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The percentages contributed by the MFA control and the SM control are shown in Figure 13 , where it can be seen that the SM control has a larger impact on the convergence rate of feedback gain than the MFA control. The RMSs of amplitude were calculated and are shown in Table 6. A similar control effect to the previous simulation can be observed.

The robust MFA-IL control in this simulation presents a better control performance and makes the learning speed of the controller faster by comparing with the P-type IL control. Figure 15 shows the sensor output signals. The added noise resulted in a decrease of system performance and divergence as long as the system was controlled by the P-type IL method, while the robust MFA-IL control could maintain the stability of the control system.

Adaptive and Robust Active Vibration Control

These comparative results validate that the proposed control method possesses excellent control performance and robustness to the noise from external excitation. To verify the feasibility and the performance of the robust MFA-IL algorithm, an active vibration control system was established. The experimental devices are illustrated in Figure The real-time code was automatically operated in the real-time semi-physical simulation system.

The dimensions of the specimen were the same as in the numerical simulations above, and exciting position point C was replaced by a metal patch. The piezoelectric patches were glued on the host plate using commercial cyanoacrylate glue. A block diagram of the experimental system is illustrated in Figure The experimental system includes three subsystems, namely: The vibration exciting system, the signal acquisition system and the vibration control feedback system.

The signal transfer paths of these three subsystems are marked by red, green and blue color with different line types. For the vibration exciting system, the excitation signal was produced by the signal generator, which was used to simulate the external excitation of the piezoelectric smart plate.

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The signal was transmitted to the electric-eddy current exciter, which could then convert the electrical signal into the vibration excitation. For the signal acquisition system, three piezoelectric sensors sensors a , b and c were used to obtain the vibration information of the piezoelectric smart plate. To remove high-frequency noise, the input signals were passed through a low-pass filter set to 14 Hz. After amplification from the high voltage amplifier, the control signals were applied to the actuators for suppressing structural vibration. The experimental sample period was specified as 3 ms.

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A chirp signal is utilized to determine the natural frequencies of the piezoelectric smart plate. Actuator a was excited by a chirp signal with an amplitude of V, while the output voltages of the Sensor a were stored after filtering. The starting frequency was 0. The sweep time was s.

Active Vibration Control in Flexible Structures Using LMIs - UNESP - Ilha Solteira, SP, Brasil

Then, the fast Fourier transform FFT of the time response was calculated. Figure 18 b depicts the frequency responses of sensor a when applying FFT to the time-domain signal plotted in Figure 18 a. The experimental natural frequencies obtained from the FFT plot are given in the same table Table 4 for comparison.

The biggest difference, Measured vibration responses excited by actuator a : a Time-domain responses of sensor a , b frequency responses of sensor a. Conditions that may lead to the difference of modal frequencies between the numerical solutions and experimental solutions are considered as follows: 1 The clamp-free boundary condition in the simulations is ideal. While in the experiments, the boundary of the plate may not be totally clamped.

The parameters used in the numerical simulations are not precisely consistent with those of the plate applied in the experimental material. The modal analysis in simulations is used to provide an approximate solution for verifying the feasibility of the control algorithms, the difference of modal frequencies between the numerical results and the experimental results is acceptable. It is clear that the FE model sufficiently predicts the natural frequencies of the piezoelectric smart plate. Filters were designed and utilized in the experiments to deal with high frequency noise.

For investigating the control algorithms, the designed low-pass filters were applied. The cutoff frequency of the low-pass filters was specified at 30 Hz. During the experiments, the robust MFA-IL control and P-type IL control algorithms were used to suppress the structural vibration of the cantilevered plate. The maximum number of iterations was set to as to avoid control spillover or system instability. The stopping criteria in the experiment are the same with those in Section 6. The sensor output signals shown in Figure 19 a,b were moved forward to compensate for the phase lag effect.

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Five seconds after harmonic excitation driving, the proposed control algorithms were implemented to suppress the structural vibration. The RMS values shown in Table 6 were used to quantitatively evaluate the control performance of the various methods. It can be concluded that the proposed control method exhibits excellent performance when integrating MFA control and SM control. The learning processes of the feedback gains are shown in Figure The percentages of contributed feedback gain from the MFA and SM methods are shown in Figure 21 , where it can be seen that SM control has a larger impact on the convergence speed of feedback gain than MFA control.

By applying evidence theory to the design of the stopping criteria, the learning processes of all controllers can be evaluated in real-time. The decision-making based on the appropriate stopping criteria makes all controllers learn sufficiently, so that a better control performance is obtained.

