A Survey of Recent Advances in Fractional Order Control for Time Delay Systems

Abstract

Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review.

A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems

“…For h and h(t), we have two delay operational matrices as D cw and D t cw . Using the Riemann-Liouville fractional integral (order α 1 ) on the left side of (46), substituting the given expressions and using (14) now yield…”

“…Fractional calculus has important engineering applications [3], for example, in the analysis of viscoelasticity structures [4,5], in mechanics [6,7], control systems [8], and in partial differential equations [9] which they arise in many fields like Navier-Stokes equations that are of practical interest [10][11][12]. Fractional time-delay optimal control has been a topic of interest during recent years [13,14]. We know that governing state equations of some mechanical and control systems may result in second-order delay differential equations [15,16].…”

Design and simulation of a normalized fuzzy logic controller for the quadruple-tank process

“…In the past decade, many mechanisms and control techniques have been used to build QTP controllers. These techniques include the predictive model controller [3][4][5][6][7], multiparametric quadratic programming-based controller [8], loop-shaping controller [9], fractional-order proportional-integralderivative (PID) controller [10][11][12][13][14] , fractional-order sliding-mode controller [15,16] , nonlinear backstepping controller with an adaptive high-gain observer [17], decoupling multivariable systems based on generalized predictive control [18], robust relay-based PID auto-tuning strategy [19], fuzzy aggregated multiparametric model predictive controller [20], novel self-tuning dual-mode adaptive fractional-order proportional-integral (PI) controller with an adaptive feedforward controller [21], and nonlinear state feedback decoupling method [22].…”

Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers

“…Likewise, numerous advanced control schemes based on FOPID controllers were proposed, such as, Smith predictors structures [25][26][27], internal mode control [28][29][30], hybrid control [31], gain scheduling [32][33][34], gain and order scheduling [35,36], among others. Current reviews in the development of FOPIDs can be found in [37][38][39][40][41][42]; likewise, few current examples of application in industry are described in [43][44][45][46][47][48][49][50].…”