Q2: In this context La is negligible compared to the mechanical properties of the system. The current through armature responses very fast compared to the Inertia of the system. Because of this we can practically ignore the inductance La. It is like ignoring the weight of a gas pedal in a car model.. it does not affect the system at all in practice.
Thank you, Steve.
I'm sorry to ask this but I still don't see any particular reason why La can be ignored. My apologies if the answer is there in your post. Perhaps, then I'm acting more dumb than usual!
Please also note that I have updated my previous post with a new question. Kindly help me.
Regards
PG
You could ignore La if, say, it was 5 μH but I don't think it has such a low value in this case.
However, it does make sense to compare the time constants themselves such as La*Ra and J0*b0.
Hi MrAl
I basically agree. It's important to have units that match. I think you meant to divide to find the time constants? For example, τ=L/R, not τ=L*R. In making the ratio r, a unitless definition is better than r=J/L because J/L has units, and you can't compare something with units to 1 meaningfully in general.
However, I disagree that "Comparing La to Ra does not help", because this seems to be the exact argument that the textbook is making, but obviously it is sL compared to R. Hence, this is the best answer to give to PG, unless you disagree with the treatment given by the book. Also, comparing Jo and bo suffers from the same problem of units that don't match. We must compare sJ with b, to compare, and this depends on frequency. However, the book treatment assumes bo and Jo are both important and they are retained in the analysis.
Also, what did you mean when you wanted to use wL to compare to R, what do you intend to make 'w' here?
I intended the omega (ω), not w, to mean the frequency. Basically sL+R shows up in the transfer function. The book replaces sL+R with R to make the approximation that L is negligible. This one simplification allows a very simple transfer function to be established in eqn. 3.120. However, s is really jω for typical sinusoidal driving. Hence, the complex value sL+R is being replaced by the real value of R at low frequency. In other words, there is a high frequency pole that can be ignored for typical frequencies in motor control.
As far as what values to use for ω to see if the approximation is valid, I tried to answer this twice already. The mechanical frequency of the motor can be related to the electrical frequency as ω=N ωr, where ωr is the mechanical frequency, ω is the electrical frequency and N is the number of pole pairs per revolution on the motor construction. This is strictly correct for synchronous motors in steady state, and approximately correct for all motors in typical transient cases. In other words, the motor operating speed gives some hint at the electrical bandwidth required for control, and this sets the frequency range to consider for the inductance, to see if it can be neglected.
I dont see any reference in the text that suggests that La is being eliminated due to a "high frequency component" of any kind. I checked it again, and i dont see it. Did i miss it anyway? That's possible, so if you can point it out i can understand what you are getting at a little better perhaps.
Until then, i still see the fact that La and R are not enough to look at in order to determine what is significant and what is not.
You mentioned that "5uH is not significant at radio frequencies" but i believe that is the wrong view to take, even though it might seem correct, because the basic issue is the response due to R and La and the response due to J and f, and both need to be considered in order to determine what is negligible and what is not. Suppose J is negligible instead of L, how would we know looking at only R and L (or R and wL)?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?