Comparative Study of Identification Using Nonlinear Least Squares Errors and Particle Swarm Optimization Algorithms for a Nonlinear DC Motor Model

Abstract

For an accurate dynamic analysis of the real-world systems, there is an extensive demand for developing the mathematical models. An accurate mathematical model can be used for optimization, fault diagnosis, controller design, etc. Many studies have been performed for developing the mathematical models of the real-world systems. They commonly utilize linear models while ignoring the possible existing nonlinearities in the model. However, having a general mathematical model including nonlinearities has great significance in performance analysis and proper control of the systems. In this paper, two algorithms including Nonlinear Least Squares Errors (NLSE) and Particle Swarm Optimization (PSO) are utilized for model identification. For this aim, the nonlinear model of a Direct Current (DC) motor is used as a case study to compare the performance of the two algorithms. In the first step, a white-box mathematical model of the DC motor including the nonlinear friction terms is developed. Then, the artificial data is generated through the developed model with the real parameters of a DC motor. Finally, NLSE and PSO algorithms are carried out to determine the unknown parameters of the nonlinear model through generated artificial data. All unknown parameters of the model are identified at the same time. The results of the two algorithms are evaluated and compared. It is shown that the PSO algorithm determines the model parameters more accurately compared to the NLSE algorithm.