In order to solve some analysis or control problems for fractional order models, integer order ap... more In order to solve some analysis or control problems for fractional order models, integer order approximations are often used. However, in many works, approximation error is not taken into account, leading to results that cannot be guaranteed for the initial fractional order model. The objective of the paper is thus to provide a new methodology that takes into account approximation error and leads to rewriting the fractional order model as an uncertain integer order model.
This paper deals with lithium-ion batteries modeling. From an electrochemical model available in ... more This paper deals with lithium-ion batteries modeling. From an electrochemical model available in the literature, several assumptions and simplifying hypotheses are proposed in order to get a simpler but accurate model. The obtained model is based on a fractional transfer function resulting in the resolution of a partial differential equation that describes the lithium ion diffusion inside the electrodes. The model involves only three parameters and a polynomial that fits the open circuit voltage of the battery. A method to estimate the model parameters and the polynomial is proposed. A single discharge test (constituted of several discharge steps) is required to operate the parameter estimation method. The accuracy for battery voltage prediction of the resulting model is evaluated with various tests.
ABSTRACT This paper concerns the application of flatness principle to fractional systems. In path... more ABSTRACT This paper concerns the application of flatness principle to fractional systems. In path planning, the flatness concept is used when the trajectory is fixed (in space and in time), to determine the controls inputs to apply without having to integrate any differential equations. A lot of developments have been made but, in the case of non-integer differential systems (or fractional systems), few developments are still to be made. So, the aim of this paper is to apply flatness principle to a fractional system. As soon as the path has been obtained by flatness, a new robust path tracking based on CRONE control is presented Firstly, flatness principle definitions used in control's theory are reminded. The fractional systems dynamic inversion is studied. A robust path tracking based on CRONE control is presented. Finally, simulations on a thenrial testing bench model, with two different controllers (PID and CRONE), illustrate the path tracking robustness.
... 12], [7]. The choice of the method (multi SISO, decentralized or fully MIMO) is made through ... more ... 12], [7]. The choice of the method (multi SISO, decentralized or fully MIMO) is made through an analysis of the coupling rate of the plant. The aim of this paper is to present how a CRONE controller can be designed and implemented into a Programmable Logic Controller (PLC). ...
Frequency methods only are used here for the study and control of continuous linear time periodic... more Frequency methods only are used here for the study and control of continuous linear time periodic systems. Using time varying frequency responses defined by L. A. Zadeh in the 1950s, the second generation CRONE control is extended to the control of linear time periodic systems. This control strategy ensures, for the closed-loop system, a near stationary behavior, performances set by the designer, and robustness of performances to gain variations of the plant. An application of the proposed control strategy to a testing bench shows its efficiency.
Communications in Nonlinear Science and Numerical Simulation, 2010
... has found applications in assorted fields, like engineering [23], physics [21], finance [25],... more ... has found applications in assorted fields, like engineering [23], physics [21], finance [25], chemistry [24], bioengineering [22 ... impulse response g(t) and the input u(t): (17) View the MathML source and thus using relation (16): (18) View the MathML source or, through an integral ...
ABSTRACT In this paper a novel controller for a flexible link manipulator based on fractional cal... more ABSTRACT In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single-link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.
Recently, for fractional order model, a distinction has emerged between real state and pseudo sta... more Recently, for fractional order model, a distinction has emerged between real state and pseudo state. Pseudo state is a vector of finite dimension but does not have the property of a state (it does not allow to determine future behavior of the system for instance). The real state is of infinite dimension as it is distributed, but is distributed on an infinite domain. A fractional model can thus be viewed as a doubly infinite model (distributed model on an infinite domain). It is shown in the paper, that this last feature induces the real state ability to store an infinite amount of energy using an electrical interpretation of fractional models. Thus, fractional models do not reflect the reality of macroscopic physical systems in terms of energy storage ability. As a consequence, even if fractional models permit to capture accurately the input-output dynamical behavior of many physical systems, such a property highlights a physical inconsistence of fractional models. They do not reflect the internal behavior of the modelled system. This analysis is made for explicit and implicit differentiation based fractional order models.
... ROBUST CONTROL OF A NON-LINEAR SYSTEM Valérie POMMIER , Patrick LANUSSE , Jocelyn SABATIE... more ... ROBUST CONTROL OF A NON-LINEAR SYSTEM Valérie POMMIER , Patrick LANUSSE , Jocelyn SABATIER and Alain OUSTALOUP ... The piston velocity of the actuator needs to be controlled and a pressure-difference inner-loop is used to improve the performance. ...
The thermal behavior of a power transistor mounted on a dissipator is considered in order to esti... more The thermal behavior of a power transistor mounted on a dissipator is considered in order to estimate the transistor temperature junction using a measure of the dissipator temperature only. The thermal transfers between the electric power applied to the transistor, the ...
In order to solve some analysis or control problems for fractional order models, integer order ap... more In order to solve some analysis or control problems for fractional order models, integer order approximations are often used. However, in many works, approximation error is not taken into account, leading to results that cannot be guaranteed for the initial fractional order model. The objective of the paper is thus to provide a new methodology that takes into account approximation error and leads to rewriting the fractional order model as an uncertain integer order model.
