并联式六维加速度传感器的解耦参数辨识及其扰动分析

针对并联式六维加速度传感器的强非线性耦合特性，从解耦方程出发，构建了一种能够适应不确定性扰动的参数辨识模型。通过输入项的坐标反变换，得到了输入、输出项在载体系内的线性映射，据此提炼出13个参数项。定义并计算参数项对输入项的影响系数矩阵,确定了两者之间的敏感性以及参数项的优化依据。通过参数分离和运动分解，构造了3个稳定的辨识方程，据此提出一种参数辨识算法。运用算子范数理论剖析辨识方程自身的性态，揭示出，影响辨识误差的关键要素为输入矩阵的条件数，故理论上存在最优输入项。辨识结果与仿真数据吻合得较好，表现为，当外界扰动不超过1%时，参数误差小于0.88%。实验室条件下，参数辨识后的传感器样机在1分钟内的测量误差为8.42%，基本满足工作要求。
Abstract：The parameter identification of the six-axis accelerometer is a difficult problem due to its higher input and output volumes and strongly coupled dynamic equations.According to this, starting with decoupling equations, a method of parameter identification was proposed, which can adapt to uncertain disturbances.By inverse transforming the coordinates of input items and combining with compatibility equations, the mapping relations between input and output items were established, and then the 13 parameter items were obtained.By defining and calculating the influence coefficient matrix, sensitive properties between input items and parameter items were derived.By separating parameters and selecting special motion models, 3 identification equations were derived, and then an identification algorithm was established.Based on the theories of operator norm, qualitative behavior of identification equations was analyzed.Research results indicate that the identification errors depend on the condition number of input matrix.Hereby, the general formula of optimal input was derived.The verification experiments show that the mathematical results are well consistent with the experimental data, and when the random disturbances are less than 1%, the maximum identification error is less than 0.88%; Further more, based on the identification value of real physical prototype, the composite error within a minute is 8.42% in the laboratory.