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Servo motor control systems with resonance often create difficult problems for designers because it causes the servo control system to over-shoot and oscillate.

An effective way to compensate for resonance in a servo system is the use of a notch filter in addition to the standard PID servo loop compensation. To understand the operation of a notch filter, note that every resonance is characterized by two parameters: the imaginary and the real part. The imaginary part sets the resonance frequency, whereas the real part sets the damping. The smaller the real part, the stronger the effect of the resonance.

A notch filter replaces one resonance with another. It places an anti-resonance on top of the existing resonance, and adds another resonance in a different location. For example, suppose the resonance has a frequency of 100 Hz and a real part of 5. The notch cancels this resonance and replaces it by one with a real part of 40. The increase in the real part results in a damped resonance.

You may ask what happens if the resonance cancellation is not perfect, or if the resonance parameters change over time? It turns out that the presence of an anti-resonance near the resonance results in a significant attenuation effect.

The mathematical behavior of the resonance is described by a pair of complex poles in the transfer function. The anti-resonance effect is done by a pair of complex zeros. The notch filter includes a pair of zeros to cancel the resonance and a pair of poles to set the new resonance.

The digital notch function is available in all new Galil servo motor controllers such as the DMC-40x0 Accelera motion controllers and DMC-41x3 Econo motion controllers. Users can program the resonance frequency with the instruction NF, the real part of the zeros with NZ, and the real part of the poles with the command NB. For more information, refer to App Note 2431 Galil’s new Frequency Analysis Software is useful for tuning servo motor control systems in the frequency domain and compensating for system resonance.