Method of Identification of the Mathematical Model of a Single Class of Linear Dynamic Systems with Variable Parameters
DOI:
https://doi.org/10.31649/1997-9266-2018-141-6-62-76Keywords:
linear dynamic system with variable parameters, mathematical model, identification method, crane electric drive, time-varying moment of inertia of rotating masses, time-varying load moment, modeling, comparative analysisAbstract
The article presents a method for identifying a mathematical model of a single class of linear dynamic systems with variable parameters, which includes a traction electric drive of a crane with variable parameters, caused by the change of the equivalent mass moment of inertia and the load moment of the traction motor when lifting (lowering) the load. The article also proposes and justifies the calculated relations to determine changes of the equivalent mass moment of inertia of the electric drive, caused by winding and unwinding of the cable, to which the load is suspended, on the reel connected through the reduction drive to the motor shaft. It also proposes and justifies calculated relations to determine changes of the load moment due to shortening and lengthening of the cable to which the load is suspended because of lifting or lowering the load. The article presents a step-by-step algorithm for determining all the parameters of a mathematical model of the dynamics of a crane electric drive with the time-varying moment of inertia of rotating masses and the load moment. The article presents the results of modeling the dynamics of the electric drive system during acceleration, braking, steady-state speed, idling and reverse of the traction motor considering variable parameters and using a mathematical model identified by specific passport characteristics of the traction motor, reduction drive and cable in the graphical programming environment Simulink of MATLAB application program package. The article also presents a comparative analysis of the obtained results and shows that the use of the classical equation of dynamics of an electric drive system with the constant moment of inertia and load moment leads to significant errors. And this is even despite the smooth speed control using frequency regulators for asynchronous motors and using power transistors for DC motors to change the voltage applied to the motor armature.
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