Mondher Farza

High-gain observer for a class of time-delay nonlinear systems

This article proposes a high-gain observer design for a class of nonlinear systems with multiple known time-varying delays intervening in the states and the inputs. In the free delay case, the class of systems under consideration coincides with a canonical form characterising a class of multi-output nonlinear systems, which are observable for any input. The underlying high-gain design has been mainly motivated by its inherent simplicity from both design and implementation points of view. Indeed, the observer gain is determined from an explicit resolution of a time-invariant Lyapunov algebraic equation up to the specification of a single design parameter. An academic observation problem is addressed to illustrate the effectiveness of the proposed observer.

Continuous-Discrete Time Observers for a Class of MIMO Nonlinear Systems

This technical note addresses the observer design problem for a class of continuous-time dynamical systems with non-uniformly sampled measurements. More specifically, we propose an observer that runs in continuous-time with an output error correction term that is updated in a mixed continuous-discrete fashion. The proposed observer is actually an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. Nevertheless, we shall show that such an impulsive system can be put under the form of a hybrid system composed of a continuous-time high gain observer coupled with an inter-sample output predictor. Two design features of the proposed observer are worth emphasizing. Firstly, the observer calibration is achieved through the tuning of a scalar design parameter. Secondly, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. Simulations results involving a flexible joint robot arm are given in order to highlight the performance of the proposed observer.

Non-linear observers for state and unknown inputs estimation

High gain observers are proposed for a class of multi-inputs multi-outputs non-linear systems with unknown inputs in order to simultaneously estimate the whole state together with the unknown inputs. The gain of these observers does not require the resolution of any dynamical system and is explicitly given. Two situations are analysed and an observer is proposed in each case. In the first situation, the dynamics of the proposed observer can be arbitrarily assigned while in the second one only a part of the observer dynamics can be freely assigned. Two simulation examples are given in order to highlight the performance of the proposed observers.

Adaptive fuzzy observer for uncertain nonlinear systems

In this paper, one presents a unified adaptive fuzzy observer design framework for a class of uncertain nonlinear systems. The corrective term of the proposed observer involves a well-defined design function which is shown to be satisfied by the commonly used high-gain (HG)-based observers, namely the usual HG observers and the sliding mode observers together with their implementable versions. Without resorting to the strictly positive real condition or the filtering of the observation error, a proportional-integral law for updating the fuzzy parameters is proposed. The proportional part is used to deal with the fuzzy approximation errors and the external disturbances. Ultimately boundedness of the error signals in the closed-loop system is shown through Lyapunovs direct method.

Simple Cascade Observer for a Class of Nonlinear Systems With Long Output Delays

This note proposes a cascade observer for a class of nonlinear systems with global Lipschitz nonlinearities in the presence of delayed output measurements. The head of the cascade is a high gain observer while the remaining systems are state predictors providing an estimate of the actual state. The key feature of the proposed observer is the introduction of a matrix design parameter that allows to tune the prediction process dominant dynamics with an identical simple structure for all the predictors. The design of the observer is carried out by considering a set of conditions under which the exponential convergence to zero of the observation error is established. In particular, it is shown that the number of the subsystems in the cascade observer depends on the size of the delay and the Lipschitz constant. The observer is first designed assuming a constant time delay. The underlying design approach is then appropriately adapted to deal with the time-varying delay. The effectiveness of the proposed observer with respect to two existing cascade observers is particularly highlighted through a comprehensive comparative analysis and simulation results.

BIOESTIM: software for automatic design of estimators in bioprocess engineering

This paper describes BIOESTIM, a software package devoted to on-line estimation in bioprocess engineering. BIOESTIM enables bioengineers automatically to design state and parameter estimators from a minimal knowledge of the process kinetics. Such estimators allow development of software sensors capable of coping with the lack of reliable instrumentation suited to real-time monitoring. The estimator building procedure through BIOESTIM starts up from a dynamical material balance model of the bioprocess. This model, supplied by the user, is next completed by other information with no requirement for numerical values: the user has only to specify available measurements, coupled reactions and the known yield coefficients. On the base of this knowledge, BIOESTIM proceeds to symbolic algebraic manipulations on the model in order to study estimation possibilities and check identifiability of yield coefficients. When the design of an estimator is possible, the corresponding equations are automatically generated. Moreover, these estimators are stored in a user-specified file which is automatically interfaced with a specialized simulation software including data treatment and numerical integration packages. Thus, the user can simulate the estimator performances under various operational conditions using available experimental measurements. A typical example dealing with microbial growth and biosynthesis reactions is given in order to illustrate the main functional capabilities of BIOESTIM. BIOESTIM has been designed and written in a modular fashion. The module dealing with estimators design makes use of symbolic computation; it is written in Mathematica and runs on every computer on which this language is available.

Output feedback controller for a class of nonlinear systems

This paper deals with an observer based output feedback controller for a class of controllable and observable nonlinear systems with an admissible tracking capability. Two fundamental features are worth to be mentioned. The first one consists in the high gain nature of the underlying state feedback control and observer designs. More specifically, a unified high gain control design framework is proposed thanks to the duality between control and observation. The second feature consists in incorporating a filtered integral action into the control design. The filtering is mainly motivated by measurement noise sensitivity reduction while the integral action allows to achieve a robust offset free performance in the presence of step like disturbances. An academic servo problem, involving a nonlinear double integrator, is addressed to show the effectiveness of the proposed control design method.

CAMBIO: software for modelling and simulation of bioprocesses

CAMBIO, a software package devoted to bioprocess modelling, which runs on Apollo computers, is described. This software enables bioengineers to easily and interactively design appropriate mathematical models directly from their perception of the process. CAMBIO provides the user with a set of design symbols and mnemonic icons in order to interactively design a functional diagram. This diagram has to exhibit the most relevant components with their related interactions through biological and physico-chemical reactions. Then, CAMBIO automatically generates the dynamical material balance equations of the process in the form of an algebraic-differential system by taking advantage of the knowledge involved in the functional diagram. The model may be used for control design purpose or completed by kinetics expressions with a view to simulation. CAMBIO offers facilities to generate a simulation model (for coding of kinetics, introducing auxiliary variables, etc.). This model is automatically interfaced with a specialized simulation software which allows an immediate visualization of the process dynamical behaviour under various operational conditions (possibly involving feedback control strategies). An example of an application dealing with yeast fermentation is given.

Sampled output observer design for a class of nonlinear systems

This paper presents a continuous-discrete time observer for a class of uncertain nonlinear systems with non uniformly sampled measurements. Two features of the proposed observer are worth to be pointed out. The first one consists in the simplicity of its calibration, while the second one lies in its comprehensive convergence analysis. More specifically, it is shown that the observation error lies in a ball centered at the origin and whose radius is proportional to the bounds of the uncertainties and the sampling partition diameter. In the free uncertainties case, the exponential convergence to zero of the observation error is established under a well-defined condition on the maximum value of the sampling partition diameter. The effectiveness of the proposed observer is emphasized throughout simulation results involving the estimation of the reaction rate in a typical bioreactor.

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.