PID controller with filtered derivative

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＜premise knowledge＞
　・PID controller
　・High pass filter
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■What is filtered derivative?

A filtered derivative is a process in which a low-pass filter is added to the differentiator, and it is used to suppress a sudden change (called a kick) in the output due to the derivative term of PID control. The transfer function is as follows. The filtered derivative is also used for highpass filters.

■PID control without filtered derivative

The following is an example of PID control of a controlled object with characteristics of dead time + first-order lag.

＜Controlled object parameters＞
　Dead time L=0.2s、Time constant T=1s、Gain=1

＜PID gain＞
　Kp = 4.75 , Ki = 3.5 , Kd = 0.447



As shown below, the behavior of the object to be controlled is distorted, and it can be seen that this is due to the influence of the differentiator.


＜Differentiator output result＞

■PID control with filtered derivative御

Replace the normal differentiator with a filtered derivative as follows.


The simulation results are as follows. The time constant t is set to 0.03 to eliminate noise, so it doesn't have to be a very large value. The distorted shape has settled, but there is a slight overshoot.



Therefore, Kd is set to a smaller value of 0.3. Overshoot has also been reduced.

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