# Shunt Damping Vibration Control Technology: A Review
## 6 Adaptive Shunt  
According to the previous summaries above, it can be deduced that shunt damping technology is a simple and effective vibration control method that can be applied for the various situations. However, in practical applications, the change of the temperature and the stiffness can result in significant movement of the structural resonance frequencies. Moreover, the capacitance of a piezo and the inductance of the electromagnetic transducer may have variation. Such variations can severely  
Figure 11: Switchable shunts, (**a**) switch capacitor, (**b**) switch R-L, (**c**) synchronized switched damping on a resistance (SSDS), (**d**) synchronized switched damping on negative capacitance (SSDNC) and (**e**) synchronized switched damping on negative capacitance and inductance (SSDNCI). reduce shunt damping performance because the electrical impedance remains tuned to the nominal resonance frequencies. [PERSON] et al. [123] presented an adaptation R-L shunted piezoelectric transducer to compensate variation of the natural frequency. The adaptation law was based on the phase match, shown in Figure 12a. The tuning direction of this adaptation law was obtained by detecting the phase shift between the velocity of the mechanical structure and the current in the shunt circuit. The phase of this transfer function is \(\phi=-\tan^{-1}(\frac{\omega R/L}{1/(LC)-\omega^{2}})\). \(\omega=1/\sqrt{LC}\) is the optimal tuning for the modal frequency, the phase will be \(\pi/2\). The tuning adaptation law was obtained by detecting the phase shift between the velocity of the mechanical structure and the current in the shunt circuit. As the exact value of the phase for this technique is not required, one can reduce the adaptation problem to multiplication and integration of current and velocity. The adaptive R-L resonant shunt overcomes the sensitivity of the traditional resonant shunt to the structural natural frequency. The results showed that: (1) when the temperature of piezo was changed from 27\({}^{\circ}\) Celsius to 15\({}^{\circ}\) Celsius, the adaptive R-L shunt can keep the same amplitude reduction (\(-11\) dB). Conversely, vibration reduction drops by 6.5 dB when an R-L shunt was used; (2) When the natural frequency was changed from 383 Hz to 375 Hz, a considerable amplitude reduction was also obtained. These results showed the robustness of the adaptive shunt when subjected to a variable situation. The passive multimodal shunts mainly utilize damped electrical resonance that consists of the inherent inductance or capacitance of the transducer and RLC network to tune the structural vibration. [PERSON] et al. [124] also discussed an online adaptation of multi-mode resonant shunts based on the phase shift method. Figure 12b is the principle of the adaptive inductance shunt that employs the multimode current-flowing circuit. The series \(C_{Fi}-L_{Fi}\) network has zero impedance for \(\omega_{i}=1/\sqrt{L_{i}C_{i}}\) and has high impedance at all other frequencies. The plate structure results implied that considerable control performance can be achieved despite the change of the modal frequencies and capacitance of the piezo. [PERSON] et al. [36] introduced an online adaptation of current-blocking and current-flowing shunts (shown in Figure 7b,c)). The system was implemented using synthetic impedance (presented in Figure 9) along with time varying transfer functions to alter the parameters of a shunt circuit in real time. Note that the impedance of the shunt is \(Z(s)\), the adaptive shunt synthesizes the impedance \(Z(s)\) twice: first, to implement the shunt damping circuit, and second to reconstruct the performance signal \(V_{\rm P}\). Experimental results showed reliable estimation of the performance functions, optimal tuning of the circuit parameters, and satisfactory mis-adjustment. The second and third modal vibrations were reduced by 22 and 19 dB.