Jigsaw Puzzle 3 rd Team Angela Purkey Jason Powell Mena Aziz Engr

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) % You have control to set what the system Gain would be but you can’t manipulate the ultimate controller Gain, Kcu

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))

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.

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.

Block Diagram Algebra e(t) = (r(t)- c(t))=0-[-(AR)*Asin(ωt)] e(t)=(AR)* Asin(ωt) KcSystem e(t) r(t) m(t) c(t)

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

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

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