2019 |
Yakoub, Zaineb; Amairi, Messaoud; Aoun, Mohamed; Chetoui, Manel On the fractional closed-loop linear parameter varying system identification under noise corrupted scheduling and output signal measurements Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 41, no. 10, p. 2909 – 2921, 2019, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Accident prevention, Calculations, Continuous time systems, Differentiation (calculus), Fractional calculus, Instrumental variables, Least Square, Linear parameters, Linear systems, Non-linear optimization, Nonlinear programming, Scheduling @article{Yakoub20192909b,It is well known that, in some industrial process identification situations, measurements can be collected from closed-loop experiments for several reasons such as stability, safety, and performance constraints. In this paper, we investigate the problem of identifying continuous-time fractional closed-loop linear parameter varying systems. The simplified refined instrumental variable method is developed to estimate both coefficients and differentiation orders. This method is established to provide consistent estimates when the output and the scheduling variable are contaminated by additive measurements noise. The proposed scheme is evaluated in comparison with other approaches in terms of a simulation example. © The Author(s) 2019. |
2017 |
Guefrachi, Ayadi; Najar, Slaheddine; Amairi, Messaoud; Aoun, Mohamed Tuning of Fractional Complex Order PID Controller Conférence vol. 50, no. 1, 2017, (Cited by: 22; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Complex order controllers, Controlled system robustness, Controllers, Delay control systems, Design, Electric control equipment, Fractional calculus, Frequency and time domains, Frequency domain analysis, Gain variations, Numeric optimization, Numerical methods, Numerical optimizations, Optimization, PID controllers, Proportional control systems, Robust control, Three term control systems, Time domain analysis @conference{Guefrachi201714563b,This paper deals with a new structure of Fractional Complex Order Controller (FCOC) with the form PIDx+iy, in which x and y are the real and imaginary parts of the derivative complex order, respectively. A tuning method for the Controller based on numerical optimization is presented to ensure the controlled system robustness toward gain variations and noise. This can be obtained by fulfilling five design requirements. The proposed design method is applied for the control of a Second Order Plus Time Delay resonant system. The effectiveness of the FCOC design method is checked through frequency and time domain analysis. © 2017 |
Yakoub, Z.; Amairi, M.; Chetoui, M.; Saidi, B.; Aoun, M. Model-free adaptive fractional order control of stable linear time-varying systems Article de journal Dans: ISA Transactions, vol. 67, p. 193 – 207, 2017, (Cited by: 22). Résumé | Liens | BibTeX | Étiquettes: Adaptive control systems, Calculations, Controllers, Fractional calculus, Fractional order control, Fractional pid controllers, Frequency characteristic, Frequency domain analysis, Linear time-varying systems, Model-free adaptive control, Numerical methods, Numerical optimizations, Optimization, Robustness (control systems), Selective filtering, Three term control systems, Time varying control systems @article{Yakoub2017193b,This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency-domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example. © 2017 ISA |
Hmed, Amina Ben; Amairi, Messaoud; Aoun, Mohamed Robust stabilization and control using fractional order integrator Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 39, no. 10, p. 1559 – 1576, 2017, (Cited by: 8). Résumé | Liens | BibTeX | Étiquettes: Calculations, Control design, Controllers, Delay control systems, Fractional calculus, Fractional-order integrator, Robust stability, Robustness (control systems), Smith predictors, Stabilization, Uncertain systems @article{BenHmed20171559b,This paper addresses the robust stabilization problem of first-order uncertain systems. To treat the robust stabilization problem, an interval-based stabilization method using stability conditions of the non-commensurate elementary fractional transfer function of the second kind is developed. Some analytic expressions are determined to compute the set of all stabilizing controller parameters and plot the stability boundary. A robust performance control is also developed to fulfil some desired time-domain performances as the iso-overshoot property. The fractional controller can be used combined with the Smith predictor to control a first-order system with time delay and achieve desired specifications. Numerical examples are presented to illustrate the obtained results. © 2017, © The Author(s) 2017. |
