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#### PROBLEMS

4.1. The two-phase ac servomotor of Problem 3.16 is used in a simple positioning system, as shown in Figure P4.1. Assume that a difference amplifier, whose gain is 10, is used as the error detector and also supplies power to the control field.

Figure P4.1

(a)  What are the undamped natural frequency ωn and the damping ratio ζ ?

(b)  what are the percent overshoot and time to peak resulting from the application of a unit step input?

(c)  Plot the error as a function of time on the application of a unit step input.

4.2. Repeat Problem 4.1 with the gain of the difference amplifier increased to 20. What conclusions can you draw from your result?

4.3. The two phase ac servomotor and load, in conjunction with the gear train specified in Problem 3.19, is used in a simple positioning system as shown in Figure P4.1. Assume that a difference amplifier, whose gain is 20, is used as the error detector and also supplies power to the control field.

(a)  What are the undamped natural frequency and damping ratio ζ?

(b)  What are the percent overshoot and time to peak resulting from the application of a unit step input?

(c)  Plot the error as a function of time on the application of a unit step input.

4.4. Repeat Problem 4.3 with the gain of the difference amplifier increased to 40. What conclusions can you draw from your results?

4.5. Repeat Problem 4.3 with the gain of the difference ...

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