Design and analysis of nonlinear feedback loop for a resonant accelerometer

A nonlinear feedback system is designed and analyzed for a surface micromachined resonant accelerometer. For this, a brief illustration of the plant dynamics is given. In the analysis, the periodic signal in the nonlinear feedback loop is obtained by the limit cycle point, which is best approximated via the describing function method. This approach is reasonable in that the describing function method gives the optimal quasi-linearization for a sinusoidal input under an adequate filtering condition. In the sequel, it is possible that the nonlinearity form in the loop is determined by the graphical analysis in complex plane. Considering the characteristic feature of plant dynamics, a simple phase shifted relay with finite slope is found for the nonlinearity implementation. Also is concisely illustrated the stability of limit cycle. Finally, simulation and experimental result is given to show the properness of the designed loop.