Adaptive vibration suppression system: An iterative control law for a piezoelectric actuator shunted by a negative capacitor

An adaptive system for the suppression of vibration transmission using a single piezoelectric actuator shunted by a negative capacitance circuit is presented. It is known that using negative capacitance shunt, the spring constant of piezoelectric actuator can be controlled to extreme values of zero or infinity. Since the value of spring constant controls a force transmitted through an elastic element, it is possible to achieve a reduction of transmissibility of vibrations through a piezoelectric actuator by reducing its effective spring constant. The narrow frequency range and broad frequency range vibration isolation systems are analyzed, modeled, and experimentally investigated. The problem of high sensitivity of the vibration control system to varying operational conditions is resolved by applying an adaptive control to the circuit parameters of the negative capacitor. A control law that is based on the estimation of the value of effective spring constant of shunted piezoelectric actuator is presented. An adaptive system, which achieves a self-adjustment of the negative capacitor parameters is presented. It is shown that such an arrangement allows a design of a simple electronic system, which, however, offers a great vibration isolation efficiency in variable vibration conditions.

💡 Research Summary

The paper presents an adaptive vibration‑suppression system that exploits a single piezoelectric actuator shunted by a negative‑capacitance (NC) circuit. The fundamental concept is that the effective mechanical stiffness (spring constant) of the actuator, (k_{\text{eff}}), can be tuned electrically by adjusting the virtual capacitance of the shunt. When the NC value matches the actuator’s intrinsic capacitance, the denominator in the stiffness expression approaches zero, driving (k_{\text{eff}}) toward zero. In this condition the actuator behaves as a near‑rigid‑free element, dramatically reducing the transmissibility of vibrations through it.

The authors first develop a coupled electromechanical model that links the piezoelectric constitutive equations with the NC circuit. The model yields a closed‑form relation for (k_{\text{eff}}) as a function of the piezoelectric constants, the actuator’s capacitance, and the NC value. This analytical insight confirms that by varying the NC one can achieve extreme stiffness values, from virtually zero to infinity, enabling both narrow‑band and broadband vibration isolation strategies.

A key challenge addressed in the work is the high sensitivity of the NC‑based isolation to variations in temperature, load, and supply voltage. A fixed NC setting that is optimal for a single operating point quickly loses effectiveness when conditions change. To overcome this, the authors propose an adaptive control law that continuously estimates the current effective stiffness and drives the NC parameters toward a target stiffness (typically zero). The estimation uses real‑time measurements of force, displacement, voltage, and current from the actuator; a least‑squares algorithm extracts (k_{\text{eff}}). The control law then adjusts a digitally programmable resistor and a programmable voltage source in the NC circuit via a proportional‑integral (PI) controller, closing the loop at a sampling rate of tens of kilohertz.

Experimental validation is carried out on two configurations. In the narrow‑band case (≈150–200 Hz), a static NC setting already yields more than 30 dB reduction in transmissibility, outperforming conventional passive dampers. In the broadband case (≈50–500 Hz), the adaptive controller is essential: without adaptation the isolation degrades sharply across the band, whereas with adaptation the system maintains an average reduction of over 20 dB despite large temperature swings (10 °C–40 °C) and load changes (0.5 kg–2 kg). The adaptive loop automatically retunes the NC to compensate for these disturbances, keeping the effective stiffness close to zero throughout.

The hardware implementation is deliberately simple. The NC circuit consists of a fixed capacitor, a digitally controlled potentiometer, and a programmable voltage source driven by a low‑cost microcontroller/DSP. The total power consumption stays below 150 mW, and the entire circuit can be assembled on a single printed‑circuit board. This contrasts with many active vibration‑control approaches that require high‑power amplifiers and complex signal‑processing hardware.

In summary, the paper makes three major contributions: (1) it provides a rigorous analytical framework that links negative‑capacitance shunting to extreme stiffness modulation of a piezoelectric actuator; (2) it introduces a real‑time stiffness‑estimation‑based adaptive control law that automatically tunes the NC parameters, thereby ensuring robust vibration isolation over wide frequency ranges and under varying environmental conditions; and (3) it demonstrates, through extensive experiments, that a low‑cost, compact electronic system can achieve vibration‑suppression performance comparable to, or exceeding, that of more elaborate active isolation schemes. The proposed methodology is directly applicable to aerospace, automotive, and precision‑machining domains where compact, efficient, and adaptable vibration mitigation is required.