无稳态非线性系统线性变参数模型辨识

Linear Parameter Varying Model Identification of Nonlinear Systems Without Steady State

针对无稳态非线性系统,提出2种线性变参数(linear parameter varying,LPV)模型辨识方法.对于线性权重LPV模型,结合高斯牛顿法和最小二乘法对局部线性模型的参数寻优;对于高斯权重LPV模型,采用Narendra-Gallman算法并根据参数与优化目标之间的关系,将参数分为线性部分和非线性部分并进行交替迭代.通过对循环流化床锅炉实际工业系统的建模结果和实测结果对比验证了所提算法的有效性.与带稳态LPV模型相比,3个主要输出蒸汽压力、蒸汽温度和炉膛温度均获得较好的输出拟合效果,最优匹配率分别提高52.8%,21.1%和32.2%以上.验证了所提算法在复杂工业非线性对象建模上的有效性和实用性.

Two kinds of identification methods of the linear parameter varying（LPV）models for the nonlinear systems without steady states are both proposed in this paper.For the LPV model with linear weights,because parameters only exist in the local linear models,Gauss-Newton method and least square method are combined to estimate all parameters.For the LPV model with Gaussian weights,parameters exist in both weighting functions and local linear models.Narendra-Gallman method is used to estimate parameters.In the method,all parameters are divided into linear and nonlinear parts according to the relationship between them and optimization objectives.Then these two parts are estimated using the alternating iterative method.The proposed algorithm is validated by identifying an industrial circulation fluidized bed boiler.The outputs of the LPV model and real process of three main outputs：steam pressure,steam temperature and furnace temperature are analyzed and compared.Best fittings of these outputs are increased by 52.8%,21.1% and 32.2% respectively,confirming the validity and practicability of the algorithm in the identification field of complex nonlinear industrial processes.