Improved Fractional Model Selection and Control with Experimental Validation

Abstract

Under certain conditions, approximation based control performs effectively [1]. Most of the dynamic systems are better characterized using a fractional-order (FO) dynamic model based on fractional calculus [2]. When dealing with FO systems, a major challenge is to select the fractional values that generally termed as \(\alpha \). Many researchers have proposed different medium to choose appropriate \(\alpha \) values whether it belongs to the fractional model or fractional controller. A ranking based on various researchers working in the field of fractional calculus is reported in [3]. Monje et al. delineate an idea of tuning the fractional value for FO \(PI^{\alpha }\) controller [4] and recommend tuning of the controller using an iterative optimization method based on a nonlinear function minimization. In [5], fractional order controller is designed for FO plant which supervises the heating furnace system to a general modified FO model and PID controller is designed. In [6], a method for tuning fractional \(PI^{\lambda }D^{\mu }\) controller is proposed to fulfil five different design specifications, and in [7], a new tuning method for FO proportional and the derivative controller is proposed for a class of second-order plants, and the plant model is an integer order model. In [8], fractional order controller is designed for a class of FO systems. In article [9] a set of tuning rules is presented for FO controllers based on a first-order-plus-dead-time model. A FO sliding mode control is presented in [10] to control the velocity of the permanent magnet synchronous motor. In [11], a tuning method of FO controller is presented for a class of FO systems. Recently in [12], a FOPID controller is designed for FO systems. A new practical tuning method development for FOPI controller is presented in [13] which is also valid for a general class of plants, and another algorithm stabilizes FO time-delay systems using FO PID controllers [14].