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i) Calculate the eigenvalues of a 100 hp, 1150 rpm dc machine at rated flux with no extra load inertia. Use the "hot" value of the armature resistance. Calculate estimates of the resulting speed overshoot and settling time (within 2%) for a step armature voltage input, beginning at an initial current of 0.
ii) Now assume that a closed-loop current regulator is introduced as shown in Fig. 2.7-3 of the book. What are the new eigenvalues of the motor-plus-regulator system if the current regulator gain Ki is set to 10? Ignore the mechanical damping constant (B=0) in Fig. 2.7-3. Calculate estimates of the resulting overshoot and settling time for a step current input, beginning at an initial current of 0.
iii) Now consider a closed-loop speed control system as shown in Fig. 2.7-5. Assume that the current regulator dynamics are very fast compared to the outer speed loop and the current regulator gain is high enough so that it is effectively "ideal". Calculate the eigenvalue of this closed-loop system for Kp=100, τz=∞. (Assume B=D=0 again.) Calculate the resulting output speed overshoot and approximate settling time of the closed-loop system for a step speed command input.
Now you have to digitally implement this circuit. Compute a difference equation which if you implement will behave exactly like this circuit.
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