Question 5.2: In this example, we will consider the drive system of Exampl......
In this example, we will consider the drive system of Example 5-1 under vector control described earlier. The initial conditions in the motor are identical to that in the previous example. We will neglect the torque loop in this example, where all the motor parameter estimates are assumed to be perfect. (We will see the effect of estimate errors in the motor parameters in the next chapter.) The objective of the speed loop is to keep the speed at its initial value, in spite of the load torque disturbance at t = 0.1 second. We will design the speed loop with a bandwidth of 25 rad/s and a phase margin of 60°, using the same procedure as in Reference [1].
Initial flux values are the same as in Example 5-1. These calculations are repeated in a MATLAB file EX5_2calc.m on the accompanying website. To design the speed loop (without the torque loop), the torque expression is derived as follows at the rated value of i^{*}_{sd} : In steady state under vector control, i_{rd} = 0 in Fig. 5-3. Therefore, in Eq. (5-9)
\lambda_{r d}=L_r i_{r d}+L_m i_{s d}.\hspace{30 pt} \text{(5-9)}
\lambda_{r d}=L_m i_{s d} \quad \text { (under vector control in steady state). }\hspace{30 pt} \text{(5-13)}
Substituting for\lambda_{r d} from Eq. (5-13) and for i_{rq} from Eq. (5-2) into the torque expression of Eq. (5-7) at the rated i^{*}_{sd} ,
i_{r q}=-\frac{L_m}{L_r} i_{s q}.\hspace{30 pt} \text{(5-2)}
T_{e m}=\frac{p}{2} \lambda_{r d}\left\lgroup\frac{L_m}{L_r} i_{s q}\right\rgroup.\hspace{30 pt} \text{(5-7)}
T_{e m}=\underbrace{\frac{p}{2} \frac{L_m^2}{L_r} i_{s d}^*}_k i_{s q}\quad \text {(under vector control in steady state),}\hspace{30 pt} \text{(5-14)}
where k is a constant. The speed loop diagram is shown in Fig. 5-9 where the PI controller constants are calculated in EX5_2calc.m on the basis that the crossover frequency of the open loop is 25 rad/s and the phase margin is 60°.
The simulation diagram of the file EX5_2.mdl (included on the accompanying website) is shown in Fig. 5-10, and the torque and speed are plotted in Fig. 5-11.
