Fractional Order Model Reference Adaptive Control Research Articles

A new output feedback adaptive control method for fractional order systems with inaccessible state

In this paper, the output tracking control problem for fractional-order (FO) systems with inaccessible state is investigated, and a new fractional-order model reference adaptive control (FOMRAC) method is proposed. The designed FO adaptive update law is able to adjust the controller parameters online in real time according to the system output information. Compared with the classical output feedback FOMRAC method, the proposed FOMRAC strategy only needs the online updating of a scalar function, which significantly reduces the complexity of the controller design and the online computational burden, and can achieve better control effect. Furthermore, the scheme ensures the boundedness of the closed-loop signals and that the mean value of the squared norm of the output error converges to zero. Finally, simulation results are carried out to verify the effectiveness of the established approach.

Fractional order adaptive MRAC controller design for high-accuracy position control of an industrial robot arm

Most of conventional feedback controllers become inefficient in hard industrial environments like in steel industry, because of uncertainties in the plant model, or process dynamics variation due to nonlinear actuators, and changes in the character of the disturbances. This paper proposes an adaptive control design based on fractional order model reference adaptive control (FOMRAC) strategy in order to deal with an uncertain horizontal positioning control of an unloading machine in a rotary hearth furnace for hot rolling operation. The proposed FOMRAC scheme uses the MIT rule as an adaptive mechanism with two main modifications comparatively to the conventional MRAC: the reference model is an adequate fractional order system and the parameter adjustment rule contains a fractional order integrator. Stability analysis of the proposed control scheme is performed using the Lyapunov stability theorem. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes applied to an industrial robot arm loading round steel blocks from inside a rotary hearth furnace. After comparison with the conventional MRAC, it is shown that the performances of FOMRAC are superior to classical control schemes.

Fractional-Order Multivariable Adaptive Control Based on a Nonlinear Scalar Update Law

This paper proposes a new fractional-order model reference adaptive control (FOMRAC) framework for a fractional-order multivariable system with parameter uncertainty. The designed FOMRAC scheme depends on a fractional-order nonlinear scalar update law. Specifically, the scalar update law does not change as the input–output dimension changes. The main advantage of the proposed adaptive controller is that only one parameter online update is needed such that the computational burden in the existing FOMRAC can be relieved. Furthermore, we show that all signals in this adaptive scheme are bounded and the mean value of the squared norm of the error converges to zero. Two illustrative numerical examples are presented to demonstrate the efficiency of the proposed control scheme.

Adaptive Cruise Control System for an Electric Vehicle Using a Fractional Order Model Reference Adaptive Strategy

Abstract With the depletion of fossil fuels, and the increased environment concerns, there is more and more interest in Electric Vehicles (EVs) from automobile manufacturer and governments in the entire world. In this paper, a fractional order model reference adaptive control (FOMRAC) system is designed for the cruise control of a DC motor-driven electric vehicle. The vehicles powertrain model is exposed and the control design is developed and detailed. The major contribution in this work is to use fractional order reference adaptive controllers for both two layer control loops: regulating the current for the inner loop and the desired speed tracking for the outer. Numerical simulations illustrate the performance improvement using the proposed control strategy.

Fractional-order model reference adaptive control of a multi-source renewable energy system with coupled DC/DC converters power compensation

We propose a supervision strategy based on a fractional order model reference adaptive control (FO-MRAC) design for the control of electrical energy transfers in a multi-source renewable energy system. We consider a two sources system (photo-voltaic and lead-acid battery bank) with a specific zero voltage switch full-bridge isolated buck DC/DC power converter and the load which is supposed to be resistive. The global energy system involving coupled DC/DC converters on a DC bus is accurately modelized in the state space domain. Then, a fractional order MRAC control law is designed in order to stabilize the system’s current and voltage. We show by means of numerical simulation tests that the proposed FO-MRAC control is very efficient and robust even in presence of renewable sources fluctuations and load variations.

Control Adaptativo Fraccionario Optimizado por Algoritmos Genéticos, Aplicado a Reguladores Automáticos de Voltaje

The technique Fractional Order Model Reference Adaptive Control (FOMRAC) applied to an Automatic Voltage Regulator (AVR) is presented in this paper. The work is focused on tuning the adaptive gains and the derivation order of the adaptive laws of the FOMRAC, determined through the minimization of a criterion function defined for the simplified model of the AVR, by means of the genetic algorithm (GA) optimization technique. Based on the criterion function proposed by other authors a simulated comparative study is performed, comparing the proposed methodology with the integer order PID control reported in (Zamani et al., 2009). It is shown that the FOMRAC with parameters optimized by GA provides better results in terms of robustness under parameters variations of the system under control and improvements in the convergence speed of the control error.

Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems

This paper presents two new lemmas related to the Caputo fractional derivatives, when α∈0,1, for the case of general quadratic forms and for the case where the trace of the product of a rectangular matrix and its transpose appear. Those two lemmas allow using general quadratic Lyapunov functions and the trace of a matrix inside a Lyapunov function respectively, in order to apply the fractional-order extension of Lyapunov direct method, to analyze the stability of fractional order systems (FOS). Besides, the paper presents a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems. The theorem can be seen as a complement of other methods already available in the literature. The two lemmas and the theorem are applied to the stability analysis of two Fractional Order Model Reference Adaptive Control (FOMRAC) schemes, in order to prove the usefulness of the results.