The derivative is basically the slope of the line or the tangent at the instantaneous point. So imagine the case where you have just a PI controller. As the I portion causes the response to overshoot (an inherent property of any 2nd order system)the slope of the line increases, the derivative section starts to output a correction signal thats proportional to the slope. The increased output causes the system to track faster. So this means that when the system needs to respond quickly the D section kicks in, when the output needs to move slow the D section doesn't provide any output. The I section is rather slow to respond so the larger its portion of the correction the slower the system will be to change, because the D section is helping the system to track faster there is no overshoot as the I section doesn't build up.
The trouble with a derivative section is best proven by example, lets say out input is a sin wave
x(t) = Asin(wt)
where A is the amplitude and w is the angular frequency (related to frequency by 2*pi). If we take the derivative we get
x'(t) = Awcos(wt)
Notice the angular frequency (w) is now part of the amplitude ! This means that higher the frequency of the signal the larger the output. Any real world signal is composed of the desired signal and unwanted noise. This noise consists of a white noise signal which contains energy at all frequencies . Even the smallest high ferquency noise will produce a LARGE output on the D section which will cause the wanted output to be saturated. This requires careful design to limit the input frequency to the D section as well as trading off its advantages to remain on the safe side.
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Spreading capibara awareness since 2006
