Abstract:
The stability and performance analyses of control systems are of critical importance
in the field of engineering. While motion controllers are typically implemented using
computers or microcontrollers, continuous-time analysis methods are often utilized
due to their simplicity. However, these methods may not fully capture some of the
dynamic behaviors of robust digital motion controllers based on disturbance observer
(DOB). To address this, the Bode sensitivity integral theorem is a valuable tool for
analyzing control systems, as it can indicate the presence of the waterbed effect.
This phenomenon suggests that the sensitivity of controllers to disturbance estimation
may worsen at certain frequencies. As such, it is crucial to consider this effect
when selecting the appropriate discretization method for analyzing and designing
digital DOB-based control systems. In this study, we analyze the performance of
DOB-based cascade PI-PI speed control systems in the discrete-time domain, which
provides a more comprehensive understanding of the dynamic responses of digital
motion control systems compared to continuous-time analysis methods. Our theoretical
and experimental analyses demonstrate that the choice of acceleration and speed
measurements, as well as the selection of discretization methods for DOB synthesis,
significantly impact the stability and performance of digital motion controllers.