自动门
自动门:非线性微分方程的线性化
发布时间:2014/4/21
自动门讯:
非线性微分方程的线性化
    严格地说,实际物理元件或系统都是非线性的。例如,弹簧的刚度与其形变有关系,因
   此弹簧系数K实际上是其位移上的函数,并非
常值}电阻、电容、电感等参数值与周围环境(温
度、湿度、压力等)及流经它们的电流有关,也并
非常值I电动机本身的牵擦、死区等非线性因素
会使其运动方程复杂化而成为非线性方程。当
然,在一定条件下,为了简化数学模型,可以忽
略它们的影响,将这些元件视为线性元件,这就
是通常使用的一种线性化方法。此外,还有一种
线性化方法,称为切线法或小偏差法,这种线性
化方法特别适合于具有连续变化的非线性特性
函数,其实质是在一个很小的范围内,将非线性特性用一段直线来代替。
   这种小偏差线性化方法对于控制系统大多数工作状态是可行的。事实上,自动控制系
统在正常情况下都处于一个稳定的工作状态,即平衡状态,这时被控量与期望值保持一
致,控制系统也不进行控制动作。一旦被控量偏离期望值产生偏差时,控制系统便开始控
制动作,以便减小或消除这个偏差,因此,控制系统中被控量的偏差一般不会很大,只是
“小偏差”。在建立控制系统的数学模型时,通常是将系统的稳定工作状态作为起始状态,
仅仅研究小偏差的运动情况,也就是只研究相对于平衡状态下,系统输入量和输出量的运
动特性,这正是增量线性化方程所描述的系统特性。
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