# Parameters Identification of Nonlinear DC Motor Model

The genetic algorithms (GA) with global optimization character and the simplex method are combined and used into the application of the parameter identification. The nonlinear dynamic model of an actual DC motor including the nonlinear friction torque is established. By means of the compound evolution algorithms proposed, the detail procedure of the all parameters identification in the DC motor with actual system’s input-output data are given. The effectiveness of identification is verified by the comparison between actual system values and model’s in the different situations including the motor running in the dead zone, saturated zone and linear zone, respectively.

DC motor has been widely used in the engineering field due to its simple structure, outstanding control performance and low cost. In high accuracy servo control system, high control performance of DC motor is needed. The traditional model of DC motor is a 2-order linear one, which ignores the dead nonlinear zone of the motor. Unfortunately, the dead zone caused by the nonlinear friction would bring great effect to servo systems. Therefore, it is vital to model the dead zone of DC motor accurately in order to improve the performance of servo system. Concerning the nonlinear friction of motor, Armstrong-helouvry B. et al. [1] have already conducted thorough research and proposed a nonlinear friction model. This friction model relates to the speed and time, and the motion goes four areas from the static friction to the coulomb friction. Moreover, this friction model structure is quite complex, and 7 parameters need to be identified. In order to simplify applications and reflect the real nonlinear friction of the motor accurately, a simplified friction model was proposed by Cong S. et al. [2], which is expressed as
Where, is the Coulomb friction torque (cTNm⋅); sT is static friction torque (Nm⋅); α is time constant; ω is the angular speed of the rotor (ra). d/s
A method used to identify the nonlinear DC motor model was introduced , which identified the linear part model and nonlinear friction model of DC motor, respectively. The parameters of linear part model were identified by using least square method, and the
parameters of nonlinear friction model were identified through experiments. Even though this method could identify all the parameters of DC motor model including the nonlinear friction, the parameters of linear part model and nonlinear friction model must be identified separately, which undoubtedly decreases the efficiency and accuracy of system identification. Due to these disadvantages, a new method which could identify the linear and nonlinear part models simultaneously is needed to increase the efficiency and accuracy of system identification.
Genetic Algorithms is a kind of stochastic search algorithm based on the rule of evolution of the biological universe, which was firstly proposed by Holland [4] in 1975. GA has the ability to search global optimal solution of the space without being trapped in local minima. There are a great amount of applications of GA in the field of nonlinear system identification, and many researchers introduce the identification of motors or power electronics systems based on GA. Though GA has the ability to search global optimal solution of the space, the local search ability of this algorithm is poor, especially when the optimization problem is complex, and GA may take relatively long time to search the global optimal solution. In addition, nonlinear system identification is a kind of quite complex optimization problem, thus just using GA to conduct parameter identification would decrease the convergence speed and practicality of the algorithm. On the other hand, simplex method [16] has the ability to converge the optimal solution more quickly and does not need the differential information of objective function, thus this method could be used to identify nonlinear system conveniently and efficiently.
In this paper, genetic algorithms and simplex method are adopted to identify the parameters of nonlinear DC motor model. GA is applied to conduct the global search and find promising regions of the search space, and then simplex method is adopted to conduct local search based on the search result of GA. Additionally, the initial value of simplex method is the search result of GA, so this algorithm can assure that the global optimal solution is searched out efficiently. Because of the fast convergence speed of simplex method, the efficiency of parameter identification would be increased significantly. And in order to increase the accuracy of the model, the nonlinear friction torque in (1) is adopted to model the dead zone of DC motor in this paper. Some of contents of this paper have published in the .

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