Frequency method for determination self oscillations in control systems with a piezo actuator for astrophysical research

Abstract

For the control system with a piezo actuator in astrophysical research the condition for the existence of self-oscillations is determined. Frequency method for determination self-oscillations in control systems is applied. By using the harmonious linearization of hysteresis and Nyquist stability criterion the condition of the existence of self-oscillations is obtained. Keywords: frequency method, control system, piezoactuator, hysteresis, self-oscillations, astrophysical research

Introduction

A piezo actuator is used in astrophysics for image stabilization and scan system.1–19 Frequency method for determination self-oscillations in scan system is applied.20–46 for Nyquist stability criterion of self-oscillations at harmonious linearization of hysteresis characteristic of a piezo actuator.

Condition of self-oscillations

The scan system with a piezo actuator is used for astrophysical research in system adaptive optics. Nyquist stability criterion of self-oscillations at harmonious linearization of hysteresis characteristic2,20–40 of a piezo actuator has the form

Discussion

By using of frequency method the parameters of self-oscillations are obtained in the scan system. Nyquist stability criterion is used for calculation the self-oscillations in the control system with a piezo actuator at harmonious linearization of hysteresis characteristic of a piezo actuator.

Conclusion

For the scan system its condition of self-oscillations is determined. For calculation the self-oscillations frequency method is applied at harmonious linearization of hysteresis characteristic of a piezo actuator.

Acknowledgments

None.

Conflicts of interest

The authors declare that there is no conflict of interest.

References

1. Uchino K. Piezoelectric actuator and ultrasonic motors. Boston, MA: Kluwer Academic Publisher; 1997. 350 p.
2. Besekersky VA, Popov EP. Theory of automatic control systems. St. Petersburg: Professiya; 2003. 752 p.
3. Afonin SM. Absolute stability conditions for a system controlling the deformation of an elecromagnetoelastic transduser. Doklady Mathematics. 2006;74(3):943­­–948.
4. Bhushan B. Springer Handbook of Nanotechnology. New York: Springer; 2004. 1222 p.
5. Shevtsov SN, Soloviev AN, Parinov IA, et al. Piezoelectric actuators and generators for energy harvesting. Switzerland: Research and Development Springer; 2018. 182 p.
6. Afonin SM. Generalized parametric structural model of a compound elecromagnetoelastic transduser. Doklady Physics. 2005;50(2):77–82.
7. Afonin SM. Structural parametric model of a piezoelectric nanodisplacement transducer. Doklady Physics. 2008;53(3):137–143.
8. Afonin SM. Solution of the wave equation for the control of an elecromagnetoelastic transduser. Doklady Mathematics. 2006;73(2):307–313.
9. Afonin SM. Optimal control of a multilayer electroelastic engine with a longitudinal piezoeffect for nanomechatronics systems. Applied System Innovation. 2020;3(4):1–7.
10. Afonin SM. Coded сontrol of a sectional electroelastic engine for nanomechatronics systems. Applied System Innovation. 2021;4(3):1–11.
11. Afonin SM. Structural-parametric model of electromagnetoelastic actuator for nanomechanics. Actuators. 2018;7(1):1–9.
12. Afonin SM. Structural-parametric model and diagram of a multilayer electromagnetoelastic actuator for nanomechanics. Actuators. 2019;8(3):1–14.
13. Cady WG. Piezoelectricity: An introduction to the theory and applications of electromechancial phenomena in crystals. New York, London: McGraw-Hill Book Company; 1946. 806 p.