Hmed, Amina Ben; Amairi, Messaoud; Aoun, Mohamed Robust stabilization and control using fractional order integrator Article de journal Dans: Transactions of the Institute of Measurement and Control, vol. 39, no. 10, p. 1559 – 1576, 2017, (Cited by: 8). Résumé | Liens | BibTeX | Étiquettes: Calculations, Control design, Controllers, Delay control systems, Fractional calculus, Fractional-order integrator, Robust stability, Robustness (control systems), Smith predictors, Stabilization, Uncertain systems @article{BenHmed20171559c,This paper addresses the robust stabilization problem of first-order uncertain systems. To treat the robust stabilization problem, an interval-based stabilization method using stability conditions of the non-commensurate elementary fractional transfer function of the second kind is developed. Some analytic expressions are determined to compute the set of all stabilizing controller parameters and plot the stability boundary. A robust performance control is also developed to fulfil some desired time-domain performances as the iso-overshoot property. The fractional controller can be used combined with the Smith predictor to control a first-order system with time delay and achieve desired specifications. Numerical examples are presented to illustrate the obtained results. © 2017, © The Author(s) 2017. |
2015 |
Hmed, A. Ben; Amairi, M.; Aoun, M. Stabilizing fractional order controller design for first and second order systems Conférence 2015, (Cited by: 1). Résumé | Liens | BibTeX | Étiquettes: Analytic expressions, Calculations, Closed loop systems, Control, Controllers, DC motors, Electric machine control, Fractional calculus, Fractional-order controllers, Invariance, Linear systems, Linear time invariant systems, Numerical methods, Resonance, Second-order systemss, Stability regions, Stabilization, Stabilization problems, Time domain analysis, Time varying control systems, Time-domain specifications @conference{BenHmed2015c,The paper deals with the stabilization problem of the Linear Time Invariant system. In this work, we present a new method of stabilization addressed to the first and second order unstable system in order to guarantee the stability and the time domain performances. Analytic expressions are developed in the purpose of setting the stabilizing parameters of the controller by describing the stability region. Moreover, the time domain-curves of the desired closed-loop system are used to show time domain specifications. Finally, some numerical examples and a control of DC motor are proposed in order to show the benefits and the reliability of the new technique. © 2015 IEEE. |
Hmed, A. Ben; Amairi, M.; Aoun, M. Stabilizing fractional order controller design for first and second order systems Conférence 2015, (Cited by: 1). Résumé | Liens | BibTeX | Étiquettes: Analytic expressions, Calculations, Closed loop systems, Control, Controllers, DC motors, Electric machine control, Fractional calculus, Fractional-order controllers, Invariance, Linear systems, Linear time invariant systems, Numerical methods, Resonance, Second-order systemss, Stability regions, Stabilization, Stabilization problems, Time domain analysis, Time varying control systems, Time-domain specifications @conference{BenHmed2015e,The paper deals with the stabilization problem of the Linear Time Invariant system. In this work, we present a new method of stabilization addressed to the first and second order unstable system in order to guarantee the stability and the time domain performances. Analytic expressions are developed in the purpose of setting the stabilizing parameters of the controller by describing the stability region. Moreover, the time domain-curves of the desired closed-loop system are used to show time domain specifications. Finally, some numerical examples and a control of DC motor are proposed in order to show the benefits and the reliability of the new technique. © 2015 IEEE. |
2014 |
Hmed, A. Ben; Amairi, M.; Najar, S.; Aoun, M. Resonance study of an elementary fractional transfer function of the third kind Conférence 2014, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Calculations, Canonical form, Damping, Damping factors, Differentiation (calculus), Fractional calculus, Frequency domain analysis, Frequency domain curves, Frequency domains, Natural frequencies, Normalized gains, Resonance, Stability condition, Systems analysis, Transfer functions @conference{BenHmed2014c,This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE. |
Yakoub, Z.; Chetoui, M.; Amairi, M.; Aoun, M. Indirect approach for closed-loop system identification with fractional models Conférence 2014, (Cited by: 4). Résumé | Liens | BibTeX | Étiquettes: Calculations, Closed loop systems, Closed loops, Differentiation (calculus), Fractional calculus, Fractional model, Identification (control systems), Least Square, Least squares approximations, Least squares techniques, Open-loop process, Religious buildings, State-variable filters @conference{Yakoub2014c,This paper deals with fractional closed-loop system identification using the indirect approach. Firstly, all differentiation orders are supposed known and only the coefficients of the closed-loop fractional transfer function are estimated using two methods based on least squares techniques. Then, the fractional open-loop process is determined by the knowledge of the regulator. A numerical example is presented to show the effectiveness of the proposed scheme. © 2014 IEEE. |
Saidi, B.; Amairi, M.; Najar, S.; Aoun, M. Min-Max optimization-based design of fractional PID controller Conférence 2014, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Algorithms, Automation, Calculations, Constrained optimization, Convergence of numerical methods, Design method, Disturbance rejection, Electric control equipment, Fractional calculus, Fractional pid controllers, Load disturbance rejection capabilities, Min-max optimization, Numerical methods, Optimization, Proportional control systems, Robustness (control systems), Simulation example, Stability margins, Three term control systems @conference{Saidi2014468b,This paper deals with a new design method of a fractional PID controller. The proposed method is based on a numerical constrained Min-Max optimization algorithm. Its main objective is the improvement of the transient response, the stability margin, the robustness and the load disturbance rejection capability. All these performances are tested through a simulation example. © 2014 IEEE. |
