Question 10.3.6: Effect of Negligible Armature Time Constant Derive the trans...
Effect of Negligible Armature Time Constant
Derive the transfer functions for the case where the armature time constant L_{a}/R_{a} is small
If T_{L} = 0, we obtain Figure 10.3.10a. We can reduce the inner loop containing K_{b} to obtain part (b) of the figure. Setting L_{a} = 0 we obtain the diagram in part (c). Part (d) is obtained by replacing K_{P} with the arbitrary controller transfer function G_{c}(s) and defining
I = \frac{N R_{a} I_{e}}{K_{T}}
c = N \frac{R_{a} c_{e} + K_{T} K_{b}}{K_{T}}
The block diagram in part (d) is obviously a simpler representation than the diagram in part (a).
This simplified diagram will help us to demonstrate the use of various control algorithms in Sections 10.6 and 10.7. Note that it does not include the disturbance. To analyze the disturbance response, we need to use the diagram in Figure 10.3.9 or the disturbance transfer function given by equations (2) and (3) in Example 10.3.5.
