Boubekeur Targui

Generalised observers for a class of non-linear systems

A general class of MIMO non-linear systems with unknown inputs is considered with a view to observer synthesis. The particularity of this class of systems lies in the fact that the expression of the outputs depends on the unknown inputs. Different situations are considered, and in each case, a non-linear observer, synthesised under appropriate hypotheses, is proposed to jointly estimate all state variables together with the unknown inputs. Simulation results are given in order to highlight the performances of the proposed observers.

A cascade observer for a class of MIMO non uniformly observable systems with delayed sampled outputs

Abstract This paper investigates the observation problem for a class of MIMO non uniformly observable systems in the presence of sampled and delayed outputs. A high gain observer is first designed for the delay-free and continuous output measurement case. The observer gain involves the resolution of an appropriate Lyapunov differential equation allowing to show that the underlying observation error converges exponentially to zero under a well defined persistent excitation condition. This observer is then redesigned to cope with the output sampling process as well as the output delay thanks to an appropriate cascade structure composed of a set of dynamical subsystems. The first subsystem in the cascade is an impulsive continuous–discrete time observer which provides the estimation of the delayed state and each remaining subsystem in the cascade is a predictor which estimates the state over a small horizon equal to a fraction of the time delay in such a way that the state of the last predictor is an estimate of the system actual state. The exponential convergence to zero of the observation error related to the cascade observer is established for arbitrarily long delays provided that the maximum value of the sampling partition diameter is lower than a certain given bound. Simulations results are given to highlight the performance and the main properties of the proposed cascade observer.

Adaptive high gain observer for uniformly observable systems with nonlinear parametrization

In this paper, an adaptive observer is proposed for a class of uniformly observable nonlinear systems with nonlinear parametrization. The main novelty of the proposed observer is the introduction of characteristic indices, which allow a natural construction of the gain matrix. The main properties of the proposed observer are highlighted in simulation through an example dealing with the identification of an engine transient fuel characterized by a delay on the input.

STATE AND UNKNOWN INPUTS ESTIMATION FOR A CLASS OF NONLINEAR SYSTEMS

Abstract A high gain observer is proposed for a class of multi-output nonlinear systems with unknown inputs in order to simultaneously estimate the whole state as well as the unknown inputs. The gain of this observer does not require the resolution of any dynamical system and is analytically given. Moreover, its tuning is reduced to the choice of two real numbers. The performances of the proposed observer are demonstrated in simulation through an illustrative example.

Observer Design for Time Delay Nonlinear Triangular Systems

Abstract In this work an observer for a class of delayed nonlinear triangular systems with multiple and simple time-delay is proposed. The main feature of this observer is that it is easy to implement because of its constant gain. First, the observer synthesis is presented for nonlinear systems with variable time-delay and is extended for nonlinear systems with multiple time-delay. The observer performance is evaluated through numerical simulations.

Cascade observer design for a class of uncertain nonlinear systems with delayed outputs

Abstract This paper proposes a state observer with a cascade structure for a class of nonlinear systems in the presence of uncertainties in the state equations and an arbitrarily long delay in the outputs. The design of the observer is achieved under an appropriate set of assumptions allowing to establish the ultimate boundedness of the observation error. Indeed, a suitable expression of the asymptotic observation error, involving the delay, the bound of the uncertainties and the Lipschitz constant of the system nonlinearities, is derived. Besides, it is shown that this ultimate bound is a decreasing function of the cascade length and is equal to zero in the uncertainty-free case. The observer design is first carried out in the case where the output measurements are continuously available and subsequently extended to the case where the outputs are available only at (non equally spaced) sampling instants. The performance of the proposed observer and its main properties are highlighted through illustrative simulation results involving an academic example.

On-line Monitoring and Modeling of Multivariable Nonlinear Systems: Methanol/Ethanol Distillation

Abstract This paper presents a simplified nonlinear dynamic model for binary distillation columns. Then, it is used for synthesize an innovative high-gain observer for on-line estimation of the plate compositions. Both, the model and the observer are evaluated via real-time laboratory experiments of a methanol-ethanol distillation process.