Oustaloup's Recursive Approximation Research Articles

An adaptive fractional order controller design: A realization for liquid level regulation in liquid level plant

In this paper, an adaptive FO − IλD1−λ controller design is proposed using a frequency domain approach. The proposed adaptive controller parameters are tuned based on the frequency domain specifications. To realize the velocity error constant for the proposed controller, Oustaloup Recursive Approximation (ORA) method is employed. The proposed controller is realized for liquid level regulation in the Liquid Level Plant (LLP). An identification technique is proposed to identify a linear adaptable parameter transfer function (LAPTF) model of LLP. The performance of the proposed controller is compared with the existing works. It is observed that the proposed controller outperforms the existing controllers in the literature.

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Novel applications of oustaloup recursive approximation and modified oustaloup recursive approximation methods in linear fractional order control design

Excitation system voltage regulator modeling with the use of fractional calculus

The article presents a new and measurement-verified approach in the modeling of a voltage regulator, which is used in the power industry and applied for the purpose of regulation of generating units. The voltage regulator extended model, proposed in this paper, involves nonlinearities and the application of fractional calculus. The addition of these features has not only significantly increased the number of parameters determining the model response, it has also established a challenge of developing a solver capable of computing the resulting complex system of fractional differential–algebraic equations (FDAE). The mathematical formulation of a single simulation of a transient process for the model has been described. The application of the Oustaloup Recursive Approximation (ORA) of the fractional derivative has been considered in order to increase the speed of the model evaluation. Generalized equations leading to an approximating system of Differential–Algebraic Equations (DAE) have been presented in detail. In order to obtain the parameters for the fractional nonlinear model, a parameter estimation procedure has been applied, which consists of implementations of several algorithms that are executed sequentially. The usefulness and drawbacks of the application of the ORA has also been discussed.

A novel fractional order controller design algorithm for a class of linear systems

In this paper, a novel fractional order controller design algorithm is proposed for a class of linear systems. The proposed control algorithm is developed by employing Riemann principal sheet stability criterion. Oustaloup recursive approximation (ORA) method is used to implement the controller. The proposed controller is implemented in simulation. The results show that the proposed fractional order controller provides better results than the existing controllers in the literature work.

Theory and Implementation of Fractional Order Controllers for Power System Applications

The paper presents the theoretical foundation and practical implementation aspects of Fractional Order Controllers (FOCs) for power system applications. With this aim, the paper provides a comprehensive mathematical background on the stability analysis of dynamic systems with inclusion of fractional order derivatives and discusses their software implementation based on the Oustaloup's Recursive Approximation (ORA) method. Then the paper illustrates a variety of examples of ORA-based FOCs, namely, automatic generation control of synchronous machines; frequency control of a converter-interfaced energy storage system; and voltage control through a static synchronous compensator. The WSCC 9-bus test system and a realistic 1,479-bus model of the Irish transmission system are employed to test and compare the examined FOCs with their integer-order versions.

An $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller design and realization for inverted decoupled Two Input Two Output-Liquid Level System

In this paper, An $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is proposed for the level control problem in Two Input Two Output-Liquid Level System (TITO-LLS). The proposed $$FO-{{I}^{\lambda }}{{D}^{1-\lambda }}$$ controller is designed based on phase margin ( $${{\phi }_{m}}$$ ), gain crossover frequency ( $${{\omega }_{gc}}$$ ) and velocity error constant ( $${{K}_{v}}$$ ) specifications. Oustaloup Recursive Approximation (ORA) method is used to realize the velocity error constant. A mathematical procedure is proposed to identify the linear dynamics of TITO-LLS from the real-time response. An inverted decoupler is used to decouple the TITO-LLS into two separate Single Input Single Output (SISO) systems. The effectiveness of the proposed controller is compared with reported works both in simulation and in real-time. It is observed that the proposed controller gives better results than the existing reported works.

An FO–[PI]λ controller for inverted decoupled two-input two-output coupled tank system

ABSTRACTIn this paper, a new structured fractional order-[proportional integral] () controller design method is demonstrated. The designed controller is implemented in decoupled Two-Input Two-Output (TITO) Coupled Tank System (CTS) for liquid level control. An inverted decoupling technique is used to decouple the TITO process into two independent SISO (single-input single-output) processes. The designed controller is implemented for each SISO process. A frequency domain approach is used to tune the parameters of the controller. While designing, to approximate the fractional integral terms of the controller, Oustaloup's Recursive Approximation (ORA) method is used in the stable frequency bands. To validate the proposed approach, the performance of the controller is compared with the existing controllers designed based on the same specifications. From the simulation and experimental studies, it is shown that proposed gives better performance than , PI and PID controllers.

