relatively popular. PPF is a second-order low-pass filter with position signal fed back to the plant. [PERSON] and [PERSON] [12] examined the noncollocated active vibration control of a free-edge sandwich composite plate where PPF control schemes have been applied experimentally. [PERSON] et al. [13] examined a rectangular carbon fiber composite plate with free edges. In their paper a fractional-order PPF compensator (FO-PPF) is proposed, implemented, and compared to the integer-order PPF. However, in this approach, the design of control for the different modes requires the design of several PPF filters closely matched to the targeted frequency, where the cross-coupling between them has to be taken into account. A similar but more flexible approach is proposed in [4]. The proposed controller with phase-shift adjustment in the feedback loop (PSAF) combines the features of the positive position feedback and strain rate feedback controllers. The obtained vibration reduction levels were highly beneficial for the three considered resonant frequencies (vibration reduction from 12 to 28 dB); The disadvantage is the each targeted frequency has to be known. In addition, many methods that use artificial intelligence have been applied to active vibration control in the engineering field, for example, [14]; however, the area of adaptive control has become one of the richest in terms of algorithm design, analytical tools and various modifications. As has been shown in a number of publications, classical controllers considered for AVC can change object behavior in response to a change in the dynamics of the process, and disturbances; therefore, when the system parameters change during the control process, one can see a degradation in the performance of such fixed parameter controllers. For these reasons, the use of adaptive control in the process of vibration reduction is an interesting alternative to controllers with fixed parameters.