Question 10.3.3: Assuming that the motor is field-controlled, draw the block ......
Assuming that the motor is field-controlled, draw the block diagram of the speed-control system shown in Figure 10.3.4 and obtain its command and disturbance transfer functions.
A field-controlled motor is controlled by varying the field current i_f while keeping the armature current constant. Figure 10.3.5 shows the block diagram of a proportional control system for controlling the speed of such a motor and was obtained by modifying the motor diagram in Figure 6.5.7 in Chapter 6.
The transfer functions can be obtained either by reducing the block diagram or by transforming the equations and eliminating all variables except the inputs and output. Recalling that K_dK_{pot} = K_{tach}, we can write the following equation from the diagram
From the diagram we can see that the motor torque is given by
T_m(s)=\frac{K_T}{L_f s+R_f} V_m(s)Finally, we have Ω_L (s) = Ω_m(s)/N. We obtain the transfer functions by eliminating V_m(s), T_m(s), and Ω_m(s) from these equations. Let
K_P=K_{\text {tach }} K_1 K_a (1)
Using the parameter K_P , the diagram can be simplified as shown in Figure 10.3.6. The transfer functions are
\frac{\Omega_L(s)}{\Omega_r(s)}=\frac{K_P K_T}{N L_f I_e s^2+N\left(R_f I_e+c_e L_f\right) s+N c_e R_f+K_P K_T} (2)
\frac{\Omega_L(s)}{T_L(s)}=-\frac{\left(L_f s+R_f\right) / N}{N L_f I_e s^2+N\left(R_f I_e+c_e L_f\right) s+N c_e R_f+K_P K_T} (3)