Saidi, B.; Amairi, M.; Najar, S.; Aoun, M. Fractional PI design for time delay systems based on min-max optimization Conférence 2014, (Cited by: 7). Résumé | Liens | BibTeX | Étiquettes: Calculations, Constrained optimization, Delay control systems, Design, Differentiation (calculus), Disturbance rejection, First order plus dead time, Fractional calculus, Frequency specifications, Load disturbance rejection, Min-max optimization, Multiobjective optimization, Numerical methods, Numerical optimizations, Robust controllers, System stability, Time delay, Time-delay systems, Timing circuits, Transient analysis @conference{Saidi2014d,This paper presents a new design method of a fractional order PI (FO-PI) for time delay systems based on the min-max numerical optimization. The proposed method uses a constrained optimization algorithm to determine the unknown parameters of the controller and has an objective to improve the transient response, stability margin, stability robustness and load disturbance rejection. A simulation example is presented to show the effectiveness of the proposed design method for a First Order Plus Dead Time system (FOPDT). © 2014 IEEE. |
Hmed, A. Ben; Amairi, M.; Najar, S.; Aoun, M. Resonance study of an elementary fractional transfer function of the third kind Conférence 2014, (Cited by: 3). Résumé | Liens | BibTeX | Étiquettes: Calculations, Canonical form, Damping, Damping factors, Differentiation (calculus), Fractional calculus, Frequency domain analysis, Frequency domain curves, Frequency domains, Natural frequencies, Normalized gains, Resonance, Stability condition, Systems analysis, Transfer functions @conference{BenHmed2014e,This work is devoted to the stability and resonance study of the elementary fractional transfer function of the third kind. Some basic properties of this transfer function which is written in the canonical form and characterized by a non commensurate order, a pseudo-damping factor and a natural frequency, are presented. A resonance and stability condition is established numerically in terms of the non commensurate order and the pseudo-damping factor. Many frequency-domain curves are given to determine graphically the pseudo-damping factor and the non commensurate order for a desired normalized gain and normalized resonant frequency. Illustrative examples are presented to show the correctness and the usefulness of these curves. © 2014 IEEE. |
2011 |
Malti, Rachid; Aoun, Mohamed; Levron, Franois; Oustaloup, Alain Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). Résumé | Liens | BibTeX | Étiquettes: Analytical computations, Closed loop control systems, Differentiation (calculus), Finiteness condition, Fractional calculus, Function coefficients, General expression, Impulse response, Impulse response energy, Integral squared error, Performance indices, Rational functions, Rational transfer functions, Relative degrees, Three term control systems, Transfer functions @article{Malti20112425b,ℋ2-norm, or impulse response energy, of any fractional commensurate transfer function is computed analytically. A general expression depending on transfer function coefficients and differentiation orders is established. Then, more concise expressions are given for elementary fractional transfer functions. Unlike stable rational transfer functions, it is proven that the ℋ2-norm of stable fractional transfer functions may be infinite. Finiteness conditions are established in terms of transfer function relative degree. Moreover, it is proven that the ℋ2-norm of a fractional transfer function with a proper integrator of order less than 0.5 may be finite. The obtained results are used to evaluate the integral squared error of closed-loop control systems. © 2011 Elsevier Ltd. All rights reserved. |
Malti, Rachid; Aoun, Mohamed; Levron, Franois; Oustaloup, Alain Analytical computation of the ℋ 2-norm of fractional commensurate transfer functions Article de journal Dans: Automatica, vol. 47, no. 11, p. 2425 – 2432, 2011, (Cited by: 50). Résumé | Liens | BibTeX | Étiquettes: Analytical computations, Closed loop control systems, Differentiation (calculus), Finiteness condition, Fractional calculus, Function coefficients, General expression, Impulse response, Impulse response energy, Integral squared error, Performance indices, Rational functions, Rational transfer functions, Relative degrees, Three term control systems, Transfer functions @article{Malti20112425,ℋ2-norm, or impulse response energy, of any fractional commensurate transfer function is computed analytically. A general expression depending on transfer function coefficients and differentiation orders is established. Then, more concise expressions are given for elementary fractional transfer functions. Unlike stable rational transfer functions, it is proven that the ℋ2-norm of stable fractional transfer functions may be infinite. Finiteness conditions are established in terms of transfer function relative degree. Moreover, it is proven that the ℋ2-norm of a fractional transfer function with a proper integrator of order less than 0.5 may be finite. The obtained results are used to evaluate the integral squared error of closed-loop control systems. © 2011 Elsevier Ltd. All rights reserved. |
