Aktivní vícerozměrné hltiče vibrací složitých mechanických konstrukcí založené na metodě zpožděného rezonátoru

Active multidimensional vibration absorbers for complex mechanical structures based on delayed resonator method

Project GACR 17-20943S supported by the Czech Science Foundation, GAČR

  • prof. Ing. Tomáš Vyhlídal, PhD. - project supervisor, Department of instrumentation and control engineering
  • prof. Ing. Zbyněk Šika, PhD. - project manager, Department of mechanics, biomechanics and mechatronics

The project focused on development of novel mechanical components – multidimensional active absorbers, based on the concept of delayed resonator. At the algorithmic side, the primary aim was to design robust algorithms for delayed resonator schemes for application in vibration suppression of complex multi-degree of freedom structures. A particular attention was paid to the optimised mechanical and mechatronic design of delayed resonator absorbers, particularly by relaxing the lumped parameter assumption or by considering their multiple deployment. The optimized design also included selection and distribution of sensors and actuators, depending on mechanical properties of both the proposed absorber and the structure. The final objective was a design of multi-degree of freedom delayed resonator absorber for multidimensional vibration suppression. In order to validate the proposed vibration suppression absorbers with delayed feedback, experimental demonstrators were developed. The proposed methods were also cross-compared with traditional vibration suppression methods.

Project results

Journal papers (WoS, published)

[1] Pilbauer, D., Vyhlídal, T. and Michiels, W., 2019. Optimized design of robust resonator with distributed time-delay. Journal of Sound and Vibration, 443, pp.576-590.
[2] Vyhlídal, T., Pilbauer, D., Alikoç, B. and Michiels, W., 2019. Analysis and design aspects of delayed resonator absorber with position, velocity or acceleration feedback. Journal of Sound and Vibration, 459, p.114831.
[3] Valášek, M., Olgac, N. and Neusser, Z., 2019. Real-time tunable single-degree of freedom, multiple-frequency vibration absorber. Mechanical Systems and Signal Processing, 133, p.106244.

Journal papers (WoS, in review)

[4] Kraus, K., Šika, Z., Beneš, P., Krivošej, J., Vyhlídal, T., (2020) Mechatronic Robot Arm With Active Vibration Absorbers, re-submitted after 1st review to Journal of Vibration and Control.
[5] Šika Z., Vyhlídal T., Neusser Z., 2020. Two dimensional delayed resonator for entire vibration absorption, submitted to Mechanical Systems and Signal Processing.
[6] Kuře M., Vyhlídal T., Boussada I., Michiels W., Bušek J., Niculescu, S.I. 2020. Assignment of double imaginary root in delayed resonator design - robustness and stability consequences, submitted to Automatica.

Journal papers (Others)

[7] Kraus K., Hlaváček V., Šika Z., Beneš P., *Dynamic Vibration Absorbers with Coupled Multiple Degrees of Freedom*, Bulletin of Applied Mechanics. 2017, 13(42), 7-10. ISSN 1801-1217

Proceedings papers

[8] Kuře, M., Vyhlídal, T., Michiels, W. and Boussaada, I., 2018. Spectral design of robust delayed resonator by double-root assignment. IFAC-PapersOnLine, 51(14), pp.72-77.
[9] Valášek, M., Olgac, M., Neusser, Z., 2019. Exploring Operational Frequency Ranges for Actively-Tuned Single-Mass, Multiple-Frequency Vibration Absorber. In 2019 Fifth Indian Control Conference (ICC), pp. 448-453. IEEE, 2019.
[10] Kučera, V., Fišer, J. and Vyhlídal, T., 2019. Double Deployment of Delayed Resonator in Active Vibration Suppression. IFAC-PapersOnLine, 52(18), pp.115-120.
[11] Šika, Z., Kraus, K., Beneš, P., Vyhlídal, T. and Valášek, M., 2018, June. Active Multidimensional Vibration Absorbers for Light Robots. In Proceedings of the 5th Joint International Conference on Multibody System Dynamics (pp. 1-12).
[12] Šika, Z., Kraus, K., Beneš, P., Krivošej, J., Vyhlídal, T., (2019). Mechatronic Robot Arm With Active Vibration Absorbers, IX ECCOMAS Thematic Conference on Smart Structures and Materials, SMART 2019, A. Benjeddou, N. Mechbal and J.F. Deü (Eds).
[13] Fenzi, L., Pilbauer, D., Michiels, W. and Vyhlidal, T., 2017. A probabilistic approach towards robust stability optimization, with application to vibration control. In Proceedings of the 9th European Nonlinear Dynamics Conference (pp. 1-10).
[14] Z. Šika, K. Kraus, J. Krivošej, P. Denk, Planar and spatial active resonator absorbers for robotics, 35th scientific conference COMPUTATIONAL MECHANICS 2019 (CM 2019), November 4 - 6, 2019, Šumava.
[15] Kraus, J. Z. Šika, LQR control of multi-DoF absorber for planar robots, 35th scientific conference COMPUTATIONAL MECHANICS 2019 (CM 2019), November 4 - 6, 2019, Šumava.

