Thomas Laurain

LMI-based control synthesis of constrained Takagi-Sugeno fuzzy systems subject to L 2 or L ∞ disturbances

This paper is devoted to the development of a new saturated non-parallel distributed compensation control law for disturbed Takagi-Sugeno fuzzy systems subject to both control input and state constraints. In order to cover a large range of real-world applications, both L 2 and L ∞ disturbances are considered which result in two different control design procedures. A parameter-dependent version of the generalized sector condition is effectively exploited in a fuzzy Lyapunov control framework to handle the control input saturation. Moreover, the proposed control method is based on the concept of robust invariant set which is able to provide an explicit characterization of the estimated domain of attraction of the closed-loop system. Different optimization algorithms are also proposed to deal with the trade-off between different closed-loop requirements in a local control context. The design conditions are expressed in terms of linear matrix inequalities which can be solved efficiently with available solvers. The numerical examples illustrate how the proposed methodology leads to less conservative results as well as less computational complexity when compared to very recent works in the literature.

Observer design to control individual cylinder spark advance for idle speed management of a SI engine

This paper aims to present an original methodology to design an observer that can be used in idle speed control using a global command for the throttle and an individual command for the spark timing. To develop an efficient control, we need previously to estimate unmeasured parameters such as the torque generated by each cylinder. Two observers are proposed: the methodology for the first one is based on a discrete periodic Takagi-Sugeno approach, and the second one on an unknown input observer. Finally, some simulation results showing the performance of the developed methodology are provided. The model used for our simulation is based on a dynamic hybrid one.

Periodic Takagi-Sugeno Observers for Individual Cylinder Spark Imbalance in Idle Speed Control Context

This paper aims to present a systematic methodology for designing periodic observers for cyclic nonlinear systems represented by Takagi-Sugeno models. An application to idle speed control of a spark-ignition engine will be proposed. Thanks to the estimated individual cylinder values, we can detect an imbalance of each cylinder (unbalanced cylinder). Based on a dynamic hybrid model, some simulation results will prove the efficiency of our method.

Non-quadratic approach for control design of constrained Takagi-Sugeno fuzzy systems subject to persistent disturbances

This paper is devoted to the development of a new saturated control law for constrained Takagi-Sugeno fuzzy systems. These systems are subject to both control input and state constraints and also persistent disturbances bounded in amplitude. The design procedure is formulated through linear matrix inequalities (LMIs) form which can be solved by means of convex optimization techniques. Based on the concept of robust invariant set in non-quadratic Lyapunov control framework, the proposed method provides a characterization of the closed-loop domain of attraction. Numerical example is given to demonstrate the interests of the proposed methodology.

Avoiding Matrix Inversion in Takagi–Sugeno-Based Advanced Controllers and Observers

Many of the recent advances on control and estimation of systems described by Takagi–Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.

A new air-fuel ratio model fixing the transport delay: Validation and control

Air-fuel ratio control is a crucial problem for engine control since it is one of the most important issues related to pollution reduction. The main difficulty in air-fuel ratio control is the time-varying delay. We propose a new model that includes the delay. This model is identified using real dataset from an engine test bench. The time-varying delay is made constant by using a change of domain. The nonlinearities of the model are handled with the Takagi-Sugeno representation and a linear controller is designed using the Lyapunov direct method. Simulation results highlight the efficiency of the proposed approach compared to classic maps-based controllers.

Replica of an Advanced Takagi-Sugeno discrete observer without matrix inversion

This paper aims to present a systematic methodology for designing a Replica of an Advanced Takagi-Sugeno (RATS) discrete observer. Advance observers for nonlinear systems under Takagi-Sugeno representation have been designed for years using efficient structure such as non-PDC (Parallel Distributed Compensation), which it is powerful and, in some cases, it is the only observer able to estimate an unknown value. However, in spite of these advantages, this observer strategy presents an inconvenient: The use of matrix inversion. This paper will present the RATS observer which is equivalent an observer using the non-PDC structure without matrix inversion. By a stability analysis, not only the efficiency is proved but also its validity. Finally, some simulation results will emphasize the originality and the power of the proposed RATS observer.

Estimation-based control law for appproximating Takagi-Sugeno-based controller

This paper aims to manage the problem of matrix inversion in advanced Takagi-Sugeno-based controllers such as most of the non-Parallel Distributed Compensation. These controllers are difficult to use in embedded computers that have limited performances due to technologic resources. The originality of the proposed method is to use an observer written under the descriptor form for approximating the fuzzy matrix inversion. Thanks to such an observer, the advanced controller can be approximated in both steady and transient phases. Consequently, an Estimation-based Control Law for Approximating Takagi-Sugeno-based (ECLATS) controller is developed using Lyapunov stability analysis and Linear Matrix Inequalities formulation. This ECLATS controller can provide similar performances than the advanced fuzzy ones, but without any matrix inversion. Numerical examples prove the efficiency of the estimation by comparison.