Arbitrary real-order cost functions for signals and systems

Romero, Miguel; Madrid, A.P. de; Vinagre, Blas M.

doi:10.1016/j.sigpro.2010.03.018

Cited by 27 publications

(14 citation statements)

References 6 publications

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“…For an islanded microgrid, Figure 2 represents a schematic diagram of FOMPC-based optimal frequency control method. More specifically, by introducing the GL definition of fractional order calculus [43] into Equation (16), a fractional-order integral cost function J FO (k) is approximated by Equations (18)- (21). The detailed derivation process from Formulation (16) to Formulation (18) can be found in Reference [43].…”

Section: Fompc-based Optimal Frequency Control Methodsmentioning

confidence: 99%

“…As one of the most important applications concerning fractional-order calculus theory in single processing and optimal control areas, a novel fractional-order integral performance index has been introduced as an improved cost function to improve the system performance. As a seminal research work, Romero et al [43] proposed a new type of arbitrary real-order integral cost function for infinite impulse response filter design. The work in Reference [44] used a real-coded genetic algorithm to optimize the weighting matrices used in Linear Quadratic Regulator (LQR) systems by designing a fractional-order integral cost function.…”

Section: Introductionmentioning

confidence: 99%

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Fractional-Order Model Predictive Frequency Control of an Islanded Microgrid

et al. 2018

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Optimal frequency control of an islanded microgrid has been a challenging issue in the research field of microgrids. Recently, fractional-order calculus theory and some related control methods have attempted to handle this issue. In this paper, a novel fractional-order model predictive control (FOMPC) method is proposed to achieve the optimal frequency control of an islanded microgrid by introducing a fractional-order integral cost function into model predictive control (MPC) algorithm. Firstly, a discrete state-space model is derived for the optimal frequency control problem of an islanded microgrid. Afterward, a fractional-order integral cost function is designed to guide the FOMPC algorithm to obtain optimal control law by borrowing the Grünwald-Letnikov (GL) definition of fractional order calculus. Six simulation studies have been carried out to illustrate the superiority of FOMPC to conventional MPC under dynamical load disturbances, perturbed system parameters and random dynamical power fluctuation of wind turbines.

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Section: Fompc-based Optimal Frequency Control Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional-Order Model Predictive Frequency Control of an Islanded Microgrid

et al. 2018

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“…Integral Secondary control output (ISU), Ratio of Integrated Absolute Relative Error (RI ARE), Ratio of Integral Secondary control output (RISU) and combined index (J). (27) where u ssi is the steady state value of i th input; C 1 ,C 2 are the two compared controllers; the weighting factors w 1 and w 2 in Equation 27are chosen as w 1 = w 2 = 0.5.…”

Section: Reference Tracking Performancementioning

confidence: 99%

The Potential of Fractional Order Distributed MPC Applied to Steam/Water Loop in Large Scale Ships

et al. 2020

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The steam/water loop is a crucial part of a steam power plant. However, satisfying control performance is difficult to obtain due to the frequent disturbance and load fluctuation. A fractional order model predictive control was studied in this paper to improve the control performance of the steam/water loop. Firstly, the dynamic of the steam/water loop was introduced in large-scale ships. Then, the model predictive control with an extended prediction self adaptive controller framework was designed for the steam/water loop with a distributed scheme. Instead of an integer cost function, a fractional order cost function was applied in the model predictive control optimization step. The superiority of the fractional order model predictive control was validated with reference tracking and load fluctuation experiments.

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“…Gutierrez et al [30] and Podlubny [32] have given the geometric illustration of fractional order differentiation and integration in a lucid manner. Now, a new cost function is proposed here with the generalization of the order of integration to be any arbitrary number ( Λ ) [25].…”

Section: Fractional Order Integral Performance Indices and Their Impamentioning

confidence: 99%

“…The present methodology selects the weighting matrices for the quadratic regulator design similar to that in [11], [12], using Genetic Algorithm while minimizing a suitable time domain performance index. Then a new arbitrary (fractional) order integral performance index has been used as the objective function of GA, as suggested by Romero et al [25] for signal processing applications. The impact of these new FO integral indices based PID design on the closed loop control performance as well as the corresponding optimality of the quadratic regulators are also highlighted in the present work.…”

Section: Introductionmentioning

confidence: 99%

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

Das

Pan

Halder

et al. 2013

Applied Mathematical Modelling

120

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The continuous and discrete time Linear Quadratic Regulator (LQR) theory has been used in this paper for the design of optimal analog and discrete PID controllers respectively. The PID controller gains are formulated as the optimal state-feedback gains, corresponding to the standard quadratic cost function involving the state variables and the controller effort. A real coded Genetic Algorithm (GA) has been used next to optimally find out the weighting matrices, associated with the respective optimal state-feedback regulator design while minimizing another time domain integral performance index, comprising of a weighted sum of Integral of Time multiplied Squared Error (ITSE) and the controller effort. The proposed methodology is extended for a new kind of fractional order (FO) integral performance indices. The impact of fractional order (as any arbitrary real order) cost function on the LQR tuned PID control loops is highlighted in the present work, along with the achievable cost of control. Guidelines for the choice of integral order of the performance index are given depending on the characteristics of the process, to be controlled.

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Arbitrary real-order cost functions for signals and systems

Cited by 27 publications

References 6 publications

Fractional-Order Model Predictive Frequency Control of an Islanded Microgrid

Fractional-Order Model Predictive Frequency Control of an Islanded Microgrid

The Potential of Fractional Order Distributed MPC Applied to Steam/Water Loop in Large Scale Ships

LQR based improved discrete PID controller design via optimum selection of weighting matrices using fractional order integral performance index

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