Jimmy Lauber

Control of a parallel hybrid powertrain: optimal control

Control strategies for hybrid powertrains are algorithms that choose the power split between the engine and motor of a hybrid vehicle in order to minimize the fuel consumption and/or emissions. The goal of this paper is to propose an efficient tool to evaluate minimal fuel consumption that is achievable in simulation. Several approaches have been proposed, using heuristics (Delprat et al. 1999) or dynamic programming (Brahma et al., 2000; Rimaux et al., 1999). One drawback of these approaches is the huge amount of time required to obtain solutions. The approach described here is based on optimal control theory (Lewis & Syrmos, 1995) and avoids this drawback. Moreover, it can be easily applied to a large family of parallel arrangements.

Discrete Tagaki-Sugeno models for control: Where are we?

Abstract This work deals with relaxed conditions for stability and stabilization of discrete-time Takagi–Sugeno (TS) models. It recalls classical results found in the literature which use quadratic Lyapunov functions leading to very conservative conditions, and various extensions based on piecewise and non-quadratic Lyapunov functions. Afterwards, a new and powerful way to enhance the previous results is depicted. The basic idea is that waiting long enough a stable model will converge towards its equilibrium and, therefore, the Lyapunov functions under consideration are not necessarily decreasing at every sample, but are allowed to decrease every k samples. Whatever it is k >1, the results are proved to include the standard one-sample case. The potential of this approach is shown through several examples in the paper.

An Efficient Lyapunov Function for Discrete T–S Models: Observer Design

This paper deals with the design of a new observer synthesis for discrete Takagi-Sugeno (T-S) fuzzy models. It is well established that quadratic synthesis for discrete T-S models and/or linear parameter-varying systems can be outperformed easily via nonquadratic syntheses. Several Lyapunov functions can be used. Nevertheless, this paper shows that with a “small” change in the initial Lyapunov function, a “better” (in the sense of solutions to the linear matrix inequality constraints problem) Lyapunov function can be reached. This one can introduce very important improvements.

Adaptive observers for TS fuzzy systems with unknown polynomial inputs

A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents. However, in practical applications, the process under consideration may be affected by unknown inputs, such as disturbances, faults or unmodeled dynamics. In this paper, we consider the problem of simultaneously estimating the state and unknown inputs in TS systems. The inputs considered in this paper are (1) polynomials in time (such as a bias in the model or an unknown ramp input acting on the model) and (2) unmodeled dynamics. The proposed observer is designed based on the known part of the fuzzy model. Conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal. The results are illustrated on a simulation example.

Control strategy optimization for an hybrid parallel powertrain

Performances of hybrid vehicles in terms of fuel consumption are strongly related to their control strategy. First studies of this problem deal with instantaneous optimization algorithms (G. Pagnelli, 1999; J. Seiler and D. Schroder, 1998; K. Yamaguchi et al., 1996), designed for real time application. Second studies are based on global optimization algorithms (S. Delprat et al., 1999; S. Rimaux et al., 1999). They outperform instantaneous optimization results, but require a lot of computing time and it seems hard to derive a real time strategy from them. The paper focuses on a control strategy issue applied to the described example of a hybrid parallel single shaft architecture. A global optimization algorithm based on optimal control theory is presented. The results obtained with the optimal theory outperform the ones obtained by local and/or global strategies. A very interesting point is that this method can be easily used for real time application.

Membership-function-dependent stability analysis of fuzzy-model-based control systems using fuzzy Lyapunov functions

This paper investigates the stability of fuzzy-model-based (FMB) control system, formed by a T-S fuzzy model and a fuzzy controller connected in a close loop, based on a fuzzy-Lyapunov function. A general FMB control system that the T-S fuzzy model and fuzzy controller not sharing the same premise membership functions and/or the same number of fuzzy rules is considered. A membership-function-dependent stability analysis approach is proposed to consider the membership functions of both the T-S fuzzy model and fuzzy controller in the stability analysis and incorporate them in the stability conditions in the form of linear matrix inequalities. As the stability conditions are membership-function dependent, they are dedicated to the FMB control system with the specified membership functions under consideration. It is thus the membership-function-dependent stability conditions are more relaxed compared to the existing membership-function-independent stability conditions. A fuzzy-Lyapunov function is a weighted sum of quadratic functions which are required to be positive definite in most of the existing work. In this paper, this criterion is not required and thus the stability conditions can be further relaxed. Some simulation examples are given to demonstrate the merits of the proposed approach.

