Lizeth Torres

A Robust Nonlinear Observer for Real-Time Attitude Estimation Using Low-Cost MEMS Inertial Sensors

This paper deals with the attitude estimation of a rigid body equipped with angular velocity sensors and reference vector sensors. A quaternion-based nonlinear observer is proposed in order to fuse all information sources and to obtain an accurate estimation of the attitude. It is shown that the observer error dynamics can be separated into two passive subsystems connected in “feedback”. Then, this property is used to show that the error dynamics is input-to-state stable when the measurement disturbance is seen as an input and the error as the state. These results allow one to affirm that the observer is “robustly stable”. The proposed observer is evaluated in real-time with the design and implementation of an Attitude and Heading Reference System (AHRS) based on low-cost MEMS (Micro-Electro-Mechanical Systems) Inertial Measure Unit (IMU) and magnetic sensors and a 16-bit microcontroller. The resulting estimates are compared with a high precision motion system to demonstrate its performance.

Original article: Exponential nonlinear observer for parametric identification and synchronization of chaotic systems

This work proposes the use of a new exponential nonlinear observer for the purpose of parametric identification and synchronization of chaotic systems. The exponential convergence of the observer is guaranteed by a persistent excitation condition. This approach is shown to be suitable for a wide variety of chaotic systems. In order to illustrate the observer design procedure, several examples with simulation results are presented.

Leak detection using parameter identification

Abstract This work proposes an approach to detect single and multiple leaks. The task is carry out by identifying the parameters of finite models associated with the leak events. The identification problem is attacked by using the Prediction Error Method (PEM). In addition, a frequency evaluation is realized to check the conditions for implementing the PEM or any other method which require an excitation condition.

Liénard type model of fluid flow in pipelines: Application to estimation

This paper highlights how fluid flow in a pipeline can be represented as a nonlinear model of so-called Liénard type. It is then shown how the structure of this model is suitable for the design of algorithms to identify parameters of a pipeline or estimate unmeasurable states. This approach is illustrated by simulation results, for instance showing how to estimate the Darcy-Weisbach friction coefficient or the fluid acceleration.

Design of a state observer to approximate signals by using the concept of fractional variable-order derivative

Abstract This article proposes a state observer to find a model for a given signal, i.e. to approximate a treated signal. The design of the state observer is based on a dynamical system of equations which is generated from the increasing-order differentiation of a n-th order Fourier series. This dynamical system is set in state space representation by considering that the Fourier series is the first state and the rest of the states are the successive derivatives of the series. The purpose of the state observer is the recursive estimation of the states in order to recover the coefficients from them. This set of coefficients produces the best fit between the dynamical system and the signal. The dynamical system used for the observer conception shall be, together with the estimated coefficients, the model that will describe the signal behavior. The special feature of the proposed observer is the order of the differential equations of the model on which it is based, d α ( t ) ν ( t ) / d t α ( t ) , which can take integer and non-integer values, i.e. α ( t ) ∈ ( 0 , 1 ] . Even more important, α ( t ) can be a smooth function such that α ( t ) ∈ ( 0 , 1 ] in the interval t ∈ [ 0 , T ] . The procedure to design the state observer of variable-order as well as some examples of its use in engineering applications are presented.

Modeling and Identification of the Restoring Force of a Marine Riser

The purpose of this paper is to provide a novel model to characterize the nonlinear restoring force of a marine vertical riser by using position-and-velocity-dependent polynomials. This model permits the obtaining of a specific state space representation—via the Lienard transformation—for the design of state observers that identify the structural parameters of vertical risers. The main results presented here are: (i) an approximation of the nonlinear restoring force by means of polynomials and its incorporation into a distributed parameter (DP) model, (ii) the transformation of the DP model into a Lienard system and (iii) an analysis of its observability and identifiability properties.

Observador No Lineal para la Estimación de Concentraciones en un Proceso de Destilación Metanol/Etanol

En este articulo se presenta el diseno de un observador no lineal de ganancia constante para la estimacion de las composiciones en los platos de una columna de destilacion a partir de las mediciones de las temperaturas en el hervidor y en el condensador. El observador se basa en un modelo no lineal de un proceso de destilacion binaria metanol/etanol. Tanto el modelo, como el observador, son validados experimentalmente en una columna de destilacion de laboratorio. La caracteristica principal del observador es que las ganancias son constantes y no requieren la resolucion de ningun sistema dinamico. La buena concordancia entre las variables estimadas y las mediciones experimentales permite concluir que este observador puede ser utilizado en aplicaciones de control no lineal

Event-triggered observer-based output-feedback stabilization of linear system with communication delays in the measurements

In this paper, an original framework is proposed for the stabilization of a linear system with delays in the measurements: i) an observer estimates the full state information of the plant from a partial measurement, ii) an event-based control technique computes and updates the control signal only when a certain condition is satisfied and iii) an event-based corrector updates the model used to calculate the control law when it deviates from the estimated state. It is notably proved that such a proposal renders the closed-loop system stable for larger delays in the measurements than in the classical continuous-time control case. Simulation results are provided.

Parameter identification of periodical signals: Application to measurement and analysis of ocean wave forces

Abstract This article presents an approach based on state observers to identify the parameters of an unknown periodic force exerted on a mechanical system. This approach comprises two stages and can be executed in real time by using only displacement measurements. The first stage goal is the estimation of the coefficients of a Fourier series that approximates the periodic force. From the estimated coefficients, the phase and the amplitude of the signal can be simultaneously computed; and from the estimated force, in a second stage, the frequencies of the signal can be estimated. To perform the tasks at each stage, two state observers were designed. To show the applicability of the proposed approach, the reconstruction of a wave force affecting a marine structure as well as the computation of the amplitude and phase of its spectral components was taken as case of study. The performance of the state observer was examined by means of simulations and off-line tests carried out with experimental data. Such data were obtained by executing laboratory tests and measuring waves in the Caribbean sea.

Auxiliary Signal Design and Liénard-type Models for Identifying Pipeline Parameters

This chapter presents the implementation of optimization algorithms to build auxiliary signals that can be injected as inputs into a pipeline in order to estimate—by using state observers—physical parameters such as the friction or the wave speed. For the design of the state observers, we propose to incorporate the parameters to be estimated into the state vector of Lienard-type models of a pipeline such that the observers can be constructed from the modified models. The proposed optimization algorithms guarantee a prescribed observability degree of the modified models by building an optimal input for the identification. The optimality of the input is defined with respect to the minimization of the input energy, whereas the observability through a lower bound for the observability Gramian, which is constructed from the Lienard-type models of the pipeline. The proposed approach to construct auxiliary inputs was experimentally tested by using real data obtained from a laboratory pipeline.