直流电机模型参数的直接辨识.doc

Direct Ientifcation of DC Electromotor Model ParameterZHOU Ruxun，ZHANG Z elong，QI Yingchuan(Department of Electronic Warfare，Air Force Radar Academy，Wuhan Hubei 430019，China)ABSTRACT：How to work out the mathematic model of DC electromotor is very important to design a DC adjusted velocity systemThe parameter error of the DC electromotor model worked out by traditional method is big，and the inline parameter identification cant be acquired by traditional methodIn order to work out the model parameter of DC electromotor，this paper gives a direct identification arithmetic which is used to work outDC electromotor mathematic mode1Taking an electro motor as example，the electro motor model parameter and it s step response Curve are worked ou t by traditional method and the direct identification arithmetic respectivelyThrough the comparis on of the two simulation results，it isproved that the direct identification arithmetic is feasible and the accuracy of the model is improved clearlyKEYW ORDS： Direct identification： Direct current electromotor；Transfer function 1. Introduction In high-precision DC servo systems and DC speed control system, DC motor components are in a wide range of applications as executive ones. The design of the system depends on the model parameters calculation results of the DC motor. The mathematical model of DC motor from its two equations: electrical equation and mechanical properties equation. In the condition of knowing the parameters, we can get model parameters of the motor. The traditional method is using empirical formulas and experimental method for static parameters, but usually model errors and cannot obtain the online parameter identification. This paper gives the direct identification algorithm, using direct identification algorithm and traditional method respectively won the parameters for the model of the DC motor, and then the comparative simulation, through comparing, it can be proved that the direct identification algorithm can easily and effectively obtain DC motor transfer function model online or offline ways. And it can gain tne transfer function model of DC motor more accurate than the traditional methods. 2. The direct identification principle of DC motor model The electrical equation and mechanical equations of DC motor is as following. (1) (2) in the above, is the total inertia converted to the motor shaft, is electric potential coefficient of the motor . Make Laplace transform for the two formulas above, after a breaf calculating and sorting we can get transfer function model of DC motor speed relative to the input voltage. It is as follow: (3) In the formula above, mechanical time constant Tm=：JRa/CeCT, Electrical time constant Ta=La/ Ra. The most common and convenient way to get processing transfer function model is the direct identification method. Using direct identification algorithm to estimate transfer function parameters could comes to a accurate result. From (3) we know that the transfer function of DC motor is a second order without lag transfer function. The second order without lag transfer function model is as follow: (4) Comparing with formula (3) and (4),we can get known that the second order without lag transfer function model and transfer function of model DC motor are in corresponding relation. As to TaTm, we can approximatly think Tm+TaTm, K=1/Ce. So we can identify the transfer function model of DC motor by direct identification of second-order without lag transfer function model. For formula (4), when the step input range equal a, the step response is As follow:Set T1=T2, and joined with the white noise (t),thenTo build a linear equation, we set then Set From formula (8) can get According to the formula above, we can make least squares operations to the model parameters. For sampling points =Ts, 2Ts, 3Ts,.,NTs, Ts is sampling interval, and N is sampling points, which comes to linear equations. in the formula, Then we get the least-square estimation of parameters ,3 simulation and analysis Selecting a DC machines as example, the nameplate parameters are as follow: Rated voltage Ue=230V, rated current Ie=10.4A, rated speed ne=377rad/s, rated output power Pe=2.0KW, inertia on the motor shaft J=0.027J/s2.Give the DC motor first-order step voltage a=230V, measure the motor speed by using tachogenerator, and record the motor speed change with storage oscilloscope, then sampling the speed within 0 2s with a sampling frequency of 100Hz, totally picked 200 points. This paper emulated the step response curve of the motor by using the traditional method and direct identification respectively, and then compare with the sampling curve. 3.1 Using the traditional methods for DC motor parameters According to the nameplate parameters, and empirical formula, we can get:the internal resistance of the motorthe electric potential coefficientThe armature inductance Among them, p is pole number, p=1 in the motor, so Output rated torque of the motor The torque coefficientElectrical time constantMechanical time constant So put Tm,Ta,Ce into formula (3) for transfer function model of DC motor speed relative to the input voltage, it is as follow Set T1=Tm,T2=Ta,K=1/Ce, and then put them into formula (5), use MATLAB to emulate for the curve, and compared with sampling curve as shown in figure 1. From figure 1, we can probably values the transfer function of DC motor by using the traditional experience method, but the results not perfectly approximation the dynamic process of DC motor, it is of a larger error range and cant get parameters online, we can seek transfer function of DC motor when all the nameplate parameters are know. So the traditional methods have already cant meet the requirements.Figure1. Traditional methods of obtaining the step response simulation curve and sampling curve contrast 3.2 Using direct identification algorithm for parameters of DCmotor Set the 200 sampling data to y(iTi), i=1,2,3,.,N, N=200. Approximate obtained A(iTi), B(iTi) according to the definition of integral, and then matrix and . Put and into formula(11) for the estimation of , it can estimate transfer function model parameters T1,T2,K, take them into formula (4), then we can draw transfer function model of DC motor. Through MATLAB simulation calculation, T1=0.3023s, T2=0.0215s, K=1.6338, that is to say electromechanical time constant Tm=0.3023s, Ta=0.0215s, EMF Ce=1/K=0.612. Put T1,T2,K into formula (5) and use MATLAB to simulate speed-time curves of DC motor as figure 2 shows. Simulation results can be good approximation the dynamic process, therefore the obtained transfer function model parameters is accurate.Figure 2. Step response simulation curve by direct identification algorithm and sampling curve contrast Through the figure l and figure 2 comparison, it can be clearly seen that using direct identification algorithm to evaluate the transfer function model parameters is superior than traditional methods, it overcomes the difficulties of the traditional methods and improved the precision. The simulation results proved that direct identification method is feasible. 4. Conclusion The simulation result