User guide Owner's manual

User manual for the ZEN 3-channel X-LMS controller Soft dB inc.
3.1.3 Adding low-level white noise to reference signals
The ZEN controller allows the addition of a low-amplitude white noise to reference
signals. This white noise is useful for preventing saturation of the control filter
coefficients when the system to be controlled is ill-conditioned. If the error surface has
very flat axes, the X-LMS algorithm can make changes to the control filter coefficients
following these axes without constraint. In this particular case, some coefficients of the
control filter can take any values without having an impact on the control performance.
However, when the non–constraint filter coefficients saturate, there is a reduction in
control performance and a negative attenuation can be observed.
There are many techniques for avoiding control filter saturation. For instance, some
controllers multiply the control filter coefficients by a constant number close to 1
(0.99999 for example). This way, the number close to zero acts like a return constant on
the filter coefficients and saturation is avoided. However, this constant value must be
very close to 1 to avoid the reduction of the controller performance. This approach is not
possible if a 16-bit, fixed-point DSP board is used, because the board does not have
enough numerical precision.
The addition of a very low white noise to the reference signals can prevent saturation of
the control filter. The white noise allows avoiding the bottom of the error surface. This
way, the flat axes of the error surface are avoided. Of course, this addition of the white
noise can limit controller performance. However, the amplitude of the white noise used is
very low and most of the time control performance is only slightly limited or not at all. If
required, the user can force the amplitude of the white noise to zero to bypass this feature.
ZEN User Manual p. 14