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Jigsaw Puzzle 3 rd Team

Jigsaw Puzzle 3 rd Team. Angela Purkey Jason Powell Mena Aziz. Engr 328 4-10-2007. Outline. Controller Gain Ultimate Controller Gain Block Diagram Conclusion. Controller Gain. Controller gain ,Kc , is the change in output divided by the change in input (units) %

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Jigsaw Puzzle 3 rd Team

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  1. Jigsaw Puzzle3rd Team Angela Purkey Jason Powell Mena Aziz Engr 328 4-10-2007

  2. Outline • Controller Gain • Ultimate Controller Gain • Block Diagram • Conclusion

  3. Controller Gain • Controller gain ,Kc , is the change in output divided by the change in input (units) % • You have control to set what the system Gain would be but you can’t manipulate the ultimate controller Gain, Kcu

  4. Ultimate Controller Gain • Kcu = 1/ AR • Kcu obtains a phase shift of (-180°) When the (amplitude ratio intersects with utltimate frequency) • At that instance Kcu reaches a phase angle shift of (-180°) • Amplitude ratio = 1/kcu for • Ex: (0.08 %/(lb/min)) = (1/12 %/(lb/min))

  5. Block Diagram • M(t) = input= A sin (ωt) , A= Amplitude • C(t)= (AR) * A sin(ωt+u), AR= Amplitude Ratio • e(t) = (r(t)- c(t)) • Error = setpoint – system output.

  6. Phase Angle = (-180°) • C(t)= (AR) * A sin (ωt-180°) • sin(wt-180°)= • =sin(ωt)*cos(-180) + cos(ωt)* sin(-180) • =sin(ωt)*(-1) + cos(ωt)*(0) • =-sin(ωt) • C(t)= -(AR) * A sin (ωt-180°) • Evaluated using the dougle angle formula using trig Identity.

  7. Block Diagram Algebra e(t) = (r(t)- c(t))=0-[-(AR)*Asin(ωt)] e(t)=(AR)* Asin(ωt) e(t) m(t) r(t) c(t) Kc System c(t)

  8. Block Diagram Algebra e(t)*Kc=m(t) m(t)=(AR)* Asin(ωt)*kc m(t)=Kc*(AR)*Asin(ωt) But earlier: m(t)=Asin(ωt) e(t) m(t) Kc

  9. Block Diagram Algebra Asin(ωt)= Kc*(AR)*Asin(ωt) Asin(ωt)/Asin(ωt)=(Kc*(AR)*Asin(ωt))/Asin(ωt) 1=Kc*(AR) AR=1/Kc m(t) c(t) System

  10. Conclusion • When the phase angle =-180 , AR=1/Kc • An advantage of knowing this is that we know where AR=1/Kc occurs.

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