Sliding-Mode Analysis of the Dynamics of Sigma-Delta Controls of Dielectric Charging

The purpose of this paper is to show that sigma-delta controllers of dielectric charge can be analyzed using the tools of sliding-mode controllers, in the infinite sampling frequency approximation. This allows to study the dynamics of the hidden state variables related to the charge in the dielectric, as well as the reachability and stability of the control method. Furthermore, it is also possible to explain the response of the control bitstream as a function of the dynamical model of the system. This approach not only provides insight into the dynamics of the charge controllers, understood as hybrid systems, it also simplifies the modeling and simulations of the system.