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本文介绍了奇异摄动法在线性控制系统中的应用。利用这一方法可以将一个高阶系统的求解分为两个低阶系统分别求解问题,这样既可降低求解的系统阶次,又能克服系统方程组的刚性,从而大大减小计算量。因此它可用于控制系统的分析、综合和设计。文中对多重时间尺度模型、线性奇异摄动模型、利用逆变换的奇异摄动法、稳定性、可控性和可观测性、最佳线性调节器及最优线性控制等问题作了阐述。
This paper introduces the application of singular perturbation method in linear control system. By using this method, the solution of a higher-order system can be divided into two lower-order systems to solve the problems respectively, which can not only reduce the order of the system to be solved but also overcome the rigidity of the system of equations, thereby greatly reducing the computational cost. It can therefore be used for control system analysis, synthesis and design. In this paper, multiple time-scale models, linear singular perturbation models, singular perturbation methods using inverse transformation, stability, controllability and observability, optimal linear regulators and optimal linear control are described.