Fractional calculus has been a

Fractional calculus has been a topic of theoretical research for scientists and engineers for a very long time. In the past two decades, several potential applications of fractional order calculus have been developed. One of the areas where fractional calculus has been found to be very useful is system modeling. As real objects are generally fractional, system modeling using fractional calculus is much more accurate as compared to the integer order modeling. In a recent work on fractional order modeling, a fractional derivative model was selected to describe the arterial wall mechanics in vivo. The fractional derivative model proved to naturally mimic the elastic modulus spectrum with only four parameters and a reasonable small computational effort [2]. In another work, a nonlinear fractional order model for steer by wire system was presented. Validation of the proposed approach was done in simulation. As reported, this method is very useful in design of a robust controller for steer by wire systems [3]. Fractional order model of Permanent Magnet Synchronous Motor (PMSM) has been proposed in [4]. Simulation and experimental comparisons between the fractional order and the integer order model of PMSM were presented to show the existence of fractional order model on the PMSM speed servo system.
Process control is another area where fractional order control is being sought as an improvement over conventional control. In the conventional PID controller, integral term eliminates the steady-state error but decreases the relative Anti-infection Compound Library of the system and makes it sluggish as well. Derivative term increases the relative stability and makes the system much faster while compromising the sensitivity to noise. Fractional order control, which involves the use of fractional integrals and derivatives instead of classical integer order integral and derivative terms, is able to achieve satisfactory compromises between the above stated positive and negative effects of conventional PID control. Thus, instead of pure integral or pure derivative (s) term, fractional integral/derivative term was used i.e., (γ∈R+). [5]. In [6], a fractional order PID controller was investigated in simulation for a position servomechanism control system considering actuator saturation and the shaft tensional flexibility. This work claimed that if fractional order PID controller is properly designed and implemented, dihybrid cross will outperform the conventional integer order PID controller. Another such work presents a strategy to tune a fractional order integral and derivative controller satisfying gain and phase margins. This work aimed to apply the tuning procedure proposed to temperature control at selected points in M/S Quanser’s heat flow experimental platform. The effectiveness and validity of the technique was experimentally illustrated by comparison with the traditional PI/PID controller based on Ziegler Nichol’s tuning method [7]. In [8], explicit analytical expressions for step and impulse responses of a linear fractional-order system with fractional-order controller for open and closed loop were presented. Superiority of the fractional order control over the convention one was demonstrated with the help of an example. A fractional order controller was proposed for a class of fractional order system and a tuning procedure was developed [9]. In the same direction, an intelligent robust fractional surface sliding mode control is proposed for a nonlinear system [10]. A recent research on intelligent fractional order control proposed a novel fractional order fuzzy PID controller. Closed loop performances and controller efforts in the presented cases were compared with conventional PID, fuzzy PID and PIλDμ controller subjected to different performance indices in simulation. As reported, the fractional order fuzzy PID controller outperformed the others in most cases [11]. Several other recent interesting works on the applications of fractional order control are automatic voltage regulator [12], oscillatory fractional order processes with dead time Anti-infection Compound Library [13], robotic manipulator [14], binary distillation column [15] and hybrid electric vehicle [16].