Alain Oustaloup

On Lead-Acid-Battery Resistance and Cranking-Capability Estimation

With hybrid and electric vehicle developments, battery-monitoring systems have to meet the new requirements of the automobile industry. This paper deals with one of them, the batterys ability to start a vehicle, also called battery crankability, through battery-resistance estimation. A fractional-order model obtained by system identification is used to estimate the internal resistance of lead-acid batteries. Fractional-order modeling permits an accurate simulation of the battery electrical behavior with a low number of parameters. Moreover, the high-frequency gain of the fractional model is directly linked to the battery resistance. A resistance-estimation method based on a frequency-invalidation method is, thus, proposed. It is demonstrated that the batterys available power that defines battery crankability is correlated to the battery resistance. Thus, a battery-crankability estimator using the battery resistance is suggested. Validation tests are carried out with various batteries. This estimator cannot be embedded in a microcontroller due to the linear-matrix-inequality-based optimization algorithm in the invalidation-model method used. A simplified algorithm is finally proposed, and its efficiency is proved.

Robust Control of LTI Square Mimo Plants Using Two Crone Control Design Approaches

Abstract A multi-SISO or a MIMO design approach is proposed for the robust control of uncertain LTI square MIMO plants, depending on the extent of the plant’s diagonal nature. For the multi-SISO approach, new multivariable frequency uncertainty domains are defined using the Gershgorin and the small gains theorems. These domains are based both on the structured frequency uncertainty domains related to the diagonal elements of the plant transfer matrix, and on the Gershgorin circles related to the corresponding column elements. Each element of the diagonal controller can be thus designed independently of the others using the SISO Crone design method. The totally MIMO approach is based on the optimization of an open-loop diagonal transfer matrix to minimize the stability margin variations of the perturbed diagonal elements of the closed-loop transfer matrix.

Frequency-domain synthesis of a filter using Viete root functions

This paper proposes a noniterative method to fit a rational transfer function to a specified frequency response. A method using a smoothing of width-modulated pulses of the phase asymptotic-diagram is modified to provide an exact algebraic method. This is then used to synthesize a robust controller and a nonrational transfer function with a fractional differentiation order.

From fractal robustness to non-integer approach in vibration insulation: the CRONE suspension

We deal with the transposition of fractal robustness in automation and mechanics through the CRONE control and suspension. Fractal robustness expresses the robustness of damping in nature, and that fractality ensures through non-integer derivation. This concept is illustrated by the relaxation of water on a porous dyke, its damping being independent of the motion water mass. This robust phenomenon is paradoxical in the integer approach of mechanics, where any relaxation presents a damping linked to the carried mass. The dynamic model which governs this phenomenon is established. It consists in a differential equation of non-integer order between 1 and 2, whose solution depends on the carried water mass, but whose damping is independent of it. The transposition of this template in automation and mechanics defines the non-integer approach used by the CRONE control and suspension.

FEEDFORWARD AND CRONE FEEDBACK CONTROL STRATEGIES FOR AUTOMOBILE ABS

Summary As mechatronic subsystems and especially new emerging technologies for brake systems are more and more developed, a new control architecture for ABS is proposed. The control architecture is designed using both feedback and feedforward controls that command pressure-controlled proportional servo-valves. The methods are developed to compensate for the uncertainty associated with the state of the road surface. The advantages of this strategy compared to the existing ABS strategy are discussed including simulations results using a complete vehicle and brake system model.

A Mathematical Model for the Simulation of New and Aged Automotive Lead-Acid Batteries

Today, it is possible to design a mathematical model of lead-acid battery on a laptop from scratch with MATLAB. It still takes time to develop, but nowadays these models alone cannot be considered innovations anymore because anybody is able to do the same with the appropriate tools. More than ever, the actual innovation lies in the answer given to the most important question: a model to do what? Here, the models main goal is to simulate the flooded battery behavior in all vehicle life cycles. Thus, it seems legitimate to validate them under different operating conditions with experimental data to prove that the simulation results are reliable. It is challenging but feasible, notably by making a correct selection of the parameter value ranges and studying how they influence the output. Another goal is to understand the battery behavior changes due to the physicochemical processes involved at various rates and temperatures to explain Peukerts law and the impact of temperature on vehicle cranking. The final objective of this model is to find parameter changes corresponding to the main aging phenomena to simulate new and also used batteries.

Fractional Control-System Design for a Hydraulic Actuator

Abstract The robust control of a hydraulic actuator that is part of an evaluation system for mechanical structures is presented. The dynamic model of the system, defmed from the common laws of physics, is nonlinear. An initial input-output linearization is achieved for the nominal plant, and then a set of tangent linearized models of the input-output linearized system is computed for perturbed plants. Then the robust control-system design approach is based on Crone control.

STABILITY OF CLOSED LOOP FRACTIONAL ORDER SYSTEMS AND DEFINITION OF DAMPING CONTOURS FOR THE DESIGN OF CONTROLLERS

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open loop transfer function. However, these contours have been built using nonband-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. Also presented are how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response, and how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers.

Fractional behaviour of partial differential equations whose coefficients are exponential functions of the space variable

There exists a close link between fractional systems and infinite dimensional systems described by diffusion equations. This link can be demonstrated analytically and is reminded in this article. This fractional behaviour results in fact in the system infinite dimension along with constant geometric characteristics. This article demonstrates that several other classes of differential equations also exhibit, on a frequency band, a fractional behaviour. The fractional behaviour is obtained with these equations on a space of finite dimension but with particular geometric characteristics.

Application of the CRONE control-design method to a low-frequency active suspension system

This paper presents a control law for a low-frequency active suspension system. The structure of the proposed control law is based on cooperation between feedforward and feedback. Feedforward design is based on the vehicle physics. The feedback law is synthesised from CRONE control-design method, French acronym of Commande Robuste dOrdre Non Entier (non-integer order robust control). Modelling, robust control-design in frequency-domain, optimal approach, stability analysis and performance are presented in this paper.