  The trade-off between the noise-sensitivity and the performance of
disturbance estimation is well-known in the Disturbance Observer- (DOb-) based
motion control systems. As the bandwidth of the DOb increases, not only the
performance but also the frequency range of disturbance estimation improves yet
the motion controller becomes more sensitive to the noise of measurement
system. This trade-off is generally explained by considering only the noise of
sensors such as encoders. However, the digital implementation of the robust
motion controller may significantly influence the noise sensitivity and
performance of disturbance estimation in practice. This paper shows that the
conventional DOb implemented by estimating velocity is subject to waterbed
effect when the design parameters (i.e., sampling-time, nominal plant
parameters and the bandwidth of the DOb) are not properly tuned in the digital
motion controller synthesis. Therefore, the bandwidth of disturbance estimation
is limited by waterbed effect in addition to the noise of velocity measurement
system. To facilitate the digital motion controller synthesis, the design
constraints of the conventional DOb are analytically derived in this paper.
When the digital motion controller is implemented by estimating acceleration,
waterbed effect does not occur, and good robust stability and performance can
be achieved for all values of the design parameters of the acceleration
measurement-based DOb. The bandwidth of disturbance estimation, however, cannot
be freely increased due to the noise of acceleration sensors in practice. By
employing Bode Integral Theorem in the discrete-time domain, the design
constraints of the DOb-based digital motion control systems are clearly
explained and it is shown that acceleration measurement can be used to enhance
the bandwidth of the DOb, i.e., the performance and frequency range of
disturbance estimation.