2005 |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321b,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
Aoun, Mohamed; Malti, Rachid; Oustaloup, Alain Synthesis and simulation of fractional orthonormal bases Conférence vol. 16, 2005, (Cited by: 1; All Open Access, Green Open Access). Résumé | Liens | BibTeX | Étiquettes: Calculations, Dynamical systems, Fractional calculus, Fractional derivatives, Fractional systems, Identification (control systems), Multimodes, Orthogonal basis, Orthogonal functions, Orthonormal basis, Rational orthogonal basis, simulation @conference{Aoun2005321,Although rational orthogonal bases can be used to model any L2[0,∞[ system, they fail to capture the aperiodic multi-mode behaviour of fractional systems in a limited number of terms. The classical definition of orthogonal Laguerre, Kautz, and GOB functions has been extended for the use of fractional derivatives. An appropriate diagram is thus proposed for simulation. Copyright © 2005 IFAC. |
2004 |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117b,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835b,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
Aoun, Mohamed; Malti, Rachid; Levron, François; Oustaloup, Alain Numerical simulations of fractional systems: An overview of existing methods and improvements Article de journal Dans: Nonlinear Dynamics, vol. 38, no. 1-4, p. 117 – 131, 2004, (Cited by: 117). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Computer simulation, Continuous time model, Differential equations, Discrete time model, Fractional calculus, Fractional model, Functions, Identification (control systems), Laplace transforms, Mathematical models, Time domain analysis @article{Aoun2004117,An overview of the main simulation methods of fractional systems is presented. Based on Oustaloup’s recursive poles and zeros approximation of a fractional integrator in a frequency band some improvements are proposed. They take into account boundary effects around outer frequency limits and simplify the synthesis of a rational approximation by eliminating arbitrarily chosen parameters. © 2004 Kluwer Academic Publishers. |
Malti, Rachid; Aoun, Mohamed; Oustaloup, Alain Synthesis of fractional Kautz-like basis with two periodically repeating complex conjugate modes Conférence 2004, (Cited by: 19). Résumé | Liens | BibTeX | Étiquettes: Approximation theory, Differential equations, Dynamical systems, Extrapolation, Fractional calculus, Fractional derivatives, Generalized orthogonal basis (GOB), Identification (control systems), Laplace transforms, Linear control systems, Mathematical models, Model reduction, Orthogonal functions, Polynomials, Set theory, System stability, Transfer functions @conference{Malti2004835,Fractional Kautz-like functions are synthesized extrapolating the definition of classical Kautz functions to fractional derivatives. The synthesized bases has two periodically repeating complex conjugate modes. The new basis extends the definition of the fractional Laguerre basis, by allowing the modes to be complex. An example is then provided in system identification context. |
2002 |
Malti, Rachid; Cois, Olivier; Aoun, Mohammed; Levron, François; Oustaloup, Alain Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Automation, Calculations, Differentiation (calculus), Dynamical systems, Fractional calculus, Fractional order differentiations, Fractional order transfer function, Impulse response, Impulse response energy, Lebesgue space, Single mode, Square integrable, Strictly positive real, Transfer functions @conference{Malti2002449b,The objective of the paper is to compute the impulse response energy of a fractional order transfer function having a single mode. The differentiation order n, defined in the sense of Riemann-Liouville, is allowed to be a strictly positive real number. A necessary and sufficient condition is established on n, in order for the impulse response to belong to the Lebesgue space L2[0, ∞[ of square integrable functions on [0, ∞[. Copyright © 2002 IFAC. |
Malti, Rachid; Cois, Olivier; Aoun, Mohammed; Levron, François; Oustaloup, Alain Energy of fractional order transfer functions Conférence vol. 15, no. 1, 2002, (Cited by: 5; All Open Access, Bronze Open Access). Résumé | Liens | BibTeX | Étiquettes: Automation, Calculations, Differentiation (calculus), Dynamical systems, Fractional calculus, Fractional order differentiations, Fractional order transfer function, Impulse response, Impulse response energy, Lebesgue space, Single mode, Square integrable, Strictly positive real, Transfer functions @conference{Malti2002449,The objective of the paper is to compute the impulse response energy of a fractional order transfer function having a single mode. The differentiation order n, defined in the sense of Riemann-Liouville, is allowed to be a strictly positive real number. A necessary and sufficient condition is established on n, in order for the impulse response to belong to the Lebesgue space L2[0, ∞[ of square integrable functions on [0, ∞[. Copyright © 2002 IFAC. |