基于Taylor级数的分布参数系统最优控制

Optimal Control of Distributed Parameter Systems Via Taylor Series

结合钢坯加热过程讨论了分布参数系统的最优控制问题。针对钢坯加热过程,建立了分布参数系统的数学模型,利用Taylor级数近似变换,并引入Taylor级数基函数的微分运算矩阵和向量积矩阵,将钢坯温度的最优控制问题转化为相应集总参数系统的最优控制问题,然后对集总参数系统进行求解,并将求得的逼近解进行逆变换,即求得分布参数系统最优控制的逼近解。并通过仿真示例验证了该算法的有型,取得了满意的结果,为分布参数系统的控制算法提出了一条解决方案。

Based on the reheating process of the billet, the optimal control of distributed parameter system（DPS） is analysised. To the reheating of the billet, the mathematical model of the distributed parameter system is built. Using the the approximate of the Tayoloy series, and introducing the differential operational matrix and vector product operational matrix of the Taylor series, the computation of optimal temperature control for the billet is translated into that of lumped parameter systems（LPS）. The solution and the inversion of the solution are given to get the approximated solution of DPS. The simulation results show the effectiveness of the presented algorithm. The proposed method is a way to solve the optimal control problems of DPS.