通过研究脉冲密度反馈力对微机械陀螺性能的影响,设计了基于机电结合∑Δ调制器原理的微机械陀螺检测闭环电路。首先, 根据微机械陀螺敏感模态的等效形式, 分析得出脉冲密度反馈力对敏感模态的影响机理可以分为负刚度效应和增益效应两部分, 且负刚度效应与输入角速度无关。然后, 根据闭环检测理论建立了角速度和反馈脉冲密度之间的关系、量程与反馈脉冲高电平之间的关系。最后, 利用量程设计指标和实际微机械陀螺参数, 理论计算了所需的反馈脉冲高电平, 并在Simulink中进行了仿真。仿真结果表明, 所选参数满足了设计指标, 且在正交误差等效输入角速度为0、30和50(°)/s 3种情况下, 仿真得到平均脉冲密度和角速度之间的非线性分别为3.6×10-6、3.07%和5.12%。对正交误差等效输入角速度分别为30.4(°)/s和47.3(°)/s的I号陀螺和II号陀螺进行实验, 结果表明, 脉冲密度反馈力对负刚度的影响不随脉冲密度的变化而变化; 得到的平均脉冲密度和角速度之间的非线性分别为2.9%和4.8%, 实验与仿真结果符合得到较好。

The effect of Pulse Density Force Feedback (PDFF) on the performance of a micro-machined gyroscope was investigated and a closed-loop circuit for the micro-machined gyroscope was designed based on a mechanical and electrical ∑Δ modulator. Firstly, from the equivalent forms of a sense mode for the micro-machined gyroscope, the effect principle of PDFF on the performance of sense mode was analyzed and it was divided into two parts: negative stiffness and gain effects. The analysis shows that the negative stiffness is independent on the input of angular rate. Then, the relationship between pulse density and input angular rate, and that between input range and high level feedback pulse were built based on the theory of closed-loop detection. Finally, the circuit parameters were calculated by using the range design index and the actual parameters of gyroscope, then these parameters were simulated in Simulink. Simulation result shows that the parameters satisfy the design objective, and the nonlinearities between average pulse density and angular rate are 3.6×10-6, 3.07% and 5.12%, respectively, when the quadrature error equivalent input angular rates are 0(°)/s, 30(°)/s and 50(°)/s. Two gyro sample I and II with the quadrature error equivalent input angular rates of 30.4(°) /s and 47.3(°)/s were tested, and the experiment results show that the effect of PDFF on the negative stiffness doesn′t change with the pulse density; and the nonlinearities between the average pulse density and angular velocity are 2.9% and 4.8%, respectively. The experimental and simulation results get a better match.