(d) The stator parameters of the above machine are Ls = 200mH and R, =150m2, and the motor leakage coefficient is 0.01. It is to be run off a vector-controlled converter with a PWM switching frequency of 8kHz and the speed is measured with a 4096-line incremental encoder. i) Design a PI controller for the current control loops to give a natural frequency O., of 300Hz with a damping factor of 0.75. ii) Select a suitable sampling frequency for the current control loops. iii) If the encoder output is sampled with sampling frequency of (ii) above, determine the resolution of the encoder in rpm (the minimum speed it can measure). State how the resolution can be increased and how this affects the implementation of the vector control system. (d) The stator parameters of the above machine are Ls = 200mH and R, =150m2, and the motor leakage coefficient is 0.01. It is to be run off a vector-controlled converter with a PWM switching frequency of 8kHz and the speed is measured with a 4096-line incremental encoder. i) Design a PI controller for the current control loops to give a natural frequency O., of 300Hz with a damping factor of 0.75. ii) Select a suitable sampling frequency for the current control loops. iii) If the encoder output is sampled with sampling frequency of (ii) above, determine the resolution of the encoder in rpm (the minimum speed it can measure). State how the resolution can be increased and how this affects the implementation of the vector control system