鲁棒性和最坏情况分析- MATLAB & Simulink - MathWorks Australia - 万博1manbetx,s manbetx 845,万博尤文图斯

鲁棒性和最坏情况分析

In robust control design, performance is expressed and measured in terms of the peak gain (theH_∞系统的规范或峰值奇异值）。该增益越小，系统性能越好。名义上稳定的不确定系统的性能通常会随着不确定性的增加而降低。使用鲁棒性分析和最坏情况分析来检查系统中的不确定性量如何影响系统的稳定性和峰值增益。

Robustness Analysis

鲁棒性分析是关于找到与稳定性或给定性能水平兼容的最大不确定性量。下图显示了性能和鲁棒性之间的典型权衡曲线。在这里，峰值增益（Bode图上的峰值幅度或单数值图上的峰值）表征了系统性能。

Plot showing normalized uncertainty amount on the x-axis and peak closed-loop gain (performance) on the y-axis. The system performance-degradation curve begins at x=0, y=1, at the nominal system gain of 1. The curve increases to the right, going asymptotically to infinity at around y = 2.3. This value is the robust stability margin, the uncertainty amount at which the system becomes unstable.

Thex-axis quantifies the normalized amount of uncertainty. The valuex= 1 corresponds to the uncertainty ranges specified in the model.x= 2表示不确定性两倍的系统。x= 0对应于标称系统。（看actual2normalized有关标准化不确定性范围的更多详细信息。）y-axis is performance, measured as the peak gain of some closed-loop transfer function. For instance, if the closed-loop transfer function measures the sensitivity of an error signal to some disturbance, then higher peak gain corresponds to poorer disturbance rejection.

When all uncertain elements are set to their nominal values (x= 0), the gain of the system is its nominal value. In the figure, the nominal system gain is about 1. As the range of values that the uncertain elements can take increases, the peak gain over the uncertainty range increases. The heavy blue line represents the peak gain, and is called thesystem performance degradation curve。It increases monotonically as a function of the uncertainty amount.

Robust Stability Margin

The system performance degradation curve typically has a vertical asymptote corresponding to therobust stability margin。该边距是系统可以耐受的最大不确定性，同时保持稳定。对于上一个插图的系统，峰值增益在周围无限x= 2.3。换句话说，当不确定性范围是模型中指定的2.3倍（以归一化设备）中指定时，系统就会变得不稳定。因此，稳健的稳定性边缘为2.3。要计算不确定系统模型的稳健稳定余量，请使用robstab函数。

Robust Performance Margin

Therobust performance margin为了给定的收益γ, is the maximum amount of uncertainty the system can tolerate while having a peak gain less thanγ。For example, in the following illustration, suppose that you want to keep the peak closed-loop gain below 1.8. For that peak gain, the robust performance margin is about 1.7. This value means that the peak gain of the system remains below 1.8 as long as the uncertainty remains within 1.7 times the specified uncertainty (in normalized units).

Plot showing the system performance-degradation curve with the normalized uncertainty amount on the x-axis and peak closed-loop gain (performance) on the y-axis. The plot shows that the peak gain reaches 1.8 when the normalized uncertainty is 1.7 times the specified uncertainty.

To compute the robust performance margin for an uncertain system model, use therobgain函数。

最差的增益度量

The最差的收益是峰值增益可以超过特定不确定性范围的最大值。该值是强大的性能余量的对应物。尽管稳健的性能保证金可以测量与特定峰值增益水平兼容的最大不确定性量，但最差的案例增益量衡量与特定不确定性量相关的最大增益。例如，在下面的例证中，模型中指定的不确定性数量的最差案例增益约为1.20。如果这种不确定性量加倍，最差的案例增益将增加到2.5。

Plot showing the system performance-degradation curve with the normalized uncertainty amount on the x-axis and peak closed-loop gain (performance) on the y-axis. The plot shows that at the specified uncertainty (x = 1), the worst-case gain is about 1.2, and at 2 times the specified uncertainty, the worst-case gain is about 2.5.

要计算不确定系统模型的最坏情况增益，请使用wcgain函数。TheULeveloption of thewcOptionscommand lets you compute the worst-case gain for different amounts of uncertainty.