A field-oriented drive system will be applied to a 230-V, 20-kW, four-pole, 60-Hz induction motor which has the following equivalent-circuit parameters in ohms per phase referred to the stator: R_l = 0.0322 R₂ = 0.0703 X₁ = 0.344 X₂ = 0.353 X_m = 18.6. The motor is connected to a load whose torque can be assumed proportional to speed as T_load = 85(n/1800) N · m, where n is the motor speed in r/min. The field-oriented controller is adjusted such that the rotor flux linkages λ_DR are equal to the machine's rated peak flux linkages, and the motor speed is 1300 r/min. Find

a. The electrical frequency in Hz.

b. The rms armature current and line-to-line voltage.

c. The motor input kVA. If the field-oriented controller is set to maintain the motor speed at 1300 r/min, write a MATLAB script to plot the rms armature V/Hz as a percentage of the rated V/Hz as a function of λ_DR as λ_DR is varied between 80 and 120 percent of the machine's rated peak flux linkages.