1. Jigsaw Team Estrogen Stephanie Wilson Amanda Newman Jessica Raymond
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…
CLTF:

5. This Reduces to…
CLTF:
Therefore…

6. Final Value Theorem
In Laplace Domain

7. Now for C(t)… CE: 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

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

12. Solve for C

13. Solve for A

14. Solve for B

15. Substitute for m, p, q m p q

16. Separate the terms

17. Manipulate…
to Fit Page 15 Formulas…

18. Inverse LaPlace Transform

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

20. Final Value Theorem
In Time Domain

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