Simple Fractional Order Model Structures and their Applications in Control System Design

Tavakoli-Kakhki, Mahsan; Haeri, ءMohammad; Tavazoei, Mohammad Saleh

doi:10.3166/ejc.16.680-694

Cited by 64 publications

(38 citation statements)

References 28 publications

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“…However, the fractional order controllers developed to control the water distribution in irrigation main canals have been based on integerorder linear models (Monje et al, 2010). Moreover, in the field of fractional order systems, the problems related to developing useful simple fractional order models, estimating their parameters and using those in control system design have not been thoroughly addressed in control literature (Tavakoli-Kakhki et al, 2010).…”

Section: Fractional Order Operatorsmentioning

confidence: 99%

“…In the last few decades, increasing attention has been paid to fractional order calculus as a powerful tool with which to model and control real industrial processes (Bagley & Calico, 1991;Podlubny, 1999;Feliu-Batlle et al, 2005;Monje et al, 2010;Tavakoli-Kakhki et al, 2010). These controllers have been successfully applied during the control of water distribution in main irrigation canal pools (Calderon-Valdez et al, 2009;Feliu et al, 2009;Feliu-Batlle et al, 2011).…”

Section: Fractional Order Operatorsmentioning

confidence: 99%

“…Martinez-Gonzalez et al, 2009;Tavakoli-Kakhki et al, 2010). However, the fractional order controllers developed to control the water distribution in irrigation main canals have been based on integerorder linear models (Monje et al, 2010).…”

Section: Fractional Order Operatorsmentioning

confidence: 99%

“…This model has also been used to generate state-space MIMO models of complete canals by Clemmens & Schuurmans (2004) and Montazar et al (2005). Some improvements to the ID model have additionally been proposed by Litrico & Fromion (2004) and Sepulveda (2007). Nonlinear irrigation canal models have also been developed in de Halleux et al (2003) and Dulhoste et al (2004).…”

Section: Introductionmentioning

confidence: 99%

“…Various linear models of irrigation main canal pools currently exist, and are based either on Saint-Venant equations (Schuurmans et al, 1999;de Halleux et al, 2003;Litrico & Fromion, 2004;Wahlin & Clemmens, 2006) or on the use of system identification tools (Weyer, 2001;Cueto-Medina & Rivas-Perez, 2003;Sepulveda, 2007;Rivas-Perez et al, 2008). A review of the main approaches used in the development of models for irrigation main canal pools is carried out in Malaterre & Baume (1998).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fractional-order mathematical model of an irrigation main canal pool

Calderon-Valdez

Feliu-Batlle

Rivas-Pérez

2015

Span. j. agric. res.

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In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE) performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.Additional key words: prototype hydraulic canal; system identification; parameter estimation; canals automation; management of water resources.

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Section: Fractional Order Operatorsmentioning

confidence: 99%

Section: Fractional Order Operatorsmentioning

confidence: 99%

Section: Fractional Order Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fractional-order mathematical model of an irrigation main canal pool

Calderon-Valdez

Feliu-Batlle

Rivas-Pérez

2015

Span. j. agric. res.

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Identification from step response – The integral equation approach

Ahmed

2016

Can J Chem Eng

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An overview of identification of continuous‐time models from step responses using the integral equation approach is presented. Both open loop and closed loop identification as well as identification of multiple‐input‐multiple‐output (MIMO) models are considered. Solutions to practical implementation problems are provided and methods for identification with transient initial conditions using raw data as well as estimation algorithms in the presence of disturbances are outlined. The methodologies are presented in a simplified way using the example of a first order model; however, the algorithms are applicable for models with higher orders. Solution techniques for the estimation equations are also discussed. Identification results under different experimental conditions and data quality are presented to demonstrate the performance of the algorithms. A number of experimental and simulation examples are presented to demonstrate the applicability of the approach.

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Step Response-Based Identification of Fractional Order Time Delay Models

Ahmed

2020

Circuits Syst Signal Process

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Simple Fractional Order Model Structures and their Applications in Control System Design

Cited by 64 publications

References 28 publications

Fractional-order mathematical model of an irrigation main canal pool

Fractional-order mathematical model of an irrigation main canal pool

Identification from step response – The integral equation approach

Step Response-Based Identification of Fractional Order Time Delay Models

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