基于小波基的非线性抛物型系统模型预测控制

摘要

针对一类由非线性抛物型描述的分布参数系统，研究了一种基于小波分解的模型降阶和预测控制方法。利用小波配点方法，分别将一阶和二阶空间偏导数投影到拟Shannon小波基上，不需要求解系统的主导极点，得到系统的低阶常微分方程逼近模型；采用前向Eular方法离散化时间变量，将得到的差分方程组模型作为系统的预测模型，选择标准二次优化性能指标，设计相应的非线性预测控制器；将此方法应用到由一个放置在反应器中的细长催化棒组成的传输-反应系统的温度场控制问题中，取得了满意的控制效果。%For a class of nonlinear parabolic distributed parameter systems, model reduction and predic-tive control method were investigated. First, the first order and second order spatial partial derivative were projected to quasi-Shannon wavelet using wavelet collocation method respectively, eliminating the need of knowledge of solution of dominant pole of the system. The correspondent lower order model was obtained. A group of ordinary differential equations obtained through Eular’ s discretizing time variable was selected as the predictive model of the system, standard quadratic optimization performance index was selected, and the corresponding nonlinear predictive controller was designed. This method was applied to the transfer-reaction system of catalytic rod, and simulation results indicate that the proposed method meets the requirements of system control.