## 1 Introduction
Thus, the control system contains far too many coefficients as a result of the FCL and the designed sliding surface, making it very challenging to adjust the coefficients. The fine-tuning of the coefficients becomes extremely difficult because it must be performed with great care and precision while taking into account all state variables. In order to completely eliminate the aforementioned disadvantages, namely reducing the mathematical complexity in the system, preventing the state variables and switching frequency from being affected by the coefficients of the switching frequency controller, and minimizing the amount of coefficient to be tuned, in this study, a type-2 fuzzy logic control is proposed to keep the switching frequency at a desired value for the SMC-controlled DC-DC converter. In addition, a robust sliding surface has been proposed in this study to eliminate the steady-state error and to achieve a fast transient response. Since it is an essential element for a variety of applications, for example, fuel cells, electric drives, renewable energy systems, and welding machines [8; 16; 17], a DC-DC boost converter is employed to illustrate the effectiveness of the formulated control structures. Despite its widespread application, the converter has several drawbacks. It has a time-varying, non-smooth, and inherent nonlinear dynamic [8; 15]. It is also extremely vulnerable to recurring input voltage variations as a result of unstable supply and unforeseen load disturbances [15; 16]. All of these unfavorable circumstances lower the converter's performance. This also means that the systems in which the converter is employed will also suffer. Due to the fact that any increase in the converter's performance would benefit all of the involved systems, an improvement in the converter's performance becomes even more important. Apart from this, the Boost converter has a non-minimum phase structure, i.e., the control input exists in both voltage and current equations [18]. That is why controlling it is more difficult than minimum phase power converters such as buck, half-bridge, and voltage source inverters. As the control methods described in this research produce more efficient outcomes, it is ensured that they can be effortlessly used for minimum-phase power converters. When compared to the previous studies, this study introduces four advanced innovations, listed as follows:In this study, a type-2 fuzzy logic controller is employed for switching frequency control, which has never been formulated previously. 2. By providing both open-loop and closed-loop evaluation of the switching frequency, it is described how the system characteristics impact the switching frequency. 3. The effectiveness of the suggested surface for system dynamics has been demonstrated by comparing it to various sliding surfaces in the literature. 4. The results obtained by the proposed controllers and other controllers in the literature are compared, and the efficacy of the proposed methods are validated. The rest of this paper is organized as follows: The mathematical model of the boost converter is obtained in Section 2. An overview of the sliding-mode controller is given in Section 3. In Section 4, the factors that affect switching frequency are discussed in detail, along with the interval type-2 fuzzy system (IT2 FS) that is suggested for the switching frequency control. The design and implementation of the proposed strategies are introduced in Section 5. The determination of the parameters of the proposed SMC method is also covered in this section. Finally, the conclusions are drawn in Section 6.