论文标题
非理性系统的Bode积分限制
Bode Integral Limitation For Irrational Systems
论文作者
论文摘要
敏感性和敏感性函数的Bode积分以及互补的灵敏度和互补灵敏度样函数通常用于描述反馈控制系统的性能限制。在本文中，我们研究了Bode积分，并评估当反馈控制系统中使用了分数顺序成比例衍生（PID）控制器时会发生什么。我们将分析扩展到何时将分形PID控制器应用于非理性系统。我们将其分为两种情况：当无限多个右半平面开放环杆的序列没有任何限制点以及何时具有限制点时。在这两种情况下，我们都证明，在某些收敛条件下，Bode积分的结构与经典版本相似。我们还为控制器提供了足够的条件，可以降低Bode灵敏度的积分。
Bode integrals of sensitivity and sensitivity-like functions along with complementary sensitivity and complementary sensitivity-like functions are conventionally used for describing performance limitations of a feedback control system. In this paper, we investigate the Bode integral and evaluate what happens when a fractional order Proportional-Integral-Derivative (PID) controller is used in a feedback control system. We extend our analysis to when fractal PID controllers are applied to irrational systems. We split this into two cases: when the sequence of infinitely many right half plane open-loop poles doesn't have any limit points and when it does have a limit point. In both cases, we prove that the structure of the Bode Integral is similar to the classical version under certain conditions of convergence. We also provide a sufficient condition for the controller to lower the Bode sensitivity integral.
