control systems questions

(b) FIGURE 6 shows a proportional plus derivative controller that has a proportional band of 20% and a derivative action time of 0.1 minutes. Const ruc t t he sha pe of t he out put wa ve form for t he t ri a ngul a r input waveform shown, if the input rises and falls at the rate of 4 units per minute.

FIG. 6

8. (a) FIGURE 7 shows the closed-loop response of a plant to a step input when the proportional only gain was set to 4. Use the 'Quarter Amplitude Response Method' to estimate the required settings of a P + I + D controller.

FIG. 7 Plant Response to Step Input

(b) If the same plant was 'tuned' using the 'Ultimate Cycle Method', estimate the P + I + D controller settings if a proportional only gain of 6 was required to produce steady oscillations.

Time (seconds)

Pr oc

es s o

ut pu

t

+5

–5

10 20 30 40 50 600

P+Dθi θo

1 minute

9

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