## 1 Introduction  
In practical applications, many small modules are congregated to form a major dynamic system. The study, simulation and comprehensive analysis of such dynamic systems are carried out by means of mathematical modeling [1, 2]. The derived mathematical models for such congregated systems, generally, turn out to be complex involving higher order transfer functions. The practical examples of higher order systems are as follows: nuclear reactors, power systems, chemical plants, etc. The controller design becomes a bit challenging for control engineers in these cases since the order of system is high [3]. In these cases, approximation of high-order transfer functions is advised to ease the controller design process [4, 5]. The benefits of approximation include reduction in computational complexity, simplified understanding of system and minimization in cost while designing hardware for the controller [6; 7]. In industrial control applications, a proportional-integral-derivative (PID) controller is more popular. PID controller is used extensively due to its simple form and good performance. For tuning the gains of PID controllers, a large number of methods/algorithms have been developed in the literature. Over time, a significant development in fractional calculus is seen. Several studies have demonstrated the capabilities of fractional calculus in the field of pure mathematics [8; 9], engineering [10; 11], biological engineering [12] and physics [13]. It motivated the development of designing fractional order systems and controllers as far as control theory is concerned [14; 15]. Many good articles are presented in the literature on the design of fractional-order PID (FOPID) controllers [16; 17]. FOPID controller involves an additional pair of parameters (integral order and differential order) over an integer-order PID (IOPID) controller. These parameters provide better control if tuned properly. Similarly, these additional parameters are also seen as helpful in designing a system having robustness against high frequency noise signals, better disturbance rejection, etc. [18]. In [19], an FOPID controller is developed for fractional-order systems to achieve better performance over IOPID. An FOPID controller is designed for a five bar linkage robot based on modified PSO algorithm by [PERSON] [20]. In [21], the robust stability analysis of fractional-order interval systems with multiple time delays and neutral systems is investigated. Fractional integral-fractional derivative controller using small gain theorem and sensitivity function analysis to achieve desired PM and (\(\omega_{gc}\)) is discussed by [PERSON] et al. [22]. [PERSON] and [PERSON] [23] designed an FOPID controller based on the Bode optimal reference model and flat phase property that ensures desired transient performance characteristics. This design is also robust to system parameter variations. Similarly, [PERSON] et al. [24] developed three new constrained numerical optimization algorithms for tuning the parameters of FOPID controller for delay-systems and parameter uncertain systems. In this case, it is seen that the property of iso-damping is enhanced. [PERSON] et al. [25] proposed an FOPID controller based on the sine-cosine algorithm (SCA) optimization technique [26] for an automatic voltage regulator (AVR) system. Results showed that SCA tuned FOPID controller performance is superior in improving the transient response and is robust to external disturbance. An FOPID controller using SCA is designed to handle issues likes fluctuations in load and frequency, discontinuous power flow from wind turbines, etc. in a hybrid two-area power system by [PERSON] et al. [27]. Various strategies are available for model order reduction of higher order continuous and discrete interval systems. In [28], the low-order interval model is obtained using the stability equation technique, Kharitonov's theorem and minimization of integral-square-error (ISE) utilizing the differential evolution optimization technique. [PERSON] et al.