二维非稳态对流扩散边界控制问题的简化算法

A Reduced Algorithm for Two-Dimensional Unsteady Convective-Diffusion Boundary Control Problems

针对二维非稳态对流扩散边界控制问题计算量大的问题,提出了基于降阶模型的最优实时控制方法.利用POD(the Proper Orthogonal Decomposition)和奇异值分解以及Galerkin投影方法得到了具有高精度离散形式的状态空间降阶模型.在所得的降阶状态空间模型中,利用离散时间线性二次调节器方法设计出了最优控制器.对流-扩散过程的控制模拟结果说明了所提方法的有效性和准确性.

Boundary control of two-dimensional unsteady convection diffusion is a large-scale optimization problem, and an approach was presented for optimal control based on reduced-order model, which was derived from a discrete-time low-order state-space model with high accuracy by using POD(the Proper Orthogonal Decomposition), singular value decomposition (SVD)and Galerkin projection. Optimal controllers were designed based on the low-order state-space models using discrete-time linear quadratic regulator (LQR) techniques. The controlling simulation results in the convection-diffusion process illustrate the effectiveness and accuracy of the proposed method.