Samira Kamoun

Adaptive discrete-time sliding-mode control of nonlinear systems described by Wiener models

ABSTRACT In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme.

An iterative parametric estimation method for Hammerstein large-scale systems: a simulation study of hydraulic process

This paper aims at developing an iterative method which permits to estimate the parameters of single-input single-output (SISO) large-scale nonlinear systems, described by Hammerstein mathematical models. We particularly focus on the dynamic large-scale nonlinear systems, which are made up of several interconnected nonlinear monovariable subsystems. Each subsystem can operate in a stochastic environment and be described by a discrete-time Hammerstein mathematical model with known structure variables (order, delay) and unknown time-varying parameters. The problem formulation is achieved based on the prediction error method and the least-squares techniques. The convergence analysis of the recursive algorithm is provided using the differential equation approach and its performance is illustrated by treating two simulation examples.

Design of Self-Tuning Regulator for Large-Scale Interconnected Hammerstein Systems

This paper deals with the self-tuning regulator for large-scale stochastic nonlinear systems, which are composed of several interconnected nonlinear monovariable subsystems. Each interconnected subsystem is described by discrete Hammerstein model with unknown and time-varying parameters. This self-tuning control is developed on the basis of the minimum variance approach and is combined by a recursive algorithm in the estimation step. The parametric estimation step is performed on the basis of the prediction error method and the least-squares techniques. Simulation results of the proposed self-tuning regulator for two interconnected nonlinear hydraulic systems show the reliability and effectiveness of the developed method.

Parameter Estimation and Control of Induction Machine using a new Recursive Algorithm

Two schemes control for induction machine are proposed and compared. A new off-line recursive algorithm is used to estimate the parameters of a commercial 1 kW induction motor, which is described by a multivariable state space mathematical model. The self-tuning control scheme and the control scheme with disturbance compensation are proposed. Those techniques are based on the concept of quadratic optimal control. The schemes control performance is tested using stator current, voltage and speed measurements. The obtained results demonstrate the proposed schemes’s effectiveness.

Improved Discrete Techniques of Time-Delay and Order Estimation for Large-Scale Interconnected Nonlinear Systems

The selection of a suitable model structure is an essential step in system modeling. Model structure is defined by determining the class, the time delay, and the model order. This paper proposes improved structural estimation procedures for large-scale interconnected nonlinear systems which are composed of a set of interconnected Single-Input Single-Output (SISO) Hammerstein structures and described by discrete-time stochastic models with unknown time-varying parameters. An extensive Determinant Report (DR) algorithm is developed to determine the order of the process. An improved discrete-time technique based on Recursive Extended Least Squares with Varying Time (RELSVT) delay method is proposed to estimate the time delays of the considered system. The developed theoretical analysis and simulation results prove the validity and performance of the proposed algorithms.

Self-Tuning Control Scheme Based on the Robustness σ-Modification Approach

This paper deals with the self-tuning control problem of linear systems described by autoregressive exogenous (ARX) mathematical models in the presence of unmodelled dynamics. An explicit scheme of control is described, which we use a recursive algorithm on the basis of the robustness σ-modification approach to estimate the parameters of the system, to solve the problem of regulation tracking of the system. This approach was designed with the assumptions that the norm of the vector of the parameters is well-known. A new quadratic criterion is proposed to develop a modified recursive least squares (M-RLS) algorithm with σ-modification. The stability condition of the proposed estimation scheme is proved using the concepts of the small gain theorem. The effectiveness and reliability of the proposed M-RLS algorithm are shown by an illustrative simulation example. The effectiveness of the described explicit self-tuning control scheme is demonstrated by simulation results of the cruise control system for a vehicle.

A high-gain adaptive observer for discrete-time nonlinear systems

This paper focuses on the development of adaptive observer for a class of nonlinear discrete-time systems. A high-gain observer is used to estimate the unknown parameters and state variables. The problem formulation is achieved based on the Euler approximation method. The proposed algorithm is developed to guarantees the convergence of parameters and state variables to their true values. Based on a new formulation of the high-gain observer, sufficient conditions and assumptions to ensure asymptotic convergence are established. An example involving a typical bioreactor illustrates some results of the proposed observer.

Design of state and parametric estimation algorithms for nonlinear systems with hysteresis-saturation nonlinearities

The paper deals with the parameter estimation problem of Wiener state-space models with hysteresis-saturation nonlinearities. A recursive parametric and state estimation algorithm is presented for the Wiener system by combining the adjustable model idea, the least squares technique and the Kalman filter principle. The basic idea is to decompose the hysteresis-saturation nonlinearity into two asymmetric saturation nonlinearities and to estimate jointly the state variables, the parameters and the internal variable of the considered Wiener model using the available input-output data. The proposed recursive algorithm can be extended to nonlinear systems with other hard nonlinearities.

Identification of nonlinear dynamic systems described by Hammerstein state-space models with discontinuous nonlinearities

This paper deals with the parameter estimation problem of Hammerstein state-space models with different nonlinearities. The basic idea is to develop a recursive algorithm which estimate jointly the system model parameters and the state variables by combining the adjustable model method, the least squares technique and the Kalman filter. A numerical example is provided to test the flexibility and the effectiveness of the proposed algorithm.

Adaptive tracking control algorithms for large-scale interconnected nonlinear systems

The present work proposes two control algorithms for a class of large-scale deterministic systems, which are composed into a set of interconnected monovariable systems and defined by discrete oriented block model with variable parameters. The purpose of these control algorithms is to formulate the tracking problem permitting each interconnected system output to pursue a certain time-varying reference trajectory. Each control algorithm is developed with a direct or indirect scheme and is incorporated into a recursive estimator, used to estimate the system parameters. This estimation step is established using the prediction error approach and the least-squares method. A numerical simulation example is cured to validate the developed theoretical results.