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Please answer and explain Q4b)

DC-DC Converter Machine Drive Consider the circuit diagram of the DC-DC converter and separately excited DC machine in Figure 1. The parameters of this drive system are as follows: $V_{s}=220VR_{A}=2.45ΩL_{A}=5mHK_{m}=1.25V/rad/sf_{s}=5kHz$ The converter can be considered as lossless. Take further the brush voltages as zero in the calculations. Figure 1: Circuit diagram of DC-DC converter and DC motor. 1. Calculate the highest shaft speed that can be obtained with this DC machine drive. 2. With a duty cycle of $D=0.75$ and armature current of $I_{A}=5A$ calculate the speeds of the DC motor drive with two-quadrant and four-quadrant switching. 3. Calculate the supply powers of the converter to the DC machine for the operating condition of (2) with two-quadrant and with four-quadrant switching. 4. With $Q_{3}$ permanently switched off and $Q_{4}$ permanently switched on answer the following questions: (a) With the DC-machine operating in steady state at $800r/min$ and the armature current equals to $I_{A}=$ -10 A (current flowing out at terminal $A_{1}$ ), determine the switching duty cycle $D$ at which the converter is switched. (b) For the condition of (a) determine the ripple in the armature current $Δi_{A}$. (c) For the condition of (a) draw the waveforms of the armature voltage, $v_{A1−A2}$, and the armature current $i_{A}$ reasonable on scale on one graph.