Question 6.1: In an induction motor, with the nameplate data given below, ......
In an induction motor, with the nameplate data given below, under a blocked-rotor condition, the flux is initially built up to its rated value (with i_{sd}(0)=3.1 A). The toque is commanded to change as a step (i^*_{sq}=4.0 A) from zero to nearly 50% of its rated value. Plot the dynamics of i_{sd}, i_{sq}, slip speed ω_{dA}, and the error θ_{err} as functions of time if all the motor parameters are estimated correctly except the rotor resistance is estimated to be one-half its actual value.
Nameplate Data
Power: 3 HP/2.4 kW
Voltage: 460 V (L-L, rms)
Frequency: 60 Hz
Phases: 3
Full-Load Current: 4 A
Full-Load Speed: 1750 rpm
Full-Load Efficiency: 88.5%
Power Factor: 80.0%
Number of Poles: 4
Per-Phase Motor Circuit Parameters
R_s = 1.77 Ω
R_r = 1.34 Ω
X_{\ell s} = 5.25 Ω (at 60 Hz)
X_{\ell r} = 4.57 Ω (at 60 Hz)
X_m = 139.0 Ω (at 60 Hz)
Full-Load Slip = 1.72%
The iron losses are specified as 78 W and the mechanical (friction and windage) losses are specified as 24 W. The inertia of the machine is given. Assuming that the reflected load inertia is approximately the same as the motor inertia, the total equivalent inertia of the system is J_{eq} = 0.025 kg · m².
Figure 6-4 shows the simulation diagram in Simulink and the dynamics of i_{s d}, i_{s q}, slip speed \omega_{d A}, and the error \theta_{\text {err }} are plotted in Fig. 6-5. We should note that after a dynamic response, each variable comes to a constant steady state value. Also, for R_{ r _{-} \text {est }}=0.5 R_r, which results in k_\tau=0.5, \theta_{ err } has a positive value in steady state.
