DC Motor (Take class notes)Effective damping and inertia• We have driven the dynamic equation for a DC motor as(1)• From the above we can obtain effective damping and inertia• Equation (1) becomes+ ++ + + ++( + + ++ + + (+Effective damping (B) Effective inertia (J)Motor transfer function (1)• Our goal is to obtain the relationship between the input (V) and output (Θ) in the s domain:• It takes a few steps:- The first step in on the input side- The second step is to plug in I(s) and V(s) in the above equation:++ ++ =( + +(s)) Motor transfer function (2) + [( + + ]+From the above equation one can obtain the following if we ignore –treat it as a disturbance inputSince L is very small, one can haveSo the relationship between the rotational speed of the joint and the input voltage is a first order system. / = / / Typical values of the parameters (U12M4T motor)::::::::0.101 nt-m/amp (14.4 oz-in/amp)0.101 v-sec/rad3.03×10nt-m-sec/rad (0.043 oz-in-sec/rad)2.33×10nt-m-sec2/rad (0.033 oz-in-sec2/rad)1020.75Ω 100same as Plug in the values into the transfer function we can obtain = / / .Time constant =
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