Abstract
At present, resonator sensors with an auto-oscillating system have a number of advantages in comparison with the known sensors with frequency output. In this case, developed auto-oscillating systems of resonator sensors are very specific; their elements are oriented toward a particular type of resonator and possess a certain degree of nonlinearity, which makes studying and modeling such systems impossible. In the present work, analytical expressions were obtained for the reduction of parameters of mechanical systems of resonators to the lumped ones. This allowed us to apply the methods of research into nonlinear systems of control to the analysis of AOS and to receive the expression of transfer function of nonlinear resonator with consideration to the nonisochronicity. A structure of auto-oscillating system with a nonlinear resonator is devised, which was not explored earlier. With the purpose of selecting the character of nonlinearity in the elements of feedback and mechanical resonator of the assigned type in AOS to warrant the assigned stability of frequency and amplitude of auto-oscillations, we performed imitation simulation in the Matlab Simulink programming environment. The simulation demonstrated that a nonlinear amplifier at work with a nonlinear mechanical resonator provide for the auto-oscillating system that is stable by frequency and amplitude. Thus, auto-oscillating system of the devised structure can be used in the design of vibration frequency sensors.
Highlights
At the present stage of development of measurement equipment, accuracy of reproduction of the frequency standard is the highest in comparison with the standards of other physical magnitudes
Resonator sensors with AOS possess a number of advantages [2]: – high quality factor of resonators makes it possible to substantially increase precision characteristics of sensors; – there is a possibility to introduce a self-excited oscillator to the circuit for obtaining continuous output signal; – signal to noise ratio is considerably higher than in the sensors of other groups given above
A problem of the generalized analysis of auto-oscillating systems with different types of mechanical resonators is crucial when selecting the type of resonator and the characteristics of positive feedback circuits
Summary
At the present stage of development of measurement equipment, accuracy of reproduction of the frequency standard is the highest in comparison with the standards of other physical magnitudes. By the type of physical phenomenon that underlies their operating principle, all sensors with frequency output can be divided into four groups:. Resonator sensors with AOS possess a number of advantages [2]: – high quality factor of resonators makes it possible to substantially increase precision characteristics of sensors; – there is a possibility to introduce a self-excited oscillator to the circuit for obtaining continuous output signal; – signal to noise ratio is considerably higher than in the sensors of other groups given above. The auto-oscillating systems of resonator sensors already developed are oriented toward a particular type of resonator [2]. A problem of the generalized analysis of auto-oscillating systems with different types of mechanical resonators is crucial when selecting the type of resonator and the characteristics of positive feedback circuits
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