# Shunt Damping Vibration Control Technology: A Review
## 6 Adaptive Shunt
Although both current blocking and current flowing shunts provided similar performance, the current flowing technique requires a lower-order admittance transfer function, and is  
Figure 12: Adaptive shunts, (**a**) for single mode, and (**b**) multimode. easily parameterized in terms of the branch resonance frequencies. These reasons made the current flowing technique an ideal candidate for damping a large number of modes. Hereafter, [PERSON] et al. [54] also studied the adaptive electromagnetic shunt damping. A single mode RC resonant shunt controller was developed as shown in Figure 13. The impedance of the shunt \(Z(s)\) is \(R+1/Cs\). The controller will be  
\[K(s)=\frac{1/L_{e}}{s^{2}+\frac{R_{e}+R}{L_{e}}s+\frac{1}{CL_{e}}} \tag{31}\]  
The optimal damping of the mechanical resonance \(\omega_{n}\) can be achieved if the RC shunt is tuned to \(C^{*}=\left(\omega_{n}^{2}L_{e}\right)^{-1}\). The optimal capacitance is  
\[C^{*}=\underset{C>0}{\text{argmin}}E\Big{\{}v^{2}(t,C)\Big{\}} \tag{32}\]  
The adaptive RC shunt was verified experimentally on a single degree of freedom system. A vibration suppression of 22.75 dB was obtained during nominal operating condition. The relative phase adaptation was found to converge seven times faster as it is subjected to the induced changes in operating conditions. Resonant shunts have been successfully used to reduce structural vibration and this kind of shunt can be regarded as an electrical absorber. [PERSON] et al. [53] pointed out that the negative resistance shunted electromagnetic damper can produce electromagnetic shunt damping and electromagnetic shunt stiffness effect to influence o the inherent inductance of the coil. On the one hand, the electromagnetic shunt stiffness affects the vibration control effectiveness. On the other hand, it can be used to change or adjust the stiffness of the absorber. [PERSON] et al. [107] introduced o electromagnetic shunt damping into a dynamic absorber to provide controllable effective mechanical stiffness and damping. The expression of the damping and stiffness can be found in (28). A model-based feedforward controller was designed to adapt the resistance and capacitance to ensure the tuned frequency of the vibration absorber. The synthetic shunt impedance circuit (shown in Figure 9) was used to implement it. As the absorber is sensitive, the frequency can be estimated as  
\[ \begin{array}{c}\hat{\omega}^{2}=\sqrt{\frac{\widetilde{x}}{\widetilde{x}}} \\ \overline{x}^{2}=\frac{1}{T}\int_{T}^{t+T}x^{2}\text{d}t\\ \widetilde{x}^{2}=\frac{1}{T}\int_{T}^{t+T}\widetilde{x}^{2}\text{d}t\end{array}  \tag{33}\]  
Adaptive electromagnetic shunt damping shows a good response over a relative wide range of excitation frequencies (90-100 Hz). The adaptive controller provides a useful way to broaden the bandwidth of the absorber. Based on this technique, [PERSON] et al. [125] used three different feedback  
Figure 13: Adaptive RC shunt. algorithms, linear, nonlinear, polynomial, and fuzzy logic control, to compensate for errors in model parameters, and estimate the excitation frequency and environmental changes. The experimental results implied that the linear controller is unreliable, but the polynomial and fuzzy controllers work effectively. The adaptive controller can successfully adapt the system to track a variable excitation frequency while being robust with regard to errors or changes in system parameters and provides guaranteed stability in operation. The vibration reduction performance of the negative capacitance shunt may become worse when a small discrepancy in capacitance of the external shunt and piezoelectric element exists. An example is temperature sensitivity. Based on this possible failure of the shunt, [PERSON] et al. [113] proposed a method for automatic stabilization and adjustment of the negative capacitance shunt by an additional feedback control. Figure 14 shows a negative capacitance with a feedback control [114].