Stabilization of fractional-order unstable delay systems by fractional-order controllers

Abstract

In the present paper stabilization of a class of fractional-order unstable delay systems by fractional-order controllers is investigated. To derive the sufficient conditions for stability, an analysis based on the Nyquist stability criterion has been adopted. The analysis is carried out with fractional-order [proportional–integral] and [proportional–derivative] controllers to obtain the upper bound for the time delay. Furthermore, the paper proposes the conditions on the parameters of the controllers which must be fulfilled in order to have a stabilized process. Two illustrated examples using fractional-order controllers are presented for demonstrating the proposed approach.

Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional‐Order Nonsingular Fast Terminal Sliding Mode Control

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“…Meanwhile, sliding mode control is an efficient approach in the application of linear or nonlinear control. For the foregoing reasons, there are more and more new control methods composed of fractional calculus and sliding mode control [22,23], and their application fields have been gradually expanded from integerorder dynamic systems to fractional-order ones [24][25][26]. Besides, compared with traditional integer-order control, fractional-order control can offer more degrees of freedom to designers to meet a predefined set of performance criteria [27].…”

Robust adaptive fractional order proportional integral derivative controller design for uncertain fractional order nonlinear systems using sliding mode control

“…1 In recent years, fractional calculus has been extensively used in a variety of fields of physics and engineering applications, for example, dynamical systems, 2 viscoelastic damping, 3 signal processing, 4 diffusion wave, 5 biomedical applications, 6 stochastic systems, 7 and chaotic systems. [8][9][10] Recently, many fractional order controllers are developed like fractional order proportional integral derivative (FOPID) control, 11,12 fractional order proportional integral (PI) and proportional differential (PD) control, 13,14 fractional order lead-lag control, 15,16 fractional CRONE controller, 17 fractional order model reference adaptive control, 18,19 and sliding mode control of fractional order systems. 20 In most of the applications, the controllers are of proportional integral derivative (PID) type due to its simplicity and appropriate performance in a variety of applications.…”

ABC Algorithm Based System Modelling for Tuning the Fractional Order PID Controllers

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