Compensation by fractional‐order phase‐lead/lag compensators

Tavazoei, Mohammad Saleh; Tavakoli-Kakhki, Mahsan

doi:10.1049/iet-cta.2013.0138

Cited by 88 publications

(42 citation statements)

References 47 publications

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“…Many additional fractional-order controllers have been proposed, including tilt-integral derivative (TID) controllers, 7 fractional-order lead-lag compensators, 8,9 fractional-order optimal controllers, 10,11 and fractional-order adaptive controllers.…”

Section: 6mentioning

confidence: 99%

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Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

Zhang

Cao

Tang

2017

International Journal of Advanced Robotic Systems

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This article presents a new fractional-order sliding mode control (FOSMC) strategy based on a linear-quadratic regulator (LQR) for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

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Section: 6mentioning

confidence: 99%

“…which is the canonical form given by (9). The desired trajectories are defined as y d1 ¼ sinðtÞ and y d2 ¼ sinðtÞ, respectively.…”

Section: A Dynamic Model Of a Two-link Rigid Robot Manipulatormentioning

confidence: 99%

Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

Zhang

Cao

Tang

2017

International Journal of Advanced Robotic Systems

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“…On the basis of the Fractional Delay (FD) filter design methods [33], [42], [43], the factional-order part z −F of z −p due to a fixed sampling rate or frequency variations can be well approximated by a Lagrange interpolation polynomial Finite-Impulse-Response (FIR) filter. The approximation can be expressed as [32], [43],…”

Section: Frequency Adaptive Selective Harmonic Controlmentioning

confidence: 99%

“…In this paper, based on the "(nk ± m)-order harmonic RC", a hybrid SHC has been introduced and developed, which allows an optimal parameter tuning for the (nk ± m)-order harmonic RC controlled grid-connected systems in contrast with the "general parallel structure RC". However, all above IMP-based harmonic controllers, especially the (nk ± m)-order harmonic RC based schemes, are sensitive to frequency variations, and also require a specific fixed sampling rate dependent on the fundamental frequency when implemented [32], [33]. For example, for a 60 Hz system, the sampling frequency has to be multiple times of 60 Hz (e.g.…”

mentioning

confidence: 99%

Frequency Adaptive Selective Harmonic Control for Grid-Connected Inverters

Yang

Zhou

Wang

et al. 2015

IEEE Trans. Power Electron.

149

100

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In this paper, a Frequency Adaptive Selective Harmonic Control (FA-SHC) scheme is proposed. The FA-SHC method is developed from a hybrid SHC scheme based on the internal model principle, which can be designed for gridconnected inverters to optimally mitigate feed-in current harmonics. The hybrid SHC scheme consists of multiple parallel recursive (nk±m)-order (k = 0, 1, 2, . . ., and m ≤ n/2) harmonic control modules with independent control gains, which can be optimally weighted in accordance with the harmonic distribution. The hybrid SHC thus offers an optimal trade-off among cost, complexity and also performance in terms of high accuracy, fast response, easy implementation, and compatible design. The analysis and synthesis of the hybrid SHC are addressed. More important, in order to deal with the harmonics in the presence of grid frequency variations, the hybrid SHC is transformed into the FA-SHC, being the proposed fractional order controller, when it is implemented with a fixed sampling rate. The FA-SHC is implemented by substituting the fractional order elements with the Lagrange polynomial based interpolation filters. The proposed FA-SHC scheme provides fast on-line computation and frequency adaptability to compensate harmonics in gridconnected applications, where the grid frequency is usually varying within a certain range (e.g., 50±0.5 Hz). Experimental tests have demonstrated the effectiveness of the proposed FA-SHC scheme in terms of accurate frequency adaptability and also fast transient response.

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“…This is due to the fact that the fractional calculus has a great potential to improve the traditional methods in different fields of control systems; such as controller design [11][12][13][14][15][16][17][18][19][20] and system identification [21][22][23][24][25]. Fractional order concepts are employed in simple and advanced control methodologies; such as set-point weighted fractional order PID (SWFOPID) controller [11,19], phase lead and lag compensator [14,26], internal model based fractional order controller [27], Smith predictor based fractional order controller [18,21], optimal fractional order controller [28,29], robust fractional order control systems [30][31][32], fuzzy fractional order controller [33], fractional order sliding mode controller [34], fractional order switching systems [35], and adaptive fractional order controller [17,36]. It has been shown that the fractional order controllers are more effective in some industrial applications [12,15,20].…”

Section: Introductionmentioning

confidence: 99%