Comparative Study of an EKF-Based Parameter Estimation and a Nonlinear Optimization-Based Estimation on PMSM System Identification

In this study, two different parameter estimation algorithms are studied and compared. Iterated EKF and a nonlinear optimization algorithm based on on-line search methods are implemented to estimate parameters of a given permanent magnet synchronous motor whose dynamics are assumed to be known and nonlinear. In addition to parameters, initial conditions of the dynamical system are also considered to be unknown, and that comprises one of the differences of those two algorithms. The implementation of those algorithms for the problem and adaptations of the methods are detailed for some other variations of the problem that are reported in the literature. As for the computational aspect of the study, a convexity study is conducted to obtain the spherical neighborhood of the unknown terms around their correct values in the space. To obtain such a range is important to determine convexity properties of the optimization problem given in the estimation problem. In this study, an EKF-based parameter estimation algorithm and an optimization-based method are designed for a given nonlinear dynamical system. The design steps are detailed, and the efficacies and shortcomings of both algorithms are discussed regarding the numerical simulations.

Parameter Estimation of Spring-Damping System using Unconstrained Optimization by the Quasi-Newton Methods using Line Search Techniques

Optimization is the basic tools to study the behaviour of many complicated mechanical systems by having the knowledge of differential equations which determine the system. The basis of this paper was to present a method to estimate the parameters such as spring constant and damping coefficient of the spring damped system by unconstrained optimization using derivative methods Such as quasi-newton method by Broyden-Fletcher-Goldfarb-Shanno and davidon-Fletcher-Powell hessian updating method by using backtracking line search methods along with Armijo’s condition.it uses the output error approximation procedure. It shows the convergence of different methods which are used to estimate the parameters and how accurately they are measured.

A combination of Broyden-Fletcher-Goldfarb-Shanno (BFGS) and n-th section method for solving small-scale unconstrained optimization

In this research, a new inexact line search method known as n-th section method is used to obtain the step size in BFGS method. The n-th section method is the modification of the original bisection method. As in bisection method, this simple n-th section method divides each interval section with an even number of interval which is greater than two. This new proposed algorithm is compared with the original bisection, newton and secant method in terms of number of iteration. Numerical results is obtained based on small scale functions .This research shows that the algorithm is more efficient than using the ordinary line search methods. Besides, this proposed algorithm also possessed global convergence properties.