Introduction to lead/lag compensator
首先，compensator和controller有啥区别？
其实没有明确的界限，两者差不多。不必为这这个概念纠结
我找了一下关于这个问题一些人的看法，其中有很“流行”的解说
Here is an excerpt from "G. Ellis, Control System Design Guide":
"Compensators are specialized filters ...designed to provide a specific gain and phase shift, usually at one frequency. The effects on gain and phase either above or below that frequency are secondary."
My opinion: There is no clear threshold between "compensators" and "controllers".
Some authors use one or the other term (or mixed). Am I wrong?
To be more precise: I think, each compensator (P, I, PI, PID) can be regarded as a controller - but not vice versa. The bang-bang controller certainly is not a compensator.
Jul 16, 2013"Compensators are specialized filters ...designed to provide a specific gain and phase shift, usually at one frequency. The effects on gain and phase either above or below that frequency are secondary."
My opinion: There is no clear threshold between "compensators" and "controllers".
Some authors use one or the other term (or mixed). Am I wrong?
To be more precise: I think, each compensator (P, I, PI, PID) can be regarded as a controller - but not vice versa. The bang-bang controller certainly is not a compensator.
没有明确的界限，有些作者同时使用这两个名词。
什么叫相位超前。图中的黄色的正弦函数就比蓝色的余弦函数要超前90°
微分控制器s，就是超前相位调节90度
对于滞后矫正，积分作用就是个例子。极点，1/s，相位滞后90度
compensator的形式都是一样的
超前还是滞后取决于Wp和Wz的相对大小
对于超前校正，如图，Wz < Wp 于是第一幅图的绿线比黄线的转折点更靠近原点，相加合成后变成红线。
值得注意的是，此时红线比绿线和黄线位于高频段的增益大幅减少，可以有效的抑制高频噪声！多么爽啊！抑制了高频噪声！
当零点比极点靠近原点的时候，波特图的如下图
当把零点移动靠近极点，但还是保持零点在极点右侧的情况，可以发现，相位超前的频带减小了，增益开始非零的地方右移了
如果零点和极点重合呢？
如果把零点移动到极点的左侧，就是滞后矫正了
Lake Tahoe