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大系统的模型最优简化的积分平方误差法,至今仅仅对输入函数为脉冲、幂函数和正弦函数时有效。本文首先指出,指数函数等一类函数输入时的高阶模型也能用积分平方误差法进行最优简化。其次证明,和原系统有相同输出意义的等价系统具有叠加性,从而把高阶模型的最优简化工作推广到相当广泛的范围。 正弦函数输入时高阶模型的最优简化模型是与角频率有关的。本文最后给出,当角频率有偏离时,其最优简化模型可以利用正弦输入函数的渐近展开式作相应的改变的结论。而且这种方法也适用于其它输入函数的参数偏离时的情形。
The large-scale model of the optimal system simplifies the integral square-error method, which has so far been valid only for input functions of impulses, power functions and sine functions. This paper first points out that high-order models such as exponential function can also be optimized by the integral square error method. Second, we prove that the equivalence system that has the same output meaning as the original system has superposition, so that the optimal simplification of higher order models is extended to a very wide range. The optimal simplified model of high-order model at sinusoidal input is related to the angular frequency. At the end of this paper, we conclude that the optimal simplified model can make the corresponding changes as the asymptotic expansion of the sinusoidal input function when the angular frequency deviates. And this method also applies when other parameters of the input function deviate from the situation.