分布参数系统的时空ARX建模及预测控制

本文针对一类可由抛物型偏微分方程描述的分布参数系统,研究了一种基于输入输出数据的建模与控制方法.首先利用Karhunen-Loève（K-L）分解提取系统的一组主导空间基函数,并以此对系统输出进行时空分解,随后由时空分解得到的时间系数部分以及系统激励构成输入输出信息,利用最小二乘法辨识出时域ARX模型,最后针对该模型设计了广义预测控制器.仿真结果表明,上述控制方法能够对分布参数系统取得良好的控制效果.

Time-space ARX modeling and predictive control for distributed parameter system

For a class of distributed parameter systems described by parabolic partial differential equations (PDEs), we investigate their modeling and control by using the input-output data. Based on the characteristics of parabolic PDEs, the Karhunen-Loève (K-L) decomposition method is applied to extract the dominant spatial basis functions of the system, which is in turn employed for executing the time-space decomposition. After the time-space decomposition, a temporal auto-regresive model with external input (ARX) model is identified by using the temporal coefficients obtained from the decomposition along with the excitation input signal. A generalized predictive controller is developed based on this ARX model. Simulation results show that this control method results in desirable performances for a distributed parameter system.