## 5 Controller Implementation and Testing  
The test stand was built using a real-time control and measurement system working with the Matlab XPC Target software. The inputs of the measuring system card (PD2-MFS-8-500/14) were connected directly to MFC sensors (M-2807-P1) and the output of the laser vibrometer. The outputs of the D/A converter card (PD2-AO-8/16) were connected via an analog low-pass filter and amplifiers to actuators (speaker and star MFC). An analog filter was designed based on the Butterworth method and its cut-off frequency was 1 kHz. An analog filter was used to reproduce the output signal due to the low sampling frequency of the RT system (5 kHz). The voltage value on the actuator is related to the ranges of voltage signals generated by the DAC card (\(-5\) V, \(+5\) V). The structure of the implemented control system is presented in Figure 3.  
An experiment was carried out to verify the effectiveness of the adaptive controller with the the poles location on the stand for active reduction of the circular plate vibrations. The time responses of the plate vibration velocity were determined experimentally with the use of a sensor placed in the central point on the plate's surface, which coincides with the sticking point of the control actuator. The signal inducing the vibrations of the disc with the use of the loudspeaker was a chirp signal with a frequency varying from 120 Hz to 400 Hz and a sinusoidal signal with a constant amplitude and frequency of 193 Hz. During the tests, the time courses, frequency spectra and the parameters of the identified object model were compared. Tests were carried out for various model and controller structures. The results for two control structures differing in the number of coefficients of the model and the controller are presented below:  
* controller 1: \(nA=4\), \(nB=3\), \(nS=3\), \(nR=2\)The first experiment with the applied adaptive controller was realized for both the 4 th and the 6 th order models with the use the sinusoidal excitation. During the tests the plate responses in time (Figure 4) and its frequency spectra (Figure 5) were compared. The results, matched to the main resonant frequency of the plate, are presented below. The excitation signal emitted by the loudspeaker was a sinusoidal waveform with a frequency of 190 Hz and an amplitude of 0.05 V. For better observation, this excitation signal was applied to the plate for 30 s, then it was turned off for 10 s, and then turned on again for 10 s (Figure 4a). The control signal from the adaptive controller was turned on 10 s after the system was started (this enables a detailed observation of its action). It can be seen (Figure 4b) that the control signal started with a delay \(-10\) s after the excitation signal (Figure 4a) and vibration amplitude remained almost constant for 20 s of the test when the excitation force was stopped for 10 s. If the plate was not forced to vibrate,  
Figure 4: Example test of an adaptive controller for the sinusoidal disturbance of 190 Hz. (**a**) Excitation signal; (**b**) Controller output; (**c**) Plate response with the use of controller 1; (**d**) Plate response with the use of controller 2. Figure 3: Test stand realization and connection scheme. for example, between 30-40 s, and 50-60 s, the adaptive controller produced a signal with a small, almost constant amplitude. From Figure 4c, it can be stated that plate vibrations are damped very well--the vibration amplitude of plate response in the range of 10-30 s (and also 40-50 s) decreased by more than 50%. Figure 4d shows the plate response for the same input as above, but instead of controller1, the 6 th order controller 2, is turned on in the control system. This controller calculates the control signal based on a more accurate object model (nA = 6). As can be seen, a very high, about 90%, vibration reduction value was obtained in this case.