Comparing the experimental results with the numerical results, it can be seen that the vibration suppression trends performed similarly. Due to the difference of the sample period and the unknown nature of the experimental system, the parameters selected in the simulations and experiments are different. A robust MFA-IL control method was developed for the active vibration control of piezoelectric smart structures. Considering the uncertainty of interaction among all actuators in the control process, the MFA control was incorporated into P-type IL control for the adjustment of learning gain.

In order to achieve a fast control response and enhance the stability of the system, SM control was adopted to ensure a fast dynamic response and compensate for the influence of uncertain noise. The multi-source information fusion method based on the evidence theory was adopted to design the stopping criteria of the robust MFA-IL method. The vibration control equations of piezoelectric smart structures were derived from the dynamic FE equations of a linear elastic system.

The dynamic linear method was applied to transfer the vibration control equations for the design of the robust MFA-IL controller. The simulation and experimental results were presented and compared with the corresponding results using the P-type IL control approach. As long as the locations and sizes of actuators and sensors are chosen appropriately, both P-type IL control and robust MFA-IL control can effectively suppress structural vibration when the piezoelectric smart plate is excited by its first natural frequency. Furthermore, the whole structure presents good controllability, rather than small portions bonded with piezoelectric sensors, using both the P-type IL method and the robust MFA-IL method.

Based on the comprehensive comparative analysis of the numerical and experimental results, the proposed control method can achieve better control performance and is more robust to external disturbances when compared with the P-type IL control. In other words, the proposed control method overcomes the inherent drawbacks of P-type IL control and achieves the desired control performance.

Although the robust MFA-IL control method was applied for a plate structure in this paper, considering its advantages presented above, this approach can be applied for other structures, like beam structures, extending the possibilities of engineering and research applications. Dynamic linearization was an effective method in developing the proposed method for nonlinear systems. Dynamic linearization mainly introduces optimal technology as a tool for the controller design and analysis.

In future work, it will be expected that the dynamic linearization method will be combined with an online model identification technique to deal with much more practical problems, those typically encountered in industrial applications. This may result in a simpler controller structure and obtain a better degree of control precision.

National Center for Biotechnology Information , U. Journal List Micromachines Basel v. Micromachines Basel. Published online Mar Find articles by Liang Bai. Find articles by Yun-Wen Feng. Find articles by Xiao-Feng Xue. Author information Article notes Copyright and License information Disclaimer. Received Feb 11; Accepted Mar Abstract Through combining P-type iterative learning IL control, model-free adaptive MFA control and sliding mode SM control, a robust model-free adaptive iterative learning MFA-IL control approach is presented for the active vibration control of piezoelectric smart structures.

Controller Design 4. Robust MFA-IL Control The discrete-time SM is used to compensate the external disturbances and guarantee the fast convergence of feedback gain, which can increase the system robustness and control performance. Open in a separate window. Figure 1. Evidence Theory The evidence theory is a mathematical theory and general framework for reasoning with uncertainty information in systems, which allows one to combine multiple variables from multiple sources, arriving at a degree of belief.

The Design of Stopping Criterions Research on stopping criteria based on evidence theory in this paper involves extracting real-time feedback gains from each controller in the vibration control system, constructing the frame of discernment, choosing appropriate feature vectors that describe the learning process of the robust MFA-IL algorithm, calculating the BPAs based on the input signals of actuator, forming the fused BPAs using combination rule and diagnosing the learning states of the control method based on the BPA results.

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Numerical Examples 6. FE Model Validation The purpose of this subsection is to examine the accuracy of the dynamic FE model established by ANSYS, by comparison of the numerical and analytical results in the open literature. Figure 2. Table 1 Properties of the graphite-epoxy GE composite material and the piezoelectric material. Table 2 First five frequencies parameters.

Modeling and Choice of Controller Parameters In this section, a piezoelectric smart plate is considered for vibration control simulations. Figure 3.

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Table 3 Properties of the GE composite material and the piezoelectric material. Table 4 First three natural frequencies of the piezoelectric smart plate. Table 5 The control parameters. Figure 4. Displacement responses: a Point A, b point B. Figure 5. Table 6 Root mean square RMS values of amplitude. Figure 6. Figure 7. Figure 8.

Random Excitation In the last simulation, a random excitation shown in Figure 9 was applied to point C to drive the piezoelectric smart plate. Figure 9.