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All Filters. What's The Difference?
Sep 06, 2018

Filters are widely used in communication and control systems. They can be used to eliminate noise, interference, aliasing of frequency components, or to attenuate resonance at certain frequency points. In the control system, many methods and concepts are borrowed from the communication system. For example, the widely used PWM technology in the industrial control field originates from the communication field. Not to mention the technology of filters. However, the direct differences between them should be clearly understood. If you take a low pass filter, do you just set the cutoff frequency, and nothing else? Such methods of use, either do not give full play to their characteristics, or may have adverse effects on the system.

At present, the discussion of filters, including textbooks, literature, BBS, etc., is mostly for the application in communication systems. Therefore, the indexes that people are concerned about are the signal distortion, attenuation, power damage and delay characteristics caused by filters.

In the control system, it is difficult to find the practical significance of the above characteristics, and the signal features are significantly different from many applications in the communication system, that is, the frequency is often relatively low, usually only a few hundred or even dozens of Hz, and the high case is only a few thousand Hz. For example, even in A high performance motor speed control system, the current inner loop bandwidth of the closed-loop often can only reach 1 KHZ, so in these applications, in addition to the A/D anti aliasing filter at the input, the other filter cutoff frequency is basically no more than 1 KHZ (more than there is no practical significance, because the system of higher frequency signal is small, low bandwidth of system itself makes it look like A low pass filter).

In the control system, the most used is the low pass filter. The filtering effect of low pass filter is no doubt, but its negative effect on control system is also obvious. The low-pass filter will cause the phase lag of the gain frequency crossing in the porter diagram, thus reducing the stability margin and bringing instability to the control system. For example, if a double-pole low-pass filter is assumed to have a bandwidth of 800Hz, then the amplitude of the output signal is almost unattenuated for the previous several hundred Hz, and only decays to 70.7% until 800Hz. But the phase can go down rapidly from about 80Hz. If a control system has more than one such filter, then several such filters are added together, and other delay links are added, the phase margin of the whole system is very small, even easy to achieve the phase delay of 180 degrees; If the feedback gain is set to 1, the whole control system is completely unstable (equal to positive feedback). Therefore, when using the filter in the control system, we should be careful and careful to minimize the effect of phase delay on the whole closed loop system.

Second, in communication and digital signal processing materials, some window function, such as butterworth, Bessel, chebyshev, elliptical, etc are often repeated on, while in the control system, generally only the butterworth type will be used, because it does not produce convex peak, which would not lead to additional overshoot control system. For another example, we often discuss the FIR filter with finite impact response, which can realize high-order filtering, is not sensitive to the change of coefficient quantization, and will not produce limit cycle, so it is widely used in the communication system. For example, in the telephone, the steep attenuation characteristics of the FIR are very suitable. In the control system, FIR is not commonly used except for the rare occasions when it is used for sliding average filtering. On the one hand, more than 3 order is rarely used in control system of the controller (or stability), on the other hand FIR needs computing power also needs to take up a lot of CPU time, and control system of complex control algorithm itself also need processor in a short time to complete processing, such as in the timing interruption of tens of microseconds to hundred microseconds, must complete the relevant calculation.