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Transforming C(s) into C(t): Negative Feedback Control with Proportional Only Controller

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.

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Transforming C(s) into C(t): Negative Feedback Control with Proportional Only Controller

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  1. 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)

  2. Goal: Advantages and disadvantages of different t0 (dead time) values System: Any FOPDT system in a negative feedback loop with a Proportional-Only Controller

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

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

  5. This Reduces to… CLTF: Therefore…

  6. Final Value Theorem In Laplace Domain 0 0 0

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

  8. Substitute for Easier Math… CE: m p q

  9. Now Complete the Square

  10. Simplify the last term Distribute the left side Factor the right

  11. Solve for C

  12. Solve for A

  13. Solve for B

  14. Substitute for m, p, q m p q

  15. Separate the terms

  16. Manipulate… to Fit Page 15 Formulas…

  17. Inverse LaPlace Transform

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

  19. Final Value Theorem In Time Domain 0 0

  20. CONCLUSION • Disadvantages of Increased t0 • Increase in t0 results in a decrease in the ultimate 0 0gain of the loop (Kcu) • Poor performance • Limited values of stable operating gain Advantages of Increased t0 Reaches steady state faster Larger values of stable operating gain Bigger gain is better

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