## 1 Introduction
Furthermore, the SMC has several advantages when used with switching converters. First, its output is a binary signal, which fits perfectly with the converter control input, avoiding the implementation of a Pulse-Width Modulator (PWM); second, the SMC is a non-linear technique that is able to ensure global stability; third, the SMC is robust to variations in the system parameters; and finally, the SMC is integrated into a co-design process of the plant/controller, which is another contribution of this paper. The SMC algorithm proposed in this manuscript ensures three essential conditions:  
* Stable DC/DC converter operation. * Reduced harmonics in the battery current. * Safe SC voltage regulation. In summary, the device proposed in this manuscript is a semi-active HESS. Its purpose is to help the battery to deliver fast current transients to the load without altering the power management or the bus control system. Hence, the device's installation and operation are transparent to the microgrid. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Ref.** & **Storage Device** & **HESS Type** & **Control’s Algorithm** & **Converter** & **Comments** \\ \hline
[30] & SC-baterry & Fully active & SCSO-RERNN & Buck-boost & EV application \\ \hline
[29] & SC-battery & Fully active & PI (battery), MPC (SC) &
\begin{tabular}{l} BC not \\ specified \\ \end{tabular} & MG with PV \\ \hline
[28] & SC-battery & Fully active & ANN & Buck-boost &
\begin{tabular}{l} References’ generation \\ with ANN \\ \end{tabular} \\ \hline
[31] & SC-battery & Fully active & PI & Buck-boost &
\begin{tabular}{l} PI tunning with \\ LMI-PSO-GA. \\ \end{tabular} \\ \hline
[25] & SC-battery & Fully active & SSMC & Buck-boost &
\begin{tabular}{l} References’ generation \\ with fuzzy logic \\ \end{tabular} \\ \hline
[18] & SC-battery & SC Semi-active & PI & Boost & EV application \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of some works on HESS. This manuscript is organized into five more sections: Section 2 presents the modeling of the power circuit, where the switched model, average model, stability conditions, and current/voltage ripple are discussed. In addition, Section 3 shows the design and analysis of the SMC, where the switching function is defined, the global stability is demonstrated, the closed-loop dynamic is designed, and the switching frequency limitation is imposed. The design process of the converter and the controller is presented in Section 4, where the algorithms for the selection of passive components and the implementation of the SMC law are illustrated; this section also includes the design of the high-pass filter used to avoid high-frequency current harmonics in the battery. The algorithms for the adaptive SMC's digital implementation and the PSIM simulations are discussed in Section 5, where the digital implementation reduces the computational burden on a low-cost microcontroller. Finally, the conclusions close the manuscript. In summary, the contributions of this paper are:  
* Definition of the algorithms for designing the power stage and the adaptive SMC. * Providing a battery current without high-frequency transients. * Algorithms for implementing the adaptive SMC on low-cost microcontrollers with low computation burden.