H. Rafaralahy

Brief Residual generator design for singular bilinear systems subjected to unmeasurable disturbances: an LMI approach

In this paper, a method to design a bank of unknown input residual generator for fault detection and isolation is investigated. The plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances. The measurements can be bilinear.

REDUCED-ORDER OBSERVER-BASED POINT-TO-POINT AND TRAJECTORY CONTROLLERS FOR ROBOT MANIPULATORS

This paper presents a design procedure for a reduced-order observer-based controller dedicated to n-joint robot manipulators. It is assumed that only the joint angular positions are measured. The joint angular velocities are estimated via an exponential reduced-order observer. Two types of control laws based on this observer are studied: point-to-point control with gravity compensation and trajectory control. Sufficient conditions to ensure the closed-loop stability are given. Performances of the reduced-order observer used with these two control laws are illustrated in a simulation study of a two-degrees-of-freedom robot manipulator.

A Robust and Recursive Identification Method for the Hammerstein Model

Abstract In this note, a robust identification method of non linear systems using the Hammerstein model is presented. The main property of the proposed approach is that parameters of the linear and nonlinear parts are estimated in a recursive way while the global convergence is guaranted. The proposed method consists first to transform the non linear representation into an input-output model linear in parameters, after, a regular transformation based on the pseudo-inverse technique allows us to estimate in the least squares sense parameters vector of the original realization. For the case of correlated noise, to model measurement disturbances, we propose a simple technique based on the pseudo-linear regression method and we investigate all parameters dependencies to obtain a consistent solution. Sufficient conditions for global convergence are derived. Two numerical examples with different correlation structures and different Signal to Noise Ratio values are provided.

Convergence analysis of the extended Kalman filter as an observer for nonlinear discrete-time systems

In the current paper, a modified version of the extended Kalman filter (EKF), when used as an observer for nonlinear discrete-time systems, is presented. The approach proposed consists in introducing time varying matrices to enhance convergence and stability of the obtained estimator. Based on a new formulation of the first order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem.

On unknown input observers for bilinear systems

Under appropriate transformation, the design of full-order and reduced-order observers for bilinear systems subjected to unknown inputs is proved to be equivalent to that of unknown input observers for linear ones. This result simplifies considerably the observer design comparatively to those proposed in the literature, and existence conditions of observer can be easily deduced. This approach is extended to the fault detection of bilinear systems. Existence conditions of the unknown input residual observers are given.

Disturbance decoupled diagnostic observer for singular bilinear systems

In this paper, a method to design a bank of unknown input residual generator for fault detection and isolation is investigated. The plant model is assumed to be a bounded controlled input singular bilinear system, subjected to unknown disturbances. The measurements can be bilinear.

Trajectory-tracking control design for an under-actuated quadrotor

Path-tracking and trajectory-tracking for a quadrotor are basic tasks when solving the motion control. The difference between path-tracking and trajectory-tracking is that the reference trajectory is generated by a suitable virtual quadrotor whereas the reference path is not required to be generated by a virtual quadrotor. In this paper, we propose a trajectory-tracking controller for an underactuated quadrotor. A new change in describing the dynamics of the quadrotor is presented from which we can determine the direction of motion of the quadrotor in the horizontal plane through its gravity center. After this change, we can separate the dynamics of the system into three sub-groups then combine with a coordinate transformation to design control for the quadrotor. The controller synthesis is based on Lyapunov direct method and the backstepping technique. Simulations illustrate the effectiveness of the proposed controller.

Asymptotic observers for a class of nonlinear singular systems

In this paper, we present a method for designing asymptotic observers for a class of nonlinear singular systems. Sufficient conditions for the existence of such observers are given and, the stability properties of the error dynamics are studied.

State observers for a class of bilinear descriptor systems subjected to unmeasurable disturbances

The class of singular bilinear systems (SBS) subjected to unmeasurable disturbances for which there exists an unknown input observer (UIO) with a linear observation error dynamics is characterised. Necessary and sufficient conditions for the existence of this UIO are given. It is shown that the design of such an UIO is equivalent to the design of an UIO for an appropriate singular linear system (SLS). Both full- and reduced-order UIOs are treated.

Residual Generator Design for Singular Bilinear Systems Subjected to Unmeasurable Disturbances: An LMI Approach

Abstract In this paper, a method to design a bank of full-order observer-based fault detection and isolation is investigated. The plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances. The design of the k th residual observer of the bank is divided into two parts. The first one consists in solving some algebraic (equality) constraints such that the k th residual is decoupled from the unknown inputs and the k th failure component. The second part consists in transforming the residual generator design into a dual robust stabilisation problem. Then the solution of an inequality constraint to ensure the exponential stability of the residual is obtained using a Linear Matrix Inequality (LMI) approach.