**Sanjeevikumar Padmanaban 1,\*, Emre Ozsoy 1, Viliam Fedák <sup>2</sup> and Frede Blaabjerg <sup>3</sup>**


Received: 18 June 2017; Accepted: 13 July 2017; Published: 29 September 2017

**Abstract:** This paper introduces a sliding mode control (SMC)-based equivalent control method to a novel high output gain Cuk converter. An additional inductor and capacitor improves the efficiency ´ and output gain of the classical Cuk converter. Classical proportional integral (PI) controllers are ´ widely used in direct current to direct current (DC-DC) converters. However, it is a very challenging task to design a single PI controller operating in different loads and disturbances. An SMC-based equivalent control method which achieves a robust operation in a wide operation range is also proposed. Switching frequency is kept constant in appropriate intervals at different loading and disturbance conditions by implementing a dynamic hysteresis control method. Numerical simulations conducted in MATLAB/Simulink confirm the accuracy of analysis of high output gain modified Cuk ´ converter. In addition, the proposed equivalent control method is validated in different perturbations to demonstrate robust operation in wide operation range.

**Keywords:** closed loop control; Cuk converter; sliding mode control; robustness; active ´ hysteresis control

#### **1. Introduction**

Direct current to direct current (DC-DC) converters play a vital role in electrical systems due to the increasing penetration of renewable sources in electrical networks. In addition to high efficiency and reliability requirements, robust performance of the converter in a wide operating range is of great importance, since DC-DC converters are also used in diverse special-purpose applications, such as electrical vehicles, DC motor drives, and telecommunication systems.

Different DC-DC converter topologies can be encountered in the literature. Classical converter topologies suffer from the lack of voltage gain ratio. Higher output voltage gain ratio with improved efficiency increases the performance of the converter, which is especially crucial for solar applications [1]. Diverse DC-DC converter topologies are proposed in [2–9] to improve the voltage gain ratio and efficiency. Important voltage lift methods are also reviewed and compared in [10].

A DC-DC converter circuit topology must be upgraded for higher voltage output gain and improved efficiency, lowering the conduction losses, designing a smaller size converter, and minimizing voltage and current stress on the semiconductor switch. In addition to circuit modification for achieving the above goals, controller structure is also of great importance to improve the performance, robustness, and reliability in a wide operation range. Unfortunately, these converters are still bottlenecked in terms of system reliability and performance [1]. In addition to circuit and controller design requirements, the availability and reliability of a complete system in harsh environments is also an important task to

be considered. The studies given in [11–14] outline the harsh environment requirements of electronic circuits and implement different types of electronic circuit applications for automotive systems.

High performance control of a DC-DC converter is a challenge for both control engineering and power electronics practitioners due to the highly nonlinear nature of DC-DC converters. Furthermore, fast response in terms of rejection of load variations, input voltage disturbances, and parameter uncertainties is mandatory for robust operation.

A Cuk converter is a kind of buck/boost converter topology; the inverted output is either lower ´ or higher than the input voltage. Different modifications are applied to classical Cuk circuit [ ´ 15,16] to enhance the performance. Modeling and control of Cuk converters has been investigated with different ´ approaches. Linear methods [17,18] and proportional integral (PI) controllers [19] are well-known design procedures with ease of implementation. However, these classical methods do not guarantee the stability and high performance in different perturbations due to highly nonlinear behavior of Cuk ´ converters. Thus, different nonlinear control algorithms are also implemented in Cuk converters to ´ overcome this drawback, such as passivity-based control [20], neural networks [21], direct control methods [22], fuzzy logic [23], and sliding mode control (SMC) [24].

SMC for variable structure systems [25] is a robust control method of nonlinear systems due to its insensitivity to parameter variations, fast dynamic response, and ease of implementation. SMC was first applied to DC-DC converters in [26,27], and many diverse implementation examples are available in [27]. Design criteria for SMC application to DC-DC converters is outlined in [28]. SMC-based equivalent controllers are applied to buck/boost and Cuk converter topologies in [ ´ 29,30]. However, SMC is not popularly implemented in DC-DC converters due to its unavailability of integrated circuit forms for power electronic applications. Moreover, its variable switching frequency (SF) behavior depending on the converter parameters and operation regions complicates electromagnetic interference filter design and practical implementation. A scheme given in [31] outlines the SF fixing and reduction methods in SMC applications. In addition, it is known that DC-DC converters are unwanted noise generators, and this problem can be overcome with fixed frequency operation [28].

Different control techniques have been proposed to achieve constant SF operation to DC-DC converters. An equivalent controller is designed and the output of the controller is compared with a saw-tooth signal to fix the SF in [32]. Frequency locking techniques are applied in [33] to achieve constant SF operation of SMC for buck converter. An analog circuit design perspective for fixed frequency operation of SMC is given in [34]. Dynamic hysteresis control [35,36] is another contribution which is commonly used for fixed SF operation.

This study aims to improve the output voltage gain of a Cuk converter circuit by inclusion of a ´ single inductor and capacitor. The efficiency of the overall system is increased, and it is verified that voltage transformation ratio (*Vo/Vi*) is increased to 1/(1 − *δ*), just as in classical boost converters, where *δ* is the duty ratio of the converter. The proposed model is mathematically analyzed, and numerical simulations conducted on MATLAB/Simulink validate the accuracy of the analysis.

Moreover, an SMC-based cascaded equivalent controller is implemented for robust operation of the proposed converter. The general structure of SMC for DC-DC converters consists of external voltage controllers to achieve the desired output voltage requirements, and inner SMC performs the control of input current [26]. In general, a PI controller is sufficient for voltage requirements. Therefore, cascaded PI+SMC structure achieves robust operation of a novel high output gain Cuk converter ´ in a wide operation range. Constant SF operation is achieved at different loading and disturbance conditions by using a simple dynamic hysteresis controller. The control algorithm is implemented in the MATLAB/Simulink environment in different scenarios: (1) A high value of output reference voltage step; (2) Output resistance variation; (3) Input voltage drop; (4) Input inductor parameter variation. The proposed method effectively achieves performance goals for all aforementioned perturbations.
