I am reading a material about feedback control of a mass-spring-damper system. As we all know, the input for this system is force, output is displacement or position. The displacement value is obtained using a sensor. The problem is The author wants to operate the system under high frequency input(1000Hz), in order to obtain accurate displacement value the sensor's sampling rate need to at least 20kHz, but unfortunately, this is beyond the capability of the sensor the author uses. Then author said "An alternative way to control the plant that acts as a stiffness is by only using an integral action. The crossover frequency,the frequency at which the open-loop transfer function crosses 0 dB, of the integral controller is chosen several factors below the first eigenfrequency of the system, which means the required sample rate is not extremely high in this case." Could anyone explain to me why does this method work? I really don't see there is any relationship between low pass integrator and low sampling rate.
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