Question 10.3.6: Derive the transfer functions for the case where the armatur......
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.
