# Shunt Damping Vibration Control Technology: A Review
## 4 Active Shunt  
Active shunts are those where external electrical energy is needed. Compared to the passive shunt, the active one utilizes controlled electronics, e.g., operational amplifiers, transistors, electronic switches, to realize vibration control. In the view of the control system, the shunt circuit can be regarded as a controller that establishes the relationship between the control current and voltage, \(V_{z}(s)=Z(s)I(s)\). An arbitrary impedance \(Z(s)\) can be constructed using a controlled current \(I(s)\) or voltage source \(V_{z}(s)\), thus, the design problem is reduced to a standard linear regulator problem enabling the application of standard synthesis techniques. [PERSON] et al. [PERSON] et al. (2009); [PERSON] et al. [PERSON] et al. (2009) proposed active LQR, \(H_{2}\), and \(H_{\infty}\) shunt control, which can be easily applied to achieve a suitable impedance. These kinds of impedances are unrestricted in structure, and can be designed to meet any performance specification set within the flexibility of the synthesis process. The active shunt impedances are remarkably insensitive to variation in the structural resonance frequencies. The schematic of the LQR and \(H_{\infty}\) shunts can be found in [PERSON] et al. (2009). These algorithms can be implemented by using a dSPACE controller. However, it has turned out that a very well identified model of the system is needed and the control design is not straightforward due to the highly reactive impedance of the transducer. The main advantage of the active shunt is to achieve broadband or multimode vibration control. The negative impedance shunt circuit is able to cancel the inherent electrical impedance of the smart transducer. Figure 8a shows a kind of negative impedance converter (NIC) [PERSON] et al. (2009); [PERSON] et al. (2010). The equivalent impedance is  
\[Z_{in}=-\frac{Z_{1}}{Z_{2}}Z_{3} \tag{25}\]  
If \(Z_{1}=Z_{2}\)= \(R\), \(Z_{3}=C_{S}\), the shunt will be a negative capacitance converter, where \(R\) and \(C_{S}\) denote the resistance and the capacitance of the shunt, respectively. [PERSON] et al. [PERSON] et al. (2010) studied the effect of a negative capacitance controller theoretically and then validated it experimentally on a piezoelectric laminated simply supported plate. A single piezoelectric transducer was used to dampen multi-mode vibration. Experimental resonant amplitudes for the first to sixth modes were successfully reduced by 5.8 dB, 20.1 dB, 18.2 dB, 3.8 dB, 16.7 dB, and 17.2 dB. [PERSON] et al. [PERSON] et al. (2009) considered the stiffness ratio and loss factor with respect to the non-dimensional frequency to describe the characteristic behaviors of a piezoelectric damper connected to a series and a parallel resistor-negative capacitor shunt circuit. [PERSON] et al. [PERSON] et al. (2009) analyzed the effect of negative capacitance shunted piezoelectric transducers in damping and absorbing systems. L-network, R-network, RL-network, C-network, LC-network, RC-network, and LRC-network were investigated theoretically, and the corresponding optimal tuning frequency and resistance were listed. It can be shown that the damping performance is increased significantly by adding a negative capacitance to the system. [PERSON] and [PERSON] [PERSON] and [PERSON] (2009) discussed series and parallel negative capacitance, shown in Figure 8b. The open-loop frequency response function was used to draw a Nyquist plot to judge the stability of the two kinds of negative capacitance shunts. The experimental results showed that the parallel and series negative resistance can reduce the vibration of the struct by 18.4 dB and 21.9 dB. The series one has a relatively better robustness than the parallel one. [PERSON] et al. [PERSON] et al. (2009) discussed the values of electric elements composing the negative capacitance to improve vibration reduction efficiency and to avoid instability at low frequency. [PERSON] et al.