The electromechanical damping of piezo actuator resonances: Theory and practice


Piezoelectric crystal actuators, also known as piezos, exhibit high stiffness, high force and extreme resolution properties which are desirable for precision positioning applications. Electrically operated piezos have been used for a long time to stabilize the frequency of electronic oscillators. In this field, minimizing the damping and improving the resulting quality factor (Q) of the piezo is of great importance. The recent growth in the application of piezos as passive dampers and precision actuators has triggered the need to damp the intrinsic piezo actuator resonance rather than improve the quality factor. Due to the existence of this resonance, piezos are generally difficult to use for high-speed positioning applications.

Resistive (R) and resistive-inductive (RL) damping techniques have emerged as effective methods for minimizing electromechanical piezo resonances. Whereas piezos got several higher harmonic resonances, only the fundamental resonance is considered in most studies, because it is the strongest. The mechanical properties of piezos are well-known, but their corresponding properties in the electrical domain were less well understood because most studies follow mechanical resonance framework rather than electronic framework. Therefore, it was necessary to fill the gap between the passive-mechanical approaches and the less complete electronic treatment of piezo actuators by using a transfer function-based approach.

On this account, Dr. W. Merlijn van Spengen from Falco Systems and the Delft University of Technology has presented a comprehensive theory for describing the piezo actuator resonances using a resistor and resistor-inductor compensation techniques. The theory is based purely on an electronic model and the actual piezo displacements were described using an electrical-mechanical transformation. The work is currently published in the research journal, Sensors and Actuators A: Physical.

Dr. W. Merlijn van Spengen has shown that directly connecting piezo to a low impedance voltage source piezo driver results in a sharp and high mechanical resonance peak at the primary resonance frequency of the piezo. Thus, it is better to connect the piezo to its driver via a suitable coupling network comprising either a resistor (R) or a resistor and an inductor (RL). Calculating the piezo response as a function of frequency and coupling network, and considering the impact on the corresponding electromechanical damping, the basic features of the piezo system were analyzed. For high resistance damping a strong resonance at the anti-resonance frequency was found, but for resistance values in between these extremes, significant damping can be obtained. Regardless of the exact type of piezo used, the optimum series resistance was found to be Ω for Lead Zirconate Titanate piezo actuators.

The theory was validated via an interferometer-based optical displacement experiment to perform time- and frequency-domain measurements. A good fit for the mechanical and electrical behavior of the actual piezo actuator was obtained by using the new electromechanical damping theory. The presented theory accurately describes the resonance damping in both mechanical and electrical domains. Moreover, the existence of a resistance value which resulted in maximal damping of the piezo resonance was readily demonstrated. Furthermore, it was observed that series resistor values slightly less than the optimum value resulted in higher amplitude resonance than slightly higher series resistance values. Hence, using resistor values slightly larger than the calculated optimum value is recommended to achieve minimal electromechanical resonance in practice.

In summary, the theoretical and practical aspects of electromechanical damping of piezo actuator resonances are discussed in this new study using a transfer function-based approach. A comparison between the theoretical results and the experimental data has shown an excellent agreement in both the mechanical and electronic domain. The theoretical optimized damped response of piezo actuators can be obtained using a simple procedure. The findings also provide guidance for selecting the optimal electronic damping strategy for practical experiments involving piezo actuators. In a statement to Advances in Engineering, Dr. W. Merlijn van Spengen explained the study would contribute to the reduction of electromagnetic resonances of piezo actuator positioners. This expands their application scope by optimizing experiments in which high speed mechanical precision positioning is required.

Falco Systems (established in 2006) is an innovative company that designs and manufactures technology leading high voltage amplifiers for company R&D departments, research institutes and universities worldwide. These amplifiers are used in precision engineering, electronics, physics, optics, chemistry, (aero-)space engineering and metrology and control. In addition, Falco Systems supplies its amplifiers as sub-modules to OEMs.

The electromechanical damping of piezo actuator resonances: Theory and practice - Advances in Engineering

About the author

W. Merlijn van Spengen studied electrical engineering at the TU Eindhoven, The Netherlands, and earned a PhD in applied science from the KU Leuven, Belgium, while staying at the independent microelectronics research center IMEC. Here he developed models for microscale adhesion and the effect of dielectric charging on MEMS (micro-electromechanical systems) switches. Back in the Netherlands, he continued his research first at Leiden University and later as an associate professor at TU Delft, working on MEMS reliability and electronic measurement technology. He has received the prestigious Veni and Vidi grants.
Van Spengen is an experienced analog electronics design expert and founding director of the company Falco Systems. With his team at Falco Systems, he currently strives to provide the best high voltage amplifiers for driving piezo actuators and MEMS devices.


van Spengen, W. M. (2022). The electromechanical damping of piezo actuator resonances: Theory and practiceSensors And Actuators A: Physical, 333, 113300.

Go To Sensors And Actuators A: Physical

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