Pole Placement as a Dominant Second-Order System
Design the tape servomotor by the dominant second-order poles method to have no more than 5 % overshoot and a rise time of no more than $4 \text{ sec}.$ Keep the peak tension as low as possible.

Question

Pole Placement as a Dominant Second-Order System
Design the tape servomotor by the dominant second-order poles method to have no more than [latex] 5% [/latex] overshoot and a rise time of no more than [latex] 4 ext{ sec}. [/latex] Keep the peak tension as low as possible.

Accepted Answer

From the plots of the second-order transients in Fig. 3.18, a damping ratio [latex] ζ = 0.7 [/latex] will meet the overshoot requirement and, for this damping ratio, a rise time of [latex] 4 ext{ sec} [/latex] suggests a natural frequency of about [latex] 1/1.5.[/latex] There are five poles in all, so the other three need to be placed far to the left of the dominant pair. For our purposes, “far” means the transients due to the fast poles should be over well before the transients due to the dominant poles, and we assume a factor of [latex] 4 [/latex] in the respective undamped natural frequencies to be adequate. From these considerations, the desired poles are given by

Question 7.EX.20: Pole Placement as a Dominant Second-Order System Design the ...

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