Sampled output observer design for a class of nonlinear systems (original) (raw)
Related papers
Automatica, 2015
A continuous-discrete time observer is proposed for a class of uncertain nonlinear systems where the output is available only at non uniformly spaced sampling instants. The underlying correction term depends on the output observation error and is updated in a mixed continuous-discrete fashion. The proposed observer is first introduced under a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. 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 in the case of noise-free sampled outputs, the observation error lies in a ball centered at the origin and which radius is proportional to the bounds of the uncertainties and the sampling partition diameter. Moreover, 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 ability of the proposed observer to perform a suitable estimation of the reactions rates in biochemical reactors is highlighted through a simulation study dealing with an ethanolic fermentation.
Cascade observer design for a class of nonlinear uncertain systems: Application to bioreactor
IFAC-PapersOnLine, 2016
The present work 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 output. The first system in the cascade allows to estimate the delayed state while each of the remaining systems is a predictor. Each predictor estimates the state of the preceding one with a prediction 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 design of the observer is achieved by assuming a set of conditions under which the ultimate boundedness of the estimation error is established. It is in particular shown that in the absence of uncertainties, the observation error converges exponentially to zero. In the presence of uncertainties, the asymptotic observation error remains in a ball which radius depends on the delay magnitude and can be decreased by appropriately choosing the cascade length and the observer design parameters. The performance of the proposed observer and its main properties are highlighted through a typical bioreactor model.
Observer Design for Uniformly Observable Systems With Sampled Measurements
IEEE Transactions on Automatic Control, 2013
This work considers the problem of observer design for continuous-time systems with sampled output measurements (continuous-discrete time systems). In classical literature and in many applications, the continuous-discrete time extended Kalman filter (EKF) is used in order to tackle this problem. In this work, using a normal form characterizing the class of nonlinear uniformly observable single output nonlinear systems, it is shown that a particular stationary solution of a continuous discrete time Lyapunov equation can be used in order to design a constant high gain observer. Explicit conditions are given to ensure global convergence of the observer. Finally, an illustration of this result is given using an example of a biological process.
A Simple Observer for Nonlinear Systems Applications to Bioreactors
Absrract-In this note, we construct an observer for nonlinear systems under rather general technical assumptions (lhe fact that some functions are globally Lipschitz). This observer works either for autonomous systems or for nonlinear systems that are observable for any input. A tentative application to biological systems is described.
Observer Design for Systems with Continuous and Discrete Measurements
IFAC Proceedings Volumes, 2009
Classical observers are constructed on the basis of the nature of the measurement signals, namely, a continuous observer requires continuous output measurements. In this work, a novel observer which estimates continuous states when continuous and discrete measurements are available is presented. By resetting the initial condition of the observer at each sample instant, the convergence of the continuous states is guaranteed. The application to the the estimation of substrate and biomass concentrations in an anaerobic wastewater treatment process in which continuous and discrete measurements usually appear, shows the feasibility of the proposed scheme.
Bioprocess Engineering, 1997
Simple discrete-time estimators which allow the on-line estimation of the kinetic rates from the measurements of components' concentrations inside a bioreactor are proposed. In fact, the proposed estimators are obtained by a direct forward Euler discretization of continuous-time estimators. The design of the estimators in the continuous as well as in the discrete-time does not require or assume any model for the kinetic rates. One of the main characteristics of these estimators lies in the easiness of their calibration. We here emphasize on the performances of the discrete version of these estimators, whose stability and convergence are proved under the same conditions as in the continuous case with an additional mild assumption on the sampling time. Simulation and real-life experiments results corresponding to the discrete estimation are given. The accuracy of the obtained estimates as well as the easiness of the estimators' implementation do constitute reliable and powerful arguments for their use, in particular in adaptive control schemes.
A Robust Asymptotic Observer for Chemical and Biochemical Reactors
IFAC Proceedings Volumes, 2003
A simple state observer is proposed for a class of lumped nonlinear time-varying systems useful in chemical and biochemical engineering. It is shown that this asymptotic nonlinear observer is stable in the presence of time-varying elements and robust in the face of initial conditions uncertainty and a total lack of knowledge on the nonlinearities of the system. Experimental results are presented using a model of an anaerobic digestion process for the treatment of industrial wastewater from a wine distillery and tested using real data obtained from a I m 3 continuous fixed bed pilot bioreactor.
Nonlinear observers for state and parameter estimation in biochemical processes
2002
A systematic approach for the on-line estimation of the non measured component concentrations and the reaction rates inside chemical and biochemical reactors is presented. Two appealing features of the presented approach are worth to be mentioned. Firstly, the estimators of the reaction rates are easy to implement and in particular to calibrate. Secondly, the estimation of these as well as that of the non measured component concentrations does not necessitate any change of coordinates and it fully takes advantage of the process balance model. Simulation results related to a biotechnological process are given in order to illustrate the performances of the proposed estimators.
IFAC-PapersOnLine
In this paper, we address the problem of nonlinear continuous-discrete adaptive observer design for a class of system with sampled data measurements subject to sensor nonlinearities. The main difficulty of the considered class of system is coming from the fact that the output equation contains unknown parameters which renders the design of a classical sampled data observer difficult. To overcome this difficulty, we propose a new online continuousdiscrete adaptive observer which ensures a simultaneous exponential convergence of both states and parameters. Comparing to other observer structures, our design is characterized by a simpler structure thanks to the introduction of a parametric adaptation law. To show the efficiency of our proposed approach, numerical simulations have been performed for different values of sampling time. In addition, the delayed-sampled measurements case is also illustrated.
Continuous-Discrete Time Observer for a class of MIMO Nonlinear Systems
HAL (Le Centre pour la Communication Scientifique Directe), 2013
In this paper, we investigate the possibility of designing an observer for a class of continuous-time dynamical systems with non-uniformly sampled measurements. More specifically, we propose an observer with a time varying gain witch converges exponentially under some conditions on the sampling partition diameter. The proposed observer is 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. As it is customarily done in the literature, we show that such an impulsive system can be split into two subsystems and be put under the form of a hybrid system which is designed using a continuoustime observer together with an inter-sample output predictor. Simulations results involving a typical bioreactor are given to show the effectiveness of the proposed observer.