Autonomous Oscillation Control Loop Design for Amplitude Controlled, Frequency Read-Out-Type Resonant Sensors

This paper suggests an autonomous oscillation control loop for frequency read-out-type resonant sensors that produces outputs of variable frequency depending on the input of an external physical quantity. The design goal of the oscillation loop is simultaneously to stabilize the resonance characteristics of the sensor and to automatically track the resonant frequency in order to guarantee highly reliable sensor performance. To this end, the concept of automatic gain control (AGC) is applied so that the loop is designed to maintain the oscillation amplitude as one control objective. The second control objective is to achieve resonance condition tracking even when external influences such as disturbance and noise exist. For the verification of the proposed control loop design, an example resonant sensor system is modeled, and a control loop and controller that accompany the system are also designed. Finally, the proposed loop performance was demonstrated via simulations which consider practical noise elements. The theoretical results were further verified via sensor's transient responses and noise analysis.

I. Introduction

Sensors that measure input amounts indirectly through resonant frequency variation of a dynamic system, which is driven by the physical input, are collectively referred to as frequency readout-type resonant sensors. Implementation of a resonant sensor essentially necessitates the use of a self-sustained oscillation loop that can either maintain or track oscillation amplitude and resonant frequency, which inherently serves as inertial energy conversion coefficients to characterize vibration systems [1]–[3], [6]–[8], [13], [14]. A suitable candidate to implement this kind of oscillation system is a loop construction based on the basic operation of a high-precision oscillator circuit that is often used in conventional electric oscillator circuits or quartz vibrators [9], [10]. The oscillator circuit based on conventional electric oscillators typically takes the configuration of LC tuned resonance system. As such, they usually require an external reference oscillator such as quartz. While these reference-based oscillator circuits have relatively high-frequency reliability, it is quite difficult to realize additional functions that can actively control a dynamically tuned resonance status over an input range required by the electromechanical sensors of interest. Implementing resonance sensors using a single feedback loop is another method that can be used [2], [3], [15]. In this case, the feedback loop is implemented by combining hard nonlinearity components, i.e., a limiter cascaded by a variable phase shifter. A self-sustained loop structure that has the addressed single feedback connection can be applied to a resonant sensor system employing a relatively high quality factor, and results in an easily achieved oscillation status. However, due to the resonator's nonlinear dynamics and underlying phase and amplitude noise, the single-loop approach cannot guarantee an oscillation equilibrium with a fixed amplitude. This in turn may induce the nonlinearity and phase noise which will degrade overall oscillator system performance. This turns out to be a critical disadvantage when performing repeatability tests under varied initial conditions or between different samples manufactured via the same process, since the repeatability performance is subject to mechanical parameter variations.