control_handout

control_handout - Introduction to Control Systems Open-loop...

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1 Introduction to Control Systems ) ( s G C y(t) ) ( s G p r(t) + + d(t) Plant Controller Open-loop control: Control system elements: G p (s) ("plant") is the system to be controlled. G c (s) is the "controller" The objective is to make y(t) to following a specific function, e.g. r(t). In perfect world 1 ) ( s G = then y(t) = r(t) In perfect world, ) ( s G p c , then y(t) r(t) However, () p Gs is not known exactly, and disturbance d(t) is always inevitable. => Feedback is necessary
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2 The close loop transfer function is: assuming d(t) = 0 ) ( s G C y(t) ) ( s G p r(t) + + d(t) + _ Closed-loop control: () cl Ys Gs R s = Sensitivity to disturbance: D(s) -> Y(s), assuming r(t)=0 = Proportional controller: K s G c = ) ( , assuming 1 ) ( >> s KG p = Tracking a step reference: r(t)=u(t)
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3 Steady state error: () E sR sY s =−= Using the final value theorem (valid only when the closed-loop system is Using the final value theorem (valid only when the closed loop system is stable), lim ( ) ss t ee t →∞ == For a step reference r(t)=u(t), s s R 1 ) ( = ss e = ss e = 0 when (0) (0) cp GG = ∞ , i.e.
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control_handout - Introduction to Control Systems Open-loop...

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