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第47行： − 自振荡表现为动力系统静态平衡的线性不稳定性。可用于判断这种不稳定性的两个数学检验方法是劳斯-赫尔维茨准则和奈奎斯特准则。不稳定系统振动的振幅随时间呈指数增长(例如负阻尼下的小振荡)，直到非线性变得重要并限制振幅。这可以产生一个稳定和持续的振荡。在某些情况下，自激振荡可以看作是闭环系统中时滞的结果，这使得变量 x<sub>t</sub> 的变化依赖于变量x<sub>t-1</sub> 的早期估值。+
→Mathematical basis 数学基础
Self-oscillation is manifested as a linear instability of a dynamical system's static equilibrium. Two mathematical tests that can be used to diagnose such an instability are the Routh–Hurwitz and Nyquist criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude. This can produce a steady and sustained oscillation. In some cases, self-oscillation can be seen as resulting from a time lag in a closed loop system, which makes the change in variable x<sub>t</sub> dependent on the variable x<sub>t-1</sub> evaluated at an earlier time.
Self-oscillation is manifested as a linear instability of a dynamical system's static equilibrium. Two mathematical tests that can be used to diagnose such an instability are the Routh–Hurwitz and Nyquist criteria. The amplitude of the oscillation of an unstable system grows exponentially with time (i.e., small oscillations are negatively damped), until nonlinearities become important and limit the amplitude. This can produce a steady and sustained oscillation. In some cases, self-oscillation can be seen as resulting from a time lag in a closed loop system, which makes the change in variable x<sub>t</sub> dependent on the variable x<sub>t-1</sub> evaluated at an earlier time.
自振荡表现为动力系统静态平衡的线性不稳定性。可用劳斯-赫尔维茨准则和奈奎斯特准则这两个两个数学检验方法来判断这种不稳定性的。不稳定系统振动的振幅随时间呈指数增长(例如负阻尼下的小振荡)，直到非线性变得重要并限制振幅。这可以产生一个稳定和持续的振荡。在某些情况下，自激振荡可以看作是闭环系统中时滞的结果，这使得变量 x<sub>t</sub> 的变化依赖于变量x<sub>t-1</sub> 的早期估值。
==Examples in engineering 工程中的例子==
==Examples in engineering 工程中的例子==