Parameter Identification Step 2 Stiffness and Fine-Tuning

6 Parameter Identification Step 2 Stiffness and Fine-Tuning 

Benefiting from the high gear ratio between the DC motor and the lead screw and the negligible moment of inertia of worm, worm gear, and coupling elements, the 3-DOF model in Fig. 9.8 is approximated by the 1-DOF model shown in Fig. 9.19. 

lead screw angular velocity gray DC motor angular velocity 

In this new and simplified model, the input is the gear angular displacement, Bq, which is equal to aw M- Furthermore, from this point on, in the numerical simulations, it is assumed that the angular velocity output of gearbox, Bq = coq, is constant. The equation of motion of this system is given by 

As mentioned above, in the second step of the parameter identification, the response firom the mathematical model, (9.31), is matched to the measurements by adjusting a set of parameters. The matching is only performed in the instances where a (possibly short lived) limit cycle behavior is observed in the measurements. The use of (almost) periodic data enables us to reduce the effects of transients thus improving the accuracy of the matching process. Consider the following cost function 

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