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本文通过分析控制系统的响应特性,提出了响应过程的‘截断——自磨光’模型。认为响应过程相当于截断输入信号中频率超出系统频带的Fourier级数项(或频谱),并且自动磨光所产生的Gibbs波动。系统对输入响应的速度,取决于它对该输入信号产生能量损耗的特征量——响应能耗。响应能耗依赖于系统频宽、输入信号的光滑程度、频谱结构及其对系统频带的分布。响应能耗越小,系统对该输入的响应就越快。按照系统对单位阶跃输入的响应能耗e与其过渡时间t_s的正比关系,本文把响应速度标值确定为:v=6π·e/1。并且求出,对周期输入:v_T=12|F_T(ω_b)|~2ω_b/(2k+1)(2k+3);对非周期输入:v =12|F(ω_b)|~2·ω_b/(2K+1)(2K+3)。根据响应速度指标[v]及给定输入,很容易决定需要的系统颁宽。
In this paper, by analyzing the response characteristics of the control system, the ‘truncation—self-polishing” model of the response process is proposed. It is considered that the response process is equivalent to truncating the Fourier series term (or frequency spectrum) whose frequency exceeds the system band in the input signal and automatically polishes Gibbs fluctuations. The speed of the system’s response to the input depends on the amount of energy it consumes in response to the input signal. The response energy consumption depends on the system bandwidth, the smoothness of the input signal, the spectrum structure, and its distribution to the system band. The smaller the response energy consumption, the faster the system responds to this input. According to the proportional relationship between the energy consumption e of the unit input to the unit step and its transition time t_s, the response speed indicator is determined as: v=6π·e/1. And find, for the cycle input: v_T=12|F_T(ω_b)|~2ω_b/(2k+1)(2k+3); for aperiodic input: v=12|F(ω_b)|~2·ω_b/ (2K+1)(2K+3). According to the response speed index [v] and the given input, it is easy to determine the required system widening.