# Shunt Damping Vibration Control Technology: A Review
## 4 Active Shunt
[38] used a negative capacitance in synchronized switching damping (SSD) instead of an inductance in the traditional SSD technique. Therefore, there was no resonance in the circuit. The equivalent circuit of a synchronized switch damping technique based on negative capacitance system (SSDNC) is purely capacitive. Moreover, the voltage applied on the piezoelectric element is inverted by the negative capacitance. [PERSON] et al. [101] also added a negative capacitance to the resonant circuit to enhance the performance of the SSD. Considering the sensitivity and instability of the negative capacitance circuit, measurement and quantification of the power within the shunt has been difficult to obtain. The method was verified using a cantilever beam. The results showed that a pure SSD shunt can reduce the vibration by 25.2 dB, and SSD with negative capacitance can reduce the vibration by 31 dB. [PERSON] et al. [102] discussed the power output and efficiency of a negative capacitance shunt for vibration control of a flexural system. The power can be expressed in terms of the shunt impedance and the strain-induced voltage \(V_{e}\)  
\[P_{shunt}=V_{e}^{2}\frac{Z_{s}}{\left[\left(i\omega C_{P}\right)^{-1}+Z_{s} \right]^{2}} \tag{26}\]  
where \(Z_{s}\) is the total impedance of the shunt. In recent years, research on the negative capacitance shunted piezoelectric transducer has been increasing. [PERSON] et al. [103] studied the negative capacitance-inductance shunt and modeled the behavior of a negative capacitance-inductance shunt in terms of power output and efficiency. Hereafter, a new self-powered SSD technique was proposed in which the inductance in the previous self-powered SSD techniques was replaced with a negative capacitance thus making the circuit capacitive without generating resonance. The optimum damping performance is obtained by keeping the value of negative capacitance slightly greater than the inherent capacitance of the piezoelectric patch. [PERSON] et al. [104] proposed a new tuning method for shunt damping with a series resistance, inductance and negative capacitance shunted piezoelectric transducer. The part above summarizes the negative capacitance shunt in piezoelectric shunt damping vibration control. As to the electromagnetic transducer, the moving coil in the magnetic field can be electrically equivalent to an emf \(V_{e}\), a resistance \(R_{e}\) and an inductance \(L_{e}\). Therefore, the negative resistance can be used to cancel out the inherent resistance of the coil to improve the vibration control performance of the electromagnetic transducer. The vibration control principle of the negative resistance electromagnetic shunt damping (NR-EMSD) is similar to that of the negative capacitance piezoelectric shunt damping. However, NR-EMSD has special features for the difference between electromagnetic and piezoelectric transducers. Figure 8: (**a**) Schematic of the negative impedance converter (NIC), (**b**) negative capacitance shunt for the vibration control of a truss structure, reproduced with permission from [37], IOP Publishing, 2008. A negative impedance converter can be used to realize a negative resistance. Shown in Figure 8a, the shunt will be a negative resistance as \(Z_{1}=Z_{1}=R\), \(Z_{3}=R_{S}\). The negative resistance can be changed by changing the resistance of \(Z_{3}\). On the other hand, a synthetic impedance is able to construct an arbitrary impedance [35; 105]. Based on this traditional negative resistance converter, [PERSON] et al. [106] developed a 2-collinear-DoF strut for the micro-vibration isolation of a spacecraft. Figure 9a shows a kind of synthetic shunt impedance converter. The circuit works in three stages: the first is a current sensing stage; the current is multiplied by the desired impedance \(Z_{s}\) that is defined by a digital controller dSPACE. The voltage \(V_{0}=R_{0}I\) is then added to give the voltage across the terminals of the coil.