Iterative identification algorithm for Wiener nonlinear systems using the Newton method

The Wiener system is an important class of output nonlinear systems. This paper presents a Newton iterative parameter estimation algorithm for Wiener nonlinear systems. The simulation results show that the proposed algorithm is effective. The proposed algorithm can be combined with other iterative methods to identify other linear or nonlinear systems with colored noises.     

Gradient based iterative parameter identification for Wiener nonlinear systems

This paper focuses on the identification problem of Wiener nonlinear output error systems. The application of the key-term decomposition technique provides a special form of the Wiener model with polynomials, where all the model parameters to be estimated are separated. To solve the identification problem of Wiener nonlinear output error systems with the unmeasurable variables in the information vector, an auxiliary model-based gradient iterative algorithm is presented by replacing the unmeasurable variables with their corresponding iterative estimates. The performances of the proposed algorithm are analyzed and compared by using numerical examples.     

A new fault isolation and identification method for nonlinear dynamic systems: Application to a fermentation process

In this paper, a new method of fault isolation and identification based on parameter intervals for nonlinear dynamic systems is proposed. The practical domain of the value of each system parameter is divided into a certain number of intervals. After verifying all the intervals whether or not one of them contains the faulty parameter value of the system, the faulty parameter value is found, the fault is therefore isolated. The method provides the estimation of the faulty parameter value and its bounds when the fault is isolated. It fits many kinds of nonlinear dynamic systems with ideal isolation and identification speed. The performances of the proposed method are illustrated by the simulation results of a fermentation process.     

Stochastic gradient with changing forgetting factor-based parameter identification for Wiener systems

The parameter estimation problem is considered for a class Wiener systems. First, the effect of the forgetting factor on the stochastic gradient algorithm is analyzed. Then, a Wiener system stochastic gradient with a changing forgetting factor algorithm is presented which makes full use of the forgetting factor. Finally, an example is provided to test and verify the effectiveness of the proposed algorithms.     

Iterative parameter identification methods for nonlinear functions

This paper considers identification problems of nonlinear functions fitting or nonlinear systems modelling. A gradient based iterative algorithm and a Newton iterative algorithm are presented to determine the parameters of a nonlinear system by using the negative gradient search method and Newton method. Furthermore, two model transformation based iterative methods are proposed in order to enhance computational efficiencies. By means of the model transformation, a simpler nonlinear model is achieved to simplify the computation. Finally, the proposed approaches are analyzed using a numerical example.     

Recursive parameter identification for fermentation processes with the multiple model technique

This paper considers parameter identification problems for a fermentation process. Since the fermentation process is nonlinear, it is difficult to use a single-model for describing such a process and thus we use the multiple model technique to study the identification methods. The basic idea is to establish the model of the fermentation process at each operation point by means of the least squares principle, to obtain multiple models with different points, and then use the weighting functions or interpolation methods to compute the total model or the global model. Finally, a numerical example is provided to test the effectiveness of the proposed algorithm.     

Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a global optimization method is developed to seek the optimal key parameters. Numerical results show that the nonlinear time-delay system can describe the fed-batch fermentation process reasonably.     

Trajectory tracking for a class of switched nonlinear systems: Application to PMSM

This paper proposes a state-dependent switching control for a class of switched nonlinear systems, whose model describes a permanent magnet synchronous machine (PMSM) fed by a three-phase voltage source inverter. Due to its high torque density, high efficiency and wide velocity range, this electrical drive is widely used for traction and several applications in robotics, aerospace, electric vehicles among others. The proposed design conditions are based on a non-quadratic Lyapunov function, dependent on the machine shaft displacement, and assure asymptotic tracking of a pre-specified time-varying rotational velocity profile with guaranteed performance. Properties of the nonlinear system under consideration are used to derive design conditions expressed in terms of linear matrix inequalities that can be solved efficiently. Special cases involving asymptotic stability toward step and ramp velocity profiles are presented. Experimental results are used to validate the proposed technique.     

Detection,isolation and identification of multiple actuator and sensor faults in nonlinear dynamic systems: Application to a waste water treatment process

The goal in many fault detection and isolation schemes is to increase the isolation and identification speed. This paper, presents a new approach of a nonlinear model based adaptive observer method, for detection, isolation and identification of actuator and sensor faults. Firstly, we will design a new method for the actuator fault problem where, after the fault detection and before the fault isolation, we will try to estimate the output of the instrument. The method is based on the formation of nonlinear observer banks where each bank isolates each actuator fault. Secondly, for the sensor problem we will reformulate the system by introducing a new state variable, so that an augmented system can be constructed to treat sensor faults as actuator faults. A method based on the design of an adaptive observers’ bank will be used for the fault treatment. These approaches use the system model and the outputs of the adaptive observers to generate residues. Residuals are defined in such way to isolate the faulty instrument after detecting the fault occurrence. The advantages of these methods are that we can treat not only single actuator and sensor faults but also multiple faults, more over the isolation time has been decreased. In this study, we consider that only abrupt faults in the system can occur. The validity of the methods will be tested firstly in simulation by using a nonlinear model of waste water treatment process with and without measurement noise and secondly with the same nonlinear model but by using this time real data.