Wang Changhui, Gao Jinwu, Liang Mei
School of Electromechanical and Automotive Engineering, Yantai University, 32 Qingquan Road, Laishan District, 264005, Yantai, China.
Department of Control Science and Engineering, Jilin University, Changchun, China.
ISA Trans. 2018 Apr;75:64-75. doi: 10.1016/j.isatra.2018.02.012. Epub 2018 Feb 21.
In view of the relatively low computational load, look-up tables (or maps) are usually used to approximate nonlinear function or characterize operating-point-dependent system variables in typical embedded applications. Aiming at the problem of off-line identifying the look-up tables, a method based on the gradient algorithm is presented to estimate the look-up table parameters in this paper. The nonlinear function is approximated in terms of the piecewise linear interpolation model with the look-up table parameters, which can be rewritten as a dot product between the regression vector and unknown parameter vector using membership function. With the approximation error of the nonlinear function, a method for updating look-up tables using the gradient algorithm is given, and the relationship between the parameter estimation error and model approximation error is explicitly derived. To guarantee the convergence of the look-up table parameters estimation, a condition for the persistent excitation of the look-up table input is derived, which also provides a theoretical basis for the data characteristics of the look-up table input required to identify look-up table parameters offline using dynamic data. The validity of the proposed method is verified respectively by updating a one-dimensional (1D) look-up table, and the identification of the two-dimensional (2D) look-up table for the throttle discharge coefficient of a spark ignition gasoline engine form engine simulation tool enDYNA.
鉴于计算负载相对较低，在典型的嵌入式应用中，通常使用查找表（或映射）来近似非线性函数或表征与工作点相关的系统变量。针对离线识别查找表的问题，本文提出了一种基于梯度算法的方法来估计查找表参数。利用查找表参数，通过分段线性插值模型对非线性函数进行近似，使用隶属函数可将其重写为回归向量与未知参数向量之间的点积。基于非线性函数的近似误差，给出了一种使用梯度算法更新查找表的方法，并明确推导了参数估计误差与模型近似误差之间的关系。为保证查找表参数估计的收敛性，推导了查找表输入持续激励的条件，这也为使用动态数据离线识别查找表参数所需的查找表输入数据特性提供了理论依据。通过更新一维（1D）查找表以及对来自发动机仿真工具enDYNA的火花点火汽油发动机节气门流量系数的二维（2D）查找表进行识别，分别验证了所提方法的有效性。
