Two digital realizations of fractional controllers: Application to temperature control of a solid

Vinagre, Blas M.; Petráš, Ivo; Merchán, Pilar; Dorčák, Ľ.

doi:10.23919/ecc.2001.7076176

Cited by 35 publications

(15 citation statements)

References 2 publications

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“…: PLC controller [71], processor C51 or PIC [69], PCL I/O card [95], etc. Some experimental measurements with processor and PCL card were already done in [69], [95].…”

Section: A Digital Realization: Control Algorithmmentioning

confidence: 99%

Fractional order control - A tutorial

Chen

Petráš

Xue

2009

2009 American Control Conference

764

487

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Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of noninteger order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.

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“…: PLC controller [71], processor C51 or PIC [69], PCL I/O card [95], etc. Some experimental measurements with processor and PCL card were already done in [69], [95].…”

Section: A Digital Realization: Control Algorithmmentioning

confidence: 99%

Fractional order control - A tutorial

Chen

Petráš

Xue

2009

2009 American Control Conference

764

487

View full text Add to dashboard Cite

show abstract

“…Control applications to a flexible transmission (Oustaloup, Mathieu, & Lanusse, 1995;Vale´rio, 2001), an active suspension (Lanusse, Poinot, Cois, Oustaloup, & Trigeassou, 2003), a buck converter Caldero´n, Vinagre, & Feliu, 2003) and a hydraulic actuator (Pommier, Musset, Lanusse, & Oustaloup, 2003) are found in the literature. The fractional control of rigid robots is the objective in Fonseca and Tenreiro (2003), Tenreiro and Azenha (1998), and the fractional control of a thermal system is the objective in Sabatier and Oustaloup (2003), Petra´sˇand , Petra´sˇ, Vinagre, Dorcˇa´k, and Feliu (2002), Vinagre, Petra´sˇ, Mercha´n, and Dorcˇa´k (2001). Besides, other applications such as the robust control of main irrigation canals (Feliu, Rivas, & Sa´nchez, 2007) and robustness analysis of a winding system (Laroche & Knittel, 2005) can be found.…”

Section: A Reviewmentioning

confidence: 99%

Tuning and auto-tuning of fractional order controllers for industry applications

Monje

Vinagre

Feliú

et al. 2008

Control Engineering Practice

875

503

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This paper deals with the design of fractional order PI l D m controllers, in which the orders of the integral and derivative parts, l and m, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PI l D m controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method. r

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“…This generating function and its expansion determine both the form of the approximation and the coefficients [9]. For example, as shown in the last section, when a backward difference rule is used, i.e., ω(z −1 ) = (1 − z −1 )/T with T the sampling period, performing the power series expansion (PSE) of (1 − z −1 ) ±r gives the discretization formula which is actually in FIR filter form [11,31]. In [6,33], the trapezoidal (Tustin) rule is used as a generating function…”

Section: The Concept Of Generating Functionmentioning

confidence: 99%

“…Other frequency-domain fitting methods can also be used but without guaranteeing the stable minimum-phase discretization. Existing direct discretization methods include the application of the direct power series expansion (PSE) of the Euler operator [11,[31][32][33], continuous fractional expansion (CFE) of the Tustin operator [6,[31][32][33][34], and numerical integration based method [5,6,11]. However, as pointed out in [1][2][3], the Tustin operator based discretization scheme exhibits large errors in high frequency range.…”

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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Two digital realizations of fractional controllers: Application to temperature control of a solid

Cited by 35 publications

References 2 publications

Fractional order control - A tutorial

Fractional order control - A tutorial

Tuning and auto-tuning of fractional order controllers for industry applications

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

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