Samir Ladaci

Self-tuning fractional order PI λ D µ controller based on extremum seeking approach

Fractional PID (PIλDµ) controllers are not commonly used in industry when compared to classical PID controllers. The main reason is that the fractional controller parameters tuning remains an open problem. In this work we propose to generalise a classical PID tuning method based on extremum seeking (ES) approach to PIλDµ control parameters tuning in order to achieve optimal performance. ES is a non-model-based method which searches online for the parameters that minimise a cost function which is representative of the controller’s performance. The main advantage of this method is that it can be applied to a plant in which there is no knowledge of the model. Comparative simulation examples show the effectiveness of the proposed strategy for fractional order PIλDµ tuning.

Fuzzy Adaptive Control of a Fractional Order Chaotic System with Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain

In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order ( SISO ) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Grunwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

Fractional order extremum seeking control

In this paper, we propose a new control scheme based on Extremum-Seeking (ES) combined with Fractional-Order Systems (FOS). This auto-tuning strategy involving a fractional order integral action, is developed to optimize the system response without external dithering, exploiting disturbances already present in the control system. We show by mean of comparative simulation examples that the proposed fractional order ES control algorithm can improve the plant dynamics with respect to response time and disturbance rejection.

Fractionalization: A New Tool for Robust Adaptive Control of Noisy Plants

Abstract Recently, many research works have focused on fractional order control (FOC) and fractional adaptive control. It has been proven to be a good tool for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for adaptive robust control by fractionalizing an integer order integrator in the classical model reference adaptive control (MRAC) scheme. The implementation of the fractionalized terms is realized by mean of the well established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection has been improved by 50%. This approach can also be generalized to a wide range of control methods.

Robust Adaptive Fuzzy Control for a Class of Uncertain Nonlinear Fractional Systems

This paper presents a novel fuzzy logic controller (FLC) equipped with an adaptive algorithm to achieve synchronization performance for tow fractional chaotic systems. By introducing the fuzzy control design and robustness tracking approach, a desired synchronization error can be attenuated to a prescribed level, even in the presence of the high level of uncertainties and noisy training data.

Fuzzy adaptive control enhancement for non-affine systems with unknown control gain sign

A fuzzy adaptive controller scheme is presented in this work, where the system dynamics are estimated in real time by mean of fuzzy systems. The controller design is dedicated to a class of nonlinear SISO systems with unknown model and control gain sign. Such a control design becomes a true challenge, and generally impossible via the inversion if the system is non-affine. This problem is resolved by using the mean value theory to render the system model affine in the control and introducing a Nussbaum function in order to obtain an estimation of the control gain sign. A simulation example illustrates the performance enhancement realized by the present control strategy.

Fractional order self-tuning control

This paper presents an innovative design method of polynomial control laws by mean of pole placement which are actually smart solutions to many industrial applications. Even if this category of controllers is very popular in industry, most of their applications concern problems of constant reference signals. In this paper, we propose an indirect adaptive controller by fractional order pole placement, and show using a simulation example where this real time fractional order control strategy is applied to an air-lubricated capstan drive for precision positioning the improvement in systems behavior when compared to the classical control scheme with integer order poles.

Robust Adaptive Interval Type-2 Fuzzy Synchronization for a Class of Fractional Order Chaotic Systems

This chapter presents a novel Robust Adaptive Interval Type-2 Fuzzy Logic Controller (RAIT2FLC) equipped with an adaptive algorithm to achieve synchronization performance for fractional order chaotic systems. In this work, by incorporating the \( H^{\infty } \) tracking design technique and Lyapunov stability criterion, a new adaptive fuzzy control algorithm is proposed so that not only the stability of the adaptive type-2 fuzzy control system is guaranteed but also the influence of the approximation error and external disturbance on the tracking error can be attenuated to an arbitrarily prescribed level via the H ∞ tracking design technique. The main contribution in this work is the use of the interval type-2 fuzzy logic controller and the numerical approximation method of Grunwald-Letnikov in order to improve the control and synchronization performance comparatively to existing results. By introducing the type-2 fuzzy control design and robustness tracking approach, the synchronization error can be attenuated to a prescribed level, even in the presence of high level uncertainties and noisy training data. A simulation example on chaos synchronization of two fractional order Duffing systems is given to verify the robustness of the proposed AIT2FLC approach in the presence of uncertainties and bounded external disturbances.

Stabilization of fractional chen chaotic system by linear feedback control

This paper investigates the linear feedback control of the fractional-order Chen chaotic system. The analysis and implementation of the control system in the frequency domain is realized by mean of Charefs singularity function method. A numerical simulation shows the effectiveness of the proposed controller in stabilizing the system on an unstable fixed point and a periodic orbit.

Bifurcation-based fractional-order PI λ D μ controller design approach for nonlinear chaotic systems

We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PIλDμ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.