采样控制系统中线性二次型最优控制器的设计

在计算机控制系统中,受控对象是连续的,相应的二次型性能指标函数也是连续函数,而控制器则由于计算机的参与而属离散型.本文给出了这种采样控制系统的线性二次型最优设计的一整套算法.计算的关键在于性能函数及对象模型的离散化.本文导出了离散化的公式及适合计算机计算的算法,同时也给出了用于采样周期加倍时的计算公式,从而保证了计算机可按该算法及相应的计算程序可靠地运行.最后举例说明了这套算法的应用.

Design of Linear Quadratic Optimal Controllers in Sampled-Data Control Systems

For a computer system, the process as well as the linear quadratic performance indexare time-continuous, but the controller is time-discrete. A set of algorithms for optimal design of sampled-data control system is given in this paper. The key problem for the computation lies in the discretization of the process model and the performance index. Formulas and algorithms for the discretization are developed. Besides, an interval doubling procedure for increasing reliability of the algorithms and the corresponding programs are introduced. Finally, an example is given to illustrate the application of such algorithms.