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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。
In the computer control system, the controlled objects are continuous, the corresponding quadratic performance index function is also a continuous function, and the controller is discrete due to the participation of the computer. In this paper, a set of algorithms for linear quadratic optimal design of sampling control system is given. The key to the calculation is the discretization of the performance function and the object model. In this paper, we derive the formula of discretization and the algorithm which is suitable for computer calculation. At the same time, we also give the calculation formula for doubling the sampling period, which ensures that the computer can operate reliably according to the algorithm and the corresponding calculation program. The last example illustrates the application of this algorithm.