This paper deals with lithium-ion batteries modeling. From an electrochemical model available in ... more This paper deals with lithium-ion batteries modeling. From an electrochemical model available in the literature, several assumptions and simplifying hypotheses are proposed in order to get a simpler but accurate model. The obtained model is based on a fractional transfer function resulting in the resolution of a partial differential equation that describes the lithium ion diffusion inside the electrodes. The model involves only three parameters and a polynomial that fits the open circuit voltage of the battery. A method to estimate the model parameters and the polynomial is proposed. A single discharge test (constituted of several discharge steps) is required to operate the parameter estimation method. The accuracy for battery voltage prediction of the resulting model is evaluated with various tests.
ABSTRACT This paper concerns the application of flatness principle to fractional systems. In path... more ABSTRACT This paper concerns the application of flatness principle to fractional systems. In path planning, the flatness concept is used when the trajectory is fixed (in space and in time), to determine the controls inputs to apply without having to integrate any differential equations. A lot of developments have been made but, in the case of non-integer differential systems (or fractional systems), few developments are still to be made. So, the aim of this paper is to apply flatness principle to a fractional system. As soon as the path has been obtained by flatness, a new robust path tracking based on CRONE control is presented Firstly, flatness principle definitions used in control's theory are reminded. The fractional systems dynamic inversion is studied. A robust path tracking based on CRONE control is presented. Finally, simulations on a thenrial testing bench model, with two different controllers (PID and CRONE), illustrate the path tracking robustness.
... 12], [7]. The choice of the method (multi SISO, decentralized or fully MIMO) is made through ... more ... 12], [7]. The choice of the method (multi SISO, decentralized or fully MIMO) is made through an analysis of the coupling rate of the plant. The aim of this paper is to present how a CRONE controller can be designed and implemented into a Programmable Logic Controller (PLC). ...
Frequency methods only are used here for the study and control of continuous linear time periodic... more Frequency methods only are used here for the study and control of continuous linear time periodic systems. Using time varying frequency responses defined by L. A. Zadeh in the 1950s, the second generation CRONE control is extended to the control of linear time periodic systems. This control strategy ensures, for the closed-loop system, a near stationary behavior, performances set by the designer, and robustness of performances to gain variations of the plant. An application of the proposed control strategy to a testing bench shows its efficiency.
Communications in Nonlinear Science and Numerical Simulation, 2010
... has found applications in assorted fields, like engineering [23], physics [21], finance [25],... more ... has found applications in assorted fields, like engineering [23], physics [21], finance [25], chemistry [24], bioengineering [22 ... impulse response g(t) and the input u(t): (17) View the MathML source and thus using relation (16): (18) View the MathML source or, through an integral ...
ABSTRACT In this paper a novel controller for a flexible link manipulator based on fractional cal... more ABSTRACT In this paper a novel controller for a flexible link manipulator based on fractional calculus is proposed. A hybrid system that combines the advantages in terms of robustness of the fractional control and the sliding mode control is proposed. Due to adding the extra degree of freedom, the fractional order sliding mode controller can achieve better control performance than the integer order sliding mode controller. For the problem of determining the design parameters, the particle swarm optimization (PSO) algorithm is used. The proposed controller is applied for a single-link flexible manipulator robot. Finally, the performance and the significance of the closed loop system are investigated. The simulation results signify the performance of the proposed controller.
Recently, for fractional order model, a distinction has emerged between real state and pseudo sta... more Recently, for fractional order model, a distinction has emerged between real state and pseudo state. Pseudo state is a vector of finite dimension but does not have the property of a state (it does not allow to determine future behavior of the system for instance). The real state is of infinite dimension as it is distributed, but is distributed on an infinite domain. A fractional model can thus be viewed as a doubly infinite model (distributed model on an infinite domain). It is shown in the paper, that this last feature induces the real state ability to store an infinite amount of energy using an electrical interpretation of fractional models. Thus, fractional models do not reflect the reality of macroscopic physical systems in terms of energy storage ability. As a consequence, even if fractional models permit to capture accurately the input-output dynamical behavior of many physical systems, such a property highlights a physical inconsistence of fractional models. They do not reflect the internal behavior of the modelled system. This analysis is made for explicit and implicit differentiation based fractional order models.
... ROBUST CONTROL OF A NON-LINEAR SYSTEM Valérie POMMIER , Patrick LANUSSE , Jocelyn SABATIE... more ... ROBUST CONTROL OF A NON-LINEAR SYSTEM Valérie POMMIER , Patrick LANUSSE , Jocelyn SABATIER and Alain OUSTALOUP ... The piston velocity of the actuator needs to be controlled and a pressure-difference inner-loop is used to improve the performance. ...
The thermal behavior of a power transistor mounted on a dissipator is considered in order to esti... more The thermal behavior of a power transistor mounted on a dissipator is considered in order to estimate the transistor temperature junction using a measure of the dissipator temperature only. The thermal transfers between the electric power applied to the transistor, the ...
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