六维加速度传感器动力学方程的矩阵解法

The Matrix Solution of Dynamical Equations of Six-axis Accelerometer

并联式六维加速度传感器动力学方程的强耦合、非线性,给加速度六分量实时、稳定、精确的解耦带来困难。通过引入辅助角速度,系统的欧拉动力学方程由二阶非线性微分方程组化简为一阶线性非定常微分方程组。通过两次利用矩阵解法来分别获得载体辅助角速度和姿态四元数的数值解,从而求解出载体的角运动参量。将角运动参量代入系统牛顿动力学方程中可获取载体的线运动参量,继而实现了加速度六分量的完全解耦。动力学仿真试验表明,在5s内,利用矩阵解法获得的线加速度及角加速度误差分别在0.2%和0.1%以内,充分说明了所推导矩阵解法的正确性及有效性。

The strong coupling,nonlinear dynamical equations of the parallel type six-axis accelerometer have brought great difficulties to decouple six acceleration components timely,stably and accurately.By introducing an auxiliary angular velocity,the Euler dynamical differential equations were transferred from second-order nonlinear ones into first-order linear unsteady ones.The numerical results of the carrier′s angular velocity and attitude matrix were separately acquired by use of matrix solution twice,then,the angular motion parameters were solved.The linear motion parameters can be obtained by taking angular motion parameters into Newton dynamical equations,thus,the six-axis acceleration components was completely decoupled.The dynamical simulation test shows that in 5s,using matrix solution to decouple dynamical equations,the maximum fiducial errors of all three linear acceleration and three angular acceleration components were less than 0.2% and 0.1%,respectively,which has fully illustrated the correctness and efficiency of the matrix solution method deprived in this paper.