Transforming C(s) into c(t): Negative Feedback Control with Proportional Only Controller Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond.

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Presentation transcript:

Transforming C(s) into c(t): Negative Feedback Control with Proportional Only Controller Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond (We Laplace Transforms)

Goal: Advantages and disadvantages of different t 0 (dead time) values System: Any FOPDT system in a negative feedback loop with a Proportional-Only Controller

From Block Diagram Algebra… CLTF: Negative feedback control loop for FOPDT system with P-only controller

With Pade’s Approximation… Pade’s Approximation: CLTF:

This Reduces to… Therefore… CLTF:

Final Value Theorem In Laplace Domain 0 0 0

Now for C(t)… First we must simplify the denominator… for partial fraction decomposition CE:

Substitute for Easier Math… mpq CE:

Now Complete the Square

Simplify the last term Distribute the left side Factor the right

Solve for C

Solve for A

Solve for B

Substitute for m, p, q mpq

Separate the terms

Manipulate… to Fit Page 15 Formulas…

Inverse LaPlace Transform

Substitute A, B, C, m, p, q back into C(t)

Final Value Theorem In Time Domain 0 0

CONCLUSION Advantages of Increased t 0  Reaches steady state faster  Larger values of stable operating gain  Bigger gain is better Disadvantages of Increased t 0  Increase in t 0 results in a decrease in the ultimate 0 0gain of the loop (Kcu)  Poor performance  Limited values of stable operating gain