Stabilization using fractional-order PI and PID controllers

Hamamcı, Serdar Ethem

doi:10.1007/s11071-007-9214-5

Cited by 149 publications

(114 citation statements)

References 15 publications

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“…As shown in Figure 2, the system directions remained on the surface (Perruquetti 2002). The derivative of (8) with respect to time can be represented by: (10) Let x (t) changes and be the tracking error in the variable x d (t):…”

Section: Conventional Sliding Surfacementioning

confidence: 99%

“…Studies on fractional calculations are very widespread in the field of automatic control, and some of them are: Fractional systems in the context of feedback control (Zinober 1989), fractional PID controller (Hamamci 2007), and issues related to parameters selection using the Ziegler-Nichols method rules (Valério & da Costa 2006). Das and Pan (2014) designed a fractional-order PID controller for an automatic voltage regulator system to measure objectives such as the set-point tracking, load disturbance, and noise rejection controller effort, in the Pareto optimal solution.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Design of Fractional Sliding Mode Control Based on Multi-Objective Genetic Algorithm for a Two-Link Flexible Manipulator

Pouya

Pashaki

2017

Adv. Sci. Technol. Res. J.

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In this paper a novel optimal approach of control strategy is introduced by applying fractional calculus in the structure of sliding mode control for a range of dynamics system liable to ambiguity. So, a fractional sliding mode control was designed for dynamics of the two-link rigid-flexible manipulator. Furthermore, a multi-objective genetic algorithm was proposed in order to find the ideal variable structure of the sliding mode control. Optimal variables were achieved by the optimization of the conventional sliding mode control. Then the performance of both the conventional and the fractional sliding mode control were compared with respect to optimal variables. Results indicated that by applying the optimized fractional sliding mode control, the system's error was significantly reduced consequently tracking the desired value was done with a higher degree of accuracy and a smoother control action was achieved.

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Section: Conventional Sliding Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Design of Fractional Sliding Mode Control Based on Multi-Objective Genetic Algorithm for a Two-Link Flexible Manipulator

Pouya

Pashaki

2017

Adv. Sci. Technol. Res. J.

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“…Example 2 Stabilization of unstable fractional order systems is the subject of some previously published papers (for example [26][27][28]). In this example, our aim Fig.…”

Section: Figmentioning

confidence: 99%

Stability criteria for a class of fractional order systems

2009

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This paper deals with the stability problem in LTI fractional order systems having fractional orders between 1 and 1.5. Some sufficient algebraic conditions to guarantee the BIBO stability in such systems are obtained. The obtained conditions directly depend on the coefficients of the system equations, and consequently using them is easier than the use of conditions constructed based on solving the characteristic equation of the system. Some illustrations are presented to show the applicability of the obtained conditions. For example, it is shown that these conditions may be useful in stabilization of unstable fractional order systems or in taming fractional order chaotic systems.

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“…These controllers use the FO integrodifferential operators as extra tuning knobs which can be tuned to meet additional design constraints and provide additional robustness to the design [3][4]. Merging the concepts of computational intelligence techniques with FO control designs are also being recently explored with encouraging results [5].…”

Section: Introductionmentioning

confidence: 99%

On the Mixed <inline-formula><tex-math notation="TeX">${{\rm H}_2}/{{\rm H}_\infty }$</tex-math></inline-formula> Loop-Shaping Tradeoffs in Fractional-Order Control of the AVR System

Das

Pan

2014

IEEE Trans. Ind. Inf.

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I. INTRODUCTIONPPLICATION of fractional calculus based control system designs have gained impetus in recent times due to the flexibility and effectiveness that can be gained through such methodologies [1][2]. These controllers use the FO integrodifferential operators as extra tuning knobs which can be tuned to meet additional design constraints and provide additional robustness to the design [3][4]. Merging the concepts of computational intelligence techniques with FO control designs are also being recently explored with encouraging results [5].However applications of fractional order controllers for electrical power and energy systems are still largely unexplored. A few studies have been done for the application of the FOPID controller to the design of the AVR in a power system. In [6][7], the FOPID parameters are tuned for an AVR system with swarm based optimization algorithms which show better time domain performance over that with conventional PID structure. In [8] a multi-objective formalism has been Manuscript received November 17, 2013; revised February 18, 2014 developed and the time domain performance trade-offs of various design objectives have been investigated. The obtained results are mixed, with the PID performing better under some objectives and the FOPID performing better at others. However, all these investigations suffer from a common problem. The objective functions are framed in time domain and the evolutionary algorithms minimize some time domain performance index. Therefore, the obtained results give no indication of other important design focuses like robust stability, disturbance rejection capability etc. To alleviate these issues, the problems in power system control can be framed in frequency domain and the system performance can be expressed in terms of system norms which need to be minimized or maximized. In [9], the FOPID design for an AVR system has been done in frequency domain. The conflicting objectives being maximization of phase margin (for better oscillation damping) and gain crossover frequency (for higher speed of operation) are studied by coupling them with multi-objective evolutionary algorithms. In this paper, we extend this concept to an exhaustive set of frequency domain design criteria for the AVR system and show the achievable set of performances with the FOPID controller structure.The rest of the paper is organized as follows. Section II briefly introduces the theoretical background of the problem with the basics of FO control using system norms. Section III shows the design trade-offs for several combinations of conflicting objectives and compares the best compromise solutions for each controller structure. The paper ends with the conclusion as section IV. II. THEORETICAL BACKGROUND OF FRACTIONAL ORDER CONTROL DESIGN FOR AVR SYSTEM A. Fractional Calculus Based Control SystemsFractional calculus extends the common notion of integer order integration or differentiation to any arbitrary real number. B. AVR System and Controller StructureIn the conventional AVR loop in...

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Stabilization using fractional-order PI and PID controllers

Cited by 149 publications

References 15 publications

Optimal Design of Fractional Sliding Mode Control Based on Multi-Objective Genetic Algorithm for a Two-Link Flexible Manipulator

Optimal Design of Fractional Sliding Mode Control Based on Multi-Objective Genetic Algorithm for a Two-Link Flexible Manipulator

Stability criteria for a class of fractional order systems

On the Mixed <inline-formula><tex-math notation="TeX">${{\rm H}_2}/{{\rm H}_\infty }$</tex-math></inline-formula> Loop-Shaping Tradeoffs in Fractional-Order Control of the AVR System

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