PhD Thesis

- Pilbauer D.,*Spectral methods in vibration suppression control systems with time delays*, PhD Thesis (double degree PhD with KU Leuven) co-supervised by T. Vyhlidal and W. Michiels, CTU in Prague, 2017.

Experimental verification of the results

1-DOF experimental demonstrator for active vibration absorption

A one dimensional (1DoF) vibration absorber demonstrator was designed and built for experimental validation of proposed vibration suppression algorithms. According to possible extensibility of the demonstrator a custom modular design was chosen and built. The demonstrator shown in Fig. 1 consists of a platform cart and attached active absorber. The platform is connected to the base with magnetic voice-coil providing both the excitation and platform control. Actuation of the absorber is performed by another voice-coil actuator. The acceleration of the absorber and position of the platform are measured and processed by NI CompactRIO, where also the control algorithms are embedded. The parameters of the set-up are given in Table 1. A model of the setup is presented in [6, 8] where a robust control algorithm using a double root assignment (drDR) is proposed and validated.


modular construction of the 1DoF vibration absorber demonstrator
Fig. 1: Modular construction of the 1DoF vibration absorber demonstrator

Tab. 1: Parameters of the 1DoF demonstrator
Component m [kg] c [kgs-1] k [kgs-2]
Absorber 0.520 1.9869 420.5754
Platform 1.100 4.7768 1472.2504
Sensor sensitivity [ms-2V-1] deviation [ms-2] sampling rate [Hz]
Accelerometer 24.74 ± 5 % g max. 2000
Inceremental position sensor step 0.025 mm


simulation and experimental results of the classic delayed resonator
Fig. 2: Simulation and experimental results of the classic delayed resonator

Example of active vibration suppression is shown in Fig. 2. The platform is excited by a periodic force with frequency ω=30.24 s-1. After switching on the active feedback at t=40 s, the platform vibration shown in the bottom subplot is entirely damped.

3-DOF experimental demonstrator for active vibration absorption

Experimental demonstrator of 3-DoF absorber has been built in order to experimentally verify functionality of active approaches [4,5]. It is designed for multi-DoF planar system to suppress vibration in two translational and one rotational direction. From various actuators the voice-coils are most suitable for the active absorbers because they have large range of stroke and almost zero inherent stiffness. Consequently, the modal properties of the absorber can be tuned not only by optimization of mass properties but also by tuning of stiffness of springs added in parallel to voice-coil actuators. Overall parameters of the absorber are summed in the Table 2. Its CAD design scheme, photograph and frequency characteristics are shown in Figure 3. The size of prepared demonstrators has been adapted to the available VCA AVM60-25 with 26 N stable force and 110 N peak force. The demonstrator is assembled from 3 mutually perpendicular legs, each of them created by 2 voice-coils.

Tab. 2: Parameters of 3DoF absorber
Parameter Value
Absorber mass 12 kg
Base eigenfrequencies 5-11 Hz
Stroke of the actuator 25 mm
Number of springs 16
Spring stiffness 3.6 Nmm-1


2D demonstrator for active vibration absorption
Fig. 3: The 2D demonstrator for active vibration absorption

6-DOF experimental demonstrator for active vibration absorption

Demonstrator of 6-DoF absorber has been built in order to experimentally verify functionality of active approaches. It is designed for multi-DoF spatial system to suppress vibration in all directions, hence, to suppress spatially complex modes. Overall parameters of the absorber are summed in the Table 3. CAD design scheme, photograph and frequency characteristics are shown in Figure 4. The demonstrator is assembled from 6 mutually perpendicular legs. Its mass center is lowered using inner mass structure. It is possible to add various masses in order to tune dynamical parameters of the passive absorber before implementation of the active approach.

Tab. 3: Parameters of 6DoF absorber
Parameter Value
Absorber mass 23 kg
Base eigenfrequencies 5-9 Hz
Stroke of the actuator 25 mm
Number of springs 24
Spring stiffness 3.6 Nmm-1


2D demonstrator for active vibration absorption
Fig. 4: The 3D demonstrator for active vibration absorption