*Article*

### **Analysis and Comparison of Fuzzy Models and Observers for DC-DC Converters Applied to a Distillation Column Heating Actuator**

**Mario Heras-Cervantes 1 , Adriana del Carmen Téllez-Anguiano 1,\* , Juan Anzurez-Marín 2 andElisaEspinosa-Juárez2**


Received: 30 July 2020; Accepted: 26 August 2020; Published: 28 August 2020

**Abstract:** In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the process. In order to facilitate the implementation control strategies to maintain the heating power regulated in the distillation process, it is necessary to represent adequately the heating power actuator behavior; therefore, three different models (switching, nonlinear and fuzzy Takagi–Sugeno) of a DC-DC Buck-Boost power converter, selected to regulate the electric power regarding the heating power, are presented and compared. Considering that the online measurements of the two main variables of the converter, the inductor current and the capacitor voltage, are not always available, two different fuzzy observers (with and without sliding modes) are developed to allow monitoring the physical variables in the converter. The observers response is compared to determine which has a better performance. The role of the observer in estimating the state variables with the purpose of using them in the sensors fault diagnosis, using the analytical redundancy concept, likewise, from the estimation of these variables other non-measurable can be determined; for example, the caloric power. The stability analysis and observers gains are obtained by linear matrix inequalities (LMIs). The observers are validated by MATLAB simulations to verify the observers convergence and analyze their response under system disturbances.

**Keywords:** distillation column heating actuator; Buck-Boost converter; Takagi–Sugeno model; fuzzy observer with sliding modes