Controller Design for TS Models Using Delayed Nonquadratic Lyapunov Functions

In the last few years, nonquadratic Lyapunov functions have been more and more frequently used in the analysis and controller design for Takagi-Sugeno fuzzy models. In this paper, we developed relaxed conditions for controller design using nonquadratic Lyapunov functions and delayed controllers and give a general framework for the use of such Lyapunov functions. The two controller design methods developed in this framework outperform and generalize current state-of-the-art methods. The proposed methods are extended to robust and H∞ control and α-sample variation.

Energy conservation based fuzzy tracking for unmanned aerial vehicle missions under a priori known wind information

The aim of this work is to include the navigation step for the waypoint-based guidance of a UAV system and to illustrate aspects such as tracking of the reference trajectory under wind presence, while conserving total energy requirements. The mission is represented utilising graph theory tools. The mathematical modelling of an aircraft controlled by an actuator surface is presented in terms of simple analytic relationships in order to simulate the actual horizontal motion of the vehicle. Its equivalence with a Tagaki-Sugeno (T-S) fuzzy system is illustrated that can aid the control methodology involved. Additionally, the advantages of utilising such an analysis is also stressed. The model formulated is an error posture model, that depends on current and reference posture. The control law is designed through parallel distributed compensation (PDC) and the gains are computed with the help of linear matrix inequalities (LMIs). Hence stability for the system is also guaranteed provided that the state variables are bounded in a priori known compact space. Moreover the energy requirements are described. This article is contributing towards energy enhancing a UAV mission and generating safely-flyable trajectories to meet mission objectives. The control law used is calculated in the pre-flight planning and can be used in real time for any trajectory to be tracked under any environmental conditions. Provided that angular and linear velocities are bounded, the latter is feasible under the assumption that the magnitude of air speed is small compared to the ground velocity of the aerial vehicle. The methodology offers an improved visualisation to aid an analyst with the representation of a UAV mission through graph theory tools utilising energy requirements for the mission and fast computational schema using matrix analysis. A simulation example of a UAV deployed from a source to reach a destination node under windy conditions is included to illustrate the analysis. The reference trajectory used is a piecewise Bezier-Bernstein curve referred to as the Dubins path.

Air-fuel ratio control in a gasoline engine

The aim of this article is to design an air-fuel ratio control law for a gasoline IC engine. The air-fuel ratio is measured by a lambda sensor in the exhaust manifold. As a consequence, a variable transport delay arises in the model considered. A non-linear control approach based on a Takagi–Sugenos model of the system is used. Then, two structures of control law are compared based on parallel distributed compensation control laws, which take into account the variable time delay. Finally, some simulations are given to show the efficiency of the developed control law.

PDC Control Design for Non-holonomic Wheeled Mobile Robots with Delayed Outputs

This paper presents a new technique for tracking-error model-based Parallel Distributed Compensation (PDC) control for non-holonomic vehicles where the outputs (measurements) of the system are delayed and the delay is constant. Briefly, this technique consists of rewriting the kinematic error model of the mobile robot tracking problem into a TS fuzzy representation and finding a stabilizing controller by solving LMI conditions for the tracking-error model. The state variables are estimated by nonlinear predictor observer where the outputs are delayed by a constant delay. To illustrate the efficiency of the proposed approach a comparison between the TS fuzzy observer and the nonlinear predictor observer is shown. For this study the reference trajectory is built by taking into account the acceleration limits of the mobile robot. All experiments are implemented on simulation and the real-time platform.