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# How to people understand how to model objects e.g Motors using R, L and C components?

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#### matrixofdynamism

There are models for DC motors, transmission lines and other things that I would like if someone can mention here!

I have been wondering for very long time as to how people actually get the idea on how these things are to be modeled through basic R, L and C components. I mean that seems to need a lot of imagination involved. How do people know how to model things and when do they know the model fits? I mean every model only works under certain circumstances right? What I mean by fitting is that, the model is trying to somehow replicate a real world object but in a way that makes it easier to analyze it and understand it and to work out its behavior in a given circuit, a good model is able to to do this well. But how did people make such good models in the first place?

I have had class on transmission lines where the line itself is modeled using R, L and C. How did people know how the model is to look like?

There are models for DC motors, transmission lines and other things that I would like if someone can mention here!

I will give you a simple example how a dc servo motor can be transferred into a model that can me simulated by any circuit simulation program.
The main task is to find the descriptive formula(s) for the whole unit.

Step 1: What is the step response of such a motor (switch-on behaviour) - as far as the rotation cycles (revolutions) n per unit time are concerned?
Answer: After switch-on the value of n will continuously increase until it reaches the final value - depending on the applied voltage step. This can be described as a P-T1 block (like a first order low-pass with gain).
Step 2: However, the motor will not start with a constant slope from the origin - instead the slope will increase from 0 to its final value (continuous increase of n). This is caused by the moment of inertia of the motor. Thus, we have a typical P-T2 behaviour.
Step 3: For a servo we are interested not in the revolutions n but in the rotation angle phi vs. time. Therefore - knowing that n=d(phi)/dt - we have to find the integral(n*dt). Because integration in the time domain is identical to a division by "s" in the frequency domain, the transfer function of the P-T2 block is divided by "s" - resulting in a transfer function H(s)=PHI(s)/Vin(s). This transfer function belongs to an I-T2 block and can be simply modeled using frequency-dependent parts like L and/or C.

Modelling non-electrical problems with electrical circuits requires to chose an equivalence of electrical and other physical quantities. They can be chosen differently, resulting in a respective transformation with scaling factors. In some cases, the equivalence is quite obvious. For a multiphysics (electrical/mechanical) DC motor model, you'll most likely associate voltage with velocity and current with torque and use the motor constants as scaling factors. Inertia will appear as a capacitor in this model, shaft elasticity as inductance.

Combining these elements, the PT2 behaviour mentioned by LvW will be represented by armature resistance and inductance together with motor and load intertia.

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