Second generation CRONE control

Oustaloup, Alain; Benoit, M.; Lanusse, Patrick

doi:10.1109/icsmc.1993.384862

Cited by 37 publications

(36 citation statements)

References 3 publications

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“…The third generation of the CRONE 1 controller is the most popular complex order controller as extracted from the definition in (3) [5][6][7]15].…”

Section: Fractional Complex Order Controllermentioning

confidence: 99%

“…This alteration increases the degree of freedom to tune parameters when both phase and gain margins are simultaneously of interest. Complex order controllers are used in linear non-minimum phase plants, unstable [5], linear plants with low damped modes [6], linear sampled and multivariable plants [7], time varying systems [8], nonlinear plants [9], and several other industrial problems [10][11][12]. As a key issue, the parameters of the controllers (a, b) must be optimized to shape the open-loop system concerning performance criteria.…”

Section: Introductionmentioning

confidence: 99%

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Tuning Method for Fractional Complex Order Controller Using Standardized k‐Chart: Application to Pemfc Control

Shahiri

Noei

Karami

et al. 2015

Asian Journal of Control

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This manuscript presents an approach to tune parameters of fractional complex order controllers (FCOC). The design procedure uses the basic characteristics of fractional complex order dynamic for an open-loop transfer function. In essence, the procedure satisfies restrictions, which are stated in terms of the gain and phase margins, together with satisfying an upper and lower bounds of sensitivity and complementary sensitivity functions. In the FCOC algorithm, the main part of the design procedure is to solve highly nonlinear equations and inequality form constraints. This is innovatively performed and graphically provided in so-called standardized charts, regardless and independent of the plant. These charts will be plotted for different gains of the complex order open-loop transfer function, that is, k.L(s). Investigating the trend of k-chart implies that increasing k and simultaneously decreasing the value of imaginary order b, increases the closed-loop time indices without risk of instability. The provided charts propose region of possible values of FCOC parameters for different amounts of sensitivity functions constraints. Accordingly, the designer only needs to select the proper curve and the solution area according to the target of the controller. This research also proposes a routine design procedure for FCOC especially for beginners in the literature. Optimized parameters will then be selected from the small solution area according to possible extra constraint(s). Performance of the proposed approach will be verified in an application of the PEMFC model through simulation. A comparative study of the outcome will be made using the CRONE toolbox, fractional order proportional-integral (FO-PI) and H ∞ controllers. The study confirms significance of the proposed design algorithm in the field of the FCOC.

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“…The third generation of the CRONE 1 controller is the most popular complex order controller as extracted from the definition in (3) [5][6][7]15].…”

Section: Fractional Complex Order Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tuning Method for Fractional Complex Order Controller Using Standardized k‐Chart: Application to Pemfc Control

Shahiri

Noei

Karami

et al. 2015

Asian Journal of Control

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show abstract

“…For example, as in the CRONE 1 [18,21,22], fractal robustness is pursued. The desired frequency template leads to fractional transmittance [20,23] on which the CRONE controller synthesis is based. In CRONE controllers, the major ingredient is the fractionalorder derivative s r , where r is a real number and s is the Laplace transform symbol of differentiation.…”

Section: Introductionmentioning

confidence: 99%

Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

2004

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This paper attempts to present an expository review of continued fraction expansion (CFE) based discretization schemes for fractional order differentiators defined in continuous time domain. The schemes reviewed are limited to infinite impulse response (IIR) type generating functions of first and second orders, although high-order IIR type generating functions are possible. For the first-order IIR case, the widely used Tustin operator and Al-Alaoui operator are considered. For the second order IIR case, the generating function is obtained by the stable inversion of the weighted sum of Simpson integration formula and the trapezoidal integration formula, which includes many previous discretization schemes as special cases. Numerical examples and sample codes are included for illustrations.

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“…He developed a generalization of this controller called the PID controller, involving an integration action of order λ and a differentiation action of order µ. The problem of tuning and performance improvement of fractional order PID controllers was the new challenge towards practical usage of this generalized PID controller in industrial processes [8][9][10]. Consequently, the number of robust fractional order control applications is growing exponentially touching various physical processes as can be found in the fractional control literature [7,[11][12][13].…”

Section: Introductionmentioning

confidence: 99%

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Bensafia¹,

Khettab²,

Idir³

2018

IJIES

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Abstract:Recently, many research works have focused on fractional order control (FOC) and fractional systems. It has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for robust control by fractionalizing an integer order integrator in the classical PID control scheme and we use the Sub-optimal Approximation of fractional order transfer function to design the parameters of PID controller, after that we study the performance analysis of fractionalized PID controller over integer order PID controller. The implementation of the fractionalized terms is realized by mean of well-established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection is improved by 50%. This approach can also be generalized to a wide range of control methods.

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Second generation CRONE control

Cited by 37 publications

References 3 publications

Tuning Method for Fractional Complex Order Controller Using Standardized k‐Chart: Application to Pemfc Control

Tuning Method for Fractional Complex Order Controller Using Standardized k‐Chart: Application to Pemfc Control

Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives?an Expository Review

An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

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