Comparative Study Between Digital Controllers and Sampled-Data Approaches for the Stabilization of Nonlinear Systems

The choice of the sampling period for the discretization of continuous systems is a crucial step in the context of automatic control based on microprocessor devices, as it has a direct influence on the performance and efficiency of the control system. Due to the lack of a single and exclusive method to determine this parameter, several approaches can be considered, each presenting its own advantages and limitations. Traditional methods such as the Nyquist-Shannon criterion are widely used. However, this method may not be the most efficient for all types of systems. This work analyzes and compares the most widely used methods to determine the sampling period, including classical and modern approaches, as well as the Sampled-Data method, in the context of Takagi-Sugeno fuzzy systems. The Sampled-Data method offers a more flexible approach, allowing for variation in the sampling interval and potentially reducing the need for a high sampling frequency without compromising system performance. For the comparison between each of the techniques, a two-degree-of-freedom rotating inverted pendulum system is used. The applications and results found confirm the theoretical advantages of the Sampled-Data method, especially because it presents itself as an alternative to the difficulties in determining the sampling period. This is because, unlike this method, obtaining a discrete controller does not guarantee the stabilization of the continuous system and, therefore, several tests are necessary to determine an adequate sampling period.