Stabilization of all-pole unstable delay systems by fractional-order [PI] and [PD] controllers

Kheirizad, Iraj; Jalali, Ali; Khandani, Khosro

doi:10.1177/0142331212441196

Cited by 20 publications

(10 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The generalisation of the classical, most commonly used PID controller is due to Podlubny, who introduced the socalled FO PI λ D μ controllers (Podlubny, 1999). Since then, many researchers have focused on the design problem of FO controllers, especially to enhance the robustness and performance of the control systems (Cao & Cao, 2006;Caponetto, Dongola, Fortuna, & Petras, 2010;Chen & Moore, 2002;Kheirizad, Akbar Jalali, & Khandani, 2013;Luo, Chen, Wang, & Pi, 2010;Monje, Chen, Vinagre, Xue, & Feliu, 2010;Radwan, Soliman, Elwakil, & Sedeek, 2009;Tavazoei & Haeri, 2008). The CONTACT Eva H. Dulf eva.dulf@aut.utcluj.ro popularity of FO PI μ D λ controllers is based on the two additional degrees of freedom involved than in the classical PID controller, μ and λ, which can improve the control performance.…”

Section: Introductionmentioning

confidence: 99%

Tuning algorithms for fractional order internal model controllers for time delay processes

Muresan

Dutta

Dulf

et al. 2015

International Journal of Control

View full text Add to dashboard Cite

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system

show abstract

Section: Introductionmentioning

confidence: 99%

Tuning algorithms for fractional order internal model controllers for time delay processes

Muresan

Dutta

Dulf

et al. 2015

International Journal of Control

View full text Add to dashboard Cite

show abstract

“…Recently, Aghababa [14][15][16][17][18][19][20][21] has introduced fractional controllers for synchronization and stabilization of fractional-order uncertain chaotic systems. Moreover, the application of fractional calculus in control theory has been widely reported [22][23][24][25][26]. Conversely, several scholars have shown increasing interest in the study of the problems related to the chaos and complexity [27][28][29][30][31].…”

Section: Examplementioning

confidence: 99%

Fractional modeling and control of a complex nonlinear energy supply‐demand system

Aghababa

2014

Complexity

View full text Add to dashboard Cite

This article deals with the fractional‐order modeling of a complex four‐dimensional energy supply‐demand system (FOESDS). First, the fractional calculus techniques are adopted to describe the dynamics of the energy supply‐demand system. Then the complex behavior of the proposed fractional‐order FOESDS is studied using numerical simulations. It is shown that the FOESDS can exhibit stable, chaotic, and unstable states. When it exhibits chaos, the FOESDS's strange attractors are plotted to validate the chaotic behavior of the system. Moreover, we calculate the maximal Lyapunov exponents of the system to confirm the existence of chaos. Accordingly, to stabilize the system, a finite‐time active fractional‐order controller is proposed. The effects of model uncertainties and external disturbances are also taken into account. An estimation of the stabilization time is given. Based on the latest version of the fractional Lyapunov stability theory, the finite‐time stability and robustness of the proposed method are proved. Finally, two illustrative examples are provided to illustrate the usefulness and applicability of the proposed control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 74–86, 2015

show abstract

“…Akbari (Moornani and Haeri, 2012) presented a closed-loop system consisting of a fractional/integer-order system and a fractional PID controller and some easy to use theorems to investigate the robust bounded-input bounded-output stability of the resultant closed-loop system. The stabilization of all-pole unstable systems with time delay by fractional-order controllers is investigated by Kheirizad et al (2013). Sufficient conditions for stabilizability by fractional-order proportional-derivative (PD)/proportional-integral (PI) controllers are determined and also provides the stabilizing range of the controller parameters.…”

Section: Introductionmentioning

confidence: 99%

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

Ghasemi

Noei

Sadati

2016

Transactions of the Institute of Measurement and Control

View full text Add to dashboard Cite

In this paper a new type of sliding mode based fractional-order iterative learning control (ILC) is proposed for nonlinear systems in the presence of uncertainties. For the first time, a sliding mode controller is combined with fractional-order ILC. This sliding mode based [Formula: see text] and [Formula: see text]-type ILC is applied on a nonlinear robot manipulator. Convergence of the proposed method is investigated when the stability is also proved. In this method, the control signal at any iteration is generated in two parts. The first section comes from the sliding mode controller while the second part is output of the fractional-order ILC. The latter signal is assessed using its previous amount and the sliding mode error signal. The achieved control law is capable of controlling nonlinear iterative processes, perturbed by bounded disturbances with high accuracy. The same frequent disturbance is eliminated by the iterative learning part, while the effect of nonrepetitive uncertainty is improved by the sliding mode part. The sliding mode based [Formula: see text]-type ILC (as an adaptive control law) is proposed to control a single-link arm robot. The controller is then improved to sliding mode based [Formula: see text]-type ILC. The effectiveness of the proposed method is again investigated on a single-link robot manipulator through a simulation approach. It is shown that the controller for [Formula: see text] provides performance by means of faster response together with more accuracy with respect to a conventional ILC.

show abstract

Stabilization of all-pole unstable delay systems by fractional-order [PI] and [PD] controllers

Cited by 20 publications

References 20 publications

Tuning algorithms for fractional order internal model controllers for time delay processes

Tuning algorithms for fractional order internal model controllers for time delay processes

Fractional modeling and control of a complex nonlinear energy supply‐demand system

Sliding mode based fractional-order iterative learning control for a nonlinear robot manipulator with bounded disturbance

Contact Info

Product

Resources

About