# Optimal Fractional PID Controller for Buck Converter Using Cohort Intelligent Algorithm
## 1 Introduction  
Power electronic system control is a very crucial and challenging task which has attracted the attention of researchers in the past few decades. Power electronic DC-DC converters are very versatile and can be used for voltage regulation in a wide range of applications. Such converters work in different modes of operation, which introduce non-linearities and are influenced by input and parametric variations [1, 2]. The challenge is to design robust and stable controllers which also satisfy the transient response and frequency response specifications with good tracking accuracy [3]. Extensive research has been completed in the quest for improved and more robust controllers for such converters. Such systems are usually controlled using the conventional proportional integral (PI)/proportional integral derivative (PID) control, \(H_{\infty}\), sliding mode, predictive control, non-linear methods such as fuzzy and intelligent control, etc. [3, 4, 5]. PID controllers are widely used in the industry for the control of power electronic converters which are used in various applications like speed control of DC and AC motor drives, switched mode power supplies, renewable energy applications, etc. [6, 7]. These controllers act on the error between the set point value and the controlled parameters, and do not require internal state measurements and, hence, require lesser sensors. They are easy to tune, have an easier control law to implement, and, hence, are easily adaptable to industry [8]. In fact, industrial controllers are still dominated by PID controllers, asthe autotuning process is simple and robust. PID technology has survived years in the industry and is continuously undergoing updation. Even though PID controllers have these advantages, conventional tuning involves trial and error methods and is time consuming. Additionally, many applications, such as power electronic converters, require linearized plant model which limits the range of operation. In actual practice, there will be parametric and load variations, and non-linearities. Under such conditions, the PID controller does not respond well, and advanced controllers are required [9]. Non-linearities can be met by sliding mode controllers, but they are prone to chattering phenomena due to the high frequency of operation of switching converters [1; 9]. In the recent years, there has been a significant growth in the field of fractional control, which is one of the major applications of fractional calculus. Fractional order systems use non-integer derivatives and integrals, resulting in various types of fractional order (FO) controllers, including the FO integrator, FO differentiator, FOPI, FOPID controllers, etc. [10; 11]. A significant aspect of the fractional order controllers is their robustness to uncertainties and load disturbances. The isodamping property of fractional order systems makes them robust to variations in gain, and hence makes them more attractive compared to the linear PID controllers [12; 13]. A typical FO PI/PID controller has more parameters to tune compared to a PID controller, which has only 3 parameters to tune [14]. As the FOPID controllers are extensions of the PID controllers, with additional tuning parameters, the performance of these two types is often compared. The challenge in the tuning of fractional controllers can be considered to be compensated by the increased degrees of freedom, making it possible to satisfy more design requirements [15]. Hence these controllers are more flexible in meeting the design specifications, such as the gain and phase margin, settling time, overshoot, robustness to parameter variations, etc. These characteristics make the fractional order controllers give effective performance in the control of non-linear plants like power converters [16]. It has been observed that the same FOPID controller can be used without retuning on different plants of same ratings. The control effort involved is much lesser in the case of FOPID controllers [17].