Dynamic programming strategy based on a type-2 fuzzy wavelet neural network

In this paper, an optimal control scheme, based on dynamic programming strategy, is presented for synchronization of uncertain fractional-order chaotic/hyperchaotic systems. In the scheme, a type-2 fuzzy wavelet neural network (T2FWNN) is proposed for estimation of the unknown functions in dynamics of system. For solving the fractional optimal control problem, fractional-order derivative is approximated by using Oustaloup recursive approximation method. Simulation studies verify the effectiveness of the proposed control scheme and the proposed T2FWNN.

Comparison of Fractional Order Modelling and Integer Order Modelling of Fractional Order Buck Converter in Continuous Condition Mode Operation

Producing a mathematical model with high accuracy is the first and important step in control of systems. Nowadays fractional calculus has been in the spotlight and it has a lot of application especially in control engineering. Fractional modelling on one of the conventional converters is done in this paper. Fractional state space model and related fractional transfer functions for a fractional DC/DC Buck converter is established and achieved results are compared to integer order models. At the end of this paper Oustaloup's recursive approximation is introduced and imposed for one of gathered fractional transfer function.

Fractional-order control of active suspension actuator based on parallel adaptive clonal selection algorithm

In current study, a new approach for vehicle active suspension actuator control is reported. For this approach, a nonlinear model for an electro-hydraulic servo actuator and quarter suspension system is established. An Oustaloup recursive approximation (ORA) Fractionalorder proportional–integral–derivative (FOPID) controller is designed to control the displacement of the actuator, and controller parameters are optimized based on error integral criteria using the Parallel adaptive clonal selection algorithm (PACSA). The research indicates that PACSA can tune parameters of the FOPID controller accurately and efficiently, and the tuned FOPID controller performs better in terms of response speed and tracking accuracy than a regular Proportional–integral–derivative (PID) controller. The performance of the active suspension system that uses the FOPID actuator is obviously superior to that of the active suspension system that uses a PID actuator and a passive suspension system.

State-space model with non-integer order derivatives for lithium-ion battery

Lithium ion batteries have attracted wide attention due to their high energy density, long cycle life, and environmental friendliness and are widely used in electrical vehicles. An accurate and reliable battery model is needed in battery management systems (BMS) to monitor battery operating conditions, including state of charge (SOC), state of health (SOH), etc. This paper presents a state-space model with non-integer order derivatives for electrochemical batteries with a constant phase element (CPE) in order to accurately describe battery dynamics. The proposed model is a combination of electrochemical impedance spectroscopy and the 1-RC model. The Oustaloup recursive approximation was selected for model parametric identification and potential implementation. A particle-swarm optimization (PSO) algorithm was used to identify three model parameters by using time-domain test data. The model accuracy and robustness were validated by using datasets from different driving cycles, aging levels and cells of the same chemistry. The proposed FOM showed good accuracy and robustness. It is suitable for research on battery reliability, including issues like SOC estimation, SOH prediction, and charging control.

Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PI λD μ controller

Oustaloup recursive approximation (ORA) is widely used to find a rational integer-order approximation for fractional-order integrators and differentiators of the form s v , v ∈ (−1, 1). In this method the lower bound, the upper bound and the order of approximation should be determined beforehand, which is currently performed by trial and error and may be inefficient in some cases. The aim of this paper is to provide efficient rules for determining the suitable value of these parameters when a fractional-order PID controller is used in a stable linear feedback system. Two numerical examples are also presented to confirm the effectiveness of the proposed formulas.

QFT LOOP SHAPING USING A FRACTIONAL INTEGRATOR - REAL-TIME APPLICATION TO A COUPLED-TANK SYSTEM

We propose to use a fractional order integrator (1/sa, a ε +) for simplifying the loop shaping in Quantitative Feedback Theory (QFT). The controller thus obtained is approximated to integer order in frequency domain by using Oustaloup's recursive approximation. The designed controller along with the prefilter is implemented realtime on a coupled-tank system and the experimental results are found to be satisfactory.