并联式六维加速度传感器的解耦参数辨识及其扰动分析
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摘要
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。
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.
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.
引文
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[2]ROBIN B L.Measuring and managing workplace whole-body vibration exposures[J].Acoustics Australia,2016,44(1):129-135.
[3]EMELYANTSEV G I,BLAZHNOV B A,DRANITSYNA EV,et al.Calibration of a precision SINS IMU and construction of IMU-bound orthogonal frame[J].Gyroscopy and Navigation,2016,7(3):205-213.
[4]FU J,JIANG S,QIN F J,et al.Novel piecewise compensation method for FOG temperature error[J].Journal of Chinese Inertial Technology,2016,24(2):242-244.
[5]WANG D H,YUAN G.A six degree of freedom acceleration sensing method based on six coplanar single axis accelerometers[J].IEEE Transactions on Instrumentation and Measurement,2011,60(4):1433-1442.
[6]ZOU T,NI F L,GUO C Q,et al.6-DOF acceleration sensor with cylindrical configuration[J].Sensors and Actuators,2016,(251):167-178.
[7]任磊,杜建邦,王美娥.旋转惯导中加速度计尺寸效应误差分析及补偿[J].航空学报,2013,34(6):1424-1435.REN Lei,DU Jianbang,WANG Mei’e.Error analysis and compensation of size effect in INS with IMU rotation[J].Acta Aeronautica et Astronautica Sinica,2013,34(6):1424-1435.
[8]SONG J W,PARK C G.Optimal configuration of redundant inertial sensors considering lever arm effect[J].IEEESensors Journal,2016,16(9):3171-3180.
[9]SUN Z B,LIU J H,YU C Z,et al.A small range six-axis accelerometer designed with high sensitivity DCB elastic element[J].Sensors,2016,16(1552):1-17.
[10]尤晶晶,李成刚,左飞尧,等.六维加速度传感器的研究现状及发展趋势[J].振动与冲击,2015,34(11):150-160.YOU Jingjing,LI Chenggang,ZUO Feiyao,et al.Current studying status and developing trend of six-axis accelerometers[J].Journal of Vibration and Shock,2015,34(11):150-160.
[11]尤晶晶,李成刚,吴洪涛,等.预紧式并联六维加速度传感器的解耦算法研究[J].仪器仪表学报,2017,38(5):1216-1225.YOU Jingjing,LI Chenggang,WU Hongtao,et al.Research on the decoupling algorithm of pre-stressed parallel six-axis accelerometer[J].Chinese Journal of Scientific Instrument,2017,38(5):1216-1225.
[12]尤晶晶,李成刚,吴洪涛.并联式六维加速度传感器的哈密顿动力学研究[J].机械工程学报,2012,48(15):9-17.YOU Jingjing,LI Chenggang,WU Hongtao.Research on Hamiltonian dynamics of parallel type six-axis accelerometer[J].Journal of Mechanical Engineering,2012,48(15):9-17.
[13]尤晶晶.基于冗余并联机构的压电式六维加速度传感器研究[D].南京:南京航空航天大学,2013.
[14]刘俊,杜晶晶,吕华溢.垫圈式压电六维力传感器的安装动态特性[J].光学精密工程,2015,23(10):279-285.LIU Jun,DU Jingjing,LHuayi.Mounted dynamic characteristics of washer type piezoelectric six-axis force sensors[J].Optics and Precision Engineering,2015,23(10):279-285.