A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System

Gharab, Saddam; Feliu-Batlle, Vicente; Rivas-Pérez, Raul

doi:10.3390/e21030309

Cited by 7 publications

(3 citation statements)

References 34 publications

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“…Theoretical and practical studies have demonstrated the advantages of using fractional calculus in the modelling and control of dynamic systems, mainly from an industrial process control point of view [1,2]. For instance, in process modelling, several works (see, for example [3][4][5][6][7][8][9][10][11]) have shown that fractional order models with one or two fractional parameters can represent the process dynamics better than integer transfer functions of low order, such as the well-known first order plus dead time (FOPDT) and second order plus dead time (SOPDT) models. Therefore, a wider range of real-world processes can be modeled and an improved control system design can be achieved.…”

Section: Introductionmentioning

confidence: 99%

FOPI/FOPID Tuning Rule Based on a Fractional Order Model for the Process

et al. 2022

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This paper deals with the design of a control system based on fractional order models and fractional order proportional-integral-derivative (FOPID) controllers and fractional-order proportional-integral (FOPI) controllers. The controller design takes into account the trade-off between robustness and performance as well as the trade-off between the load disturbance rejection and set-point tracking tasks. The fractional order process model is able to represent an extensive range of dynamics, including over-damped and oscillatory behaviors and this simplifies the process modelling. The tuning of the FOPID and FOPI controllers is achieved by using an optimization, as a first step, and in a second step, several fitting functions were used to capture the behavior of the optimal parameters of the controllers. In this way, a new set of tuning rules called FOMCoRoT (Fractional Order Model and Controllers Robust Tuning) is obtained for both FOPID and FOPI controllers. Simulation examples show the effectiveness of the proposed control strategy based on fractional calculus.

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Section: Introductionmentioning

confidence: 99%

FOPI/FOPID Tuning Rule Based on a Fractional Order Model for the Process

et al. 2022

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“…Water scarcity has become a progressively growing problem worldwide due to the accelerated increase in water demand, which is expanding nowadays at a rate never seen before in any previous time [1][2][3][4][5]. Therefore, the effective management of water resources is a challenge to face the complexity of the real problem [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Real-Time Implementation of an Expert Model Predictive Controller in a Pilot-Scale Reverse Osmosis Plant for Brackish and Seawater Desalination

et al. 2019

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This article addresses the design and real-time implementation of an expert model predictive controller (Expert MPC) for the control of the brackish and seawater desalination process in a pilot-scale reverse osmosis (RO) plant. This pilot-scale plant is used in order to obtain the optimal operation conditions of the RO desalination process through the implementation of different control strategies, as well as in the training of operators in the new control and management technologies. A dynamical mathematical model of this plant has been developed based on the available field data and system identification procedures. Predictions of the obtained model were in good agreement with the available field data. The designed Expert MPC is distinguished by having a plant identification block and an expert system. The expert system, using a rule-based approach and the evolution of the plant variables, can modify the plant identification block, the plant prediction model, and/or the optimizer in order to improve the performance, robustness and operational safety of the overall control system. The real-time comparison results of the designed Expert MPC and a well-designed model predictive controller (MPC) show that the proposed Expert MPC has a significantly better performance and, therefore, higher accuracy and robustness.

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“…A new dynamic model is developed by taking into account the measurement errors caused by the different parts of the experimental setup. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes [ 1 ].…”

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confidence: 99%

The Fractional View of Complexity

Lopes

Machado

2019

Entropy

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Fractal analysis and fractional differential equations have been proven as useful tools for describing the dynamics of complex phenomena characterized by long memory and spatial heterogeneity. There is a general agreement about the relation between the two perspectives, but the formal mathematical arguments supporting their relation are still being developed.The fractional derivative of real order appears as the degree of structural heterogeneity between homogeneous and inhomogeneous domains. A purely real derivative order would imply a system with no characteristic scale, where a given property would hold regardless of the scale of the observations. However, in real-world systems, physical cut-offs may prevent the invariance spreading over all scales and, therefore, complex-order derivatives could yield more realistic models.Information theory addresses the quantification and communication of information. Entropy and complexity are concepts that often emerge in relation to systems composed of many elements that interact with each other, which appear intrinsically difficult to model. This Special Issue focuses on the synergies of fractals or fractional calculus and information theory tools, such as entropy, when modeling complex phenomena in engineering, physics, life, and social sciences. It includes 16 manuscripts addressing novel issues and specific topics that illustrate the role of entropy-based techniques in fractality, fractionality, and complexity. In the follow-up the selected manuscripts are presented in alphabetic order.The manuscript "A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System", by Saddam Gharab, Vicente Feliu-Batlle and Raul Rivas-Perez, addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model is developed by taking into account the measurement errors caused by the different parts of the experimental setup. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes [1].In the paper "Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag-Leffler Stability", Licai Liu, Chuanhong Du, Xiefu Zhang, Jian Li and Shuaishuai Shi investigate two novel four-dimensional, continuous, fractional-order, autonomous, and dissipative chaotic system models with high complexity. Based on the fractional Mittag-Leffler stability theory, an adaptive, large-scale, and asymptotic synchronization control method is derived [2].In "An Entropy Formulation Based on the Generalized Liouville Fractional Derivative", Rui A. C. Ferreira and J. Tenreiro Machado present a new entropy formula based in the Liouville fractional derivative. The new concept is illustrated when applied to the Dow Jones Industrial Average time series. The Jensen-Shannon divergence is also generalized and its variation with the fractional ord...

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A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System

Cited by 7 publications

References 34 publications

FOPI/FOPID Tuning Rule Based on a Fractional Order Model for the Process

FOPI/FOPID Tuning Rule Based on a Fractional Order Model for the Process

Real-Time Implementation of an Expert Model Predictive Controller in a Pilot-Scale Reverse Osmosis Plant for Brackish and Seawater Desalination

The Fractional View of Complexity

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