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Dynamic Response of Simple Transfer Functions

Dynamic Response of Simple Transfer Functions. Standard process inputs. Step input Ramp input Rectangular pulse Sinusoidal input Impulse input. Response of 1 st -order process --- Step input. Response of 1 st -order process --- Ramp input. Response of 1 st -order process

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Dynamic Response of Simple Transfer Functions

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  1. Dynamic Response of Simple Transfer Functions

  2. Standard process inputs • Step input • Ramp input • Rectangular pulse • Sinusoidal input • Impulse input

  3. Response of 1st-order process --- Step input

  4. Response of 1st-order process --- Ramp input

  5. Response of 1st-order process ---- Sinusoidal input

  6. Response of 1ST-order process --- Step response with dead time

  7. Over damped process Under damped process

  8. Y(t)/kp t/t

  9. Areaa = m Slope=S y Inflection Point K I3 I2 tm q I1 qS

  10. 0.73 y/k t0.73/(t1+t2) 0.5

  11. 0.73 y/k 0.5

  12. y/k t/t

  13. Response of under damped processes b d c a

  14. Rise time= t0.9-t0.1 b d c a

  15. Overshoot =(y1-yss)/yss b y1 y3 d c yss a y2

  16. Decay ratio=(y3-yss)/(y1-yss ) b y1 y3 yss d c yss a y2

  17. Settling time b y1 y3 yss d c yss a y2 ts

  18. y/k t/t

  19. Dynamic Response Characteristics of More Complicated Process • Pole and zero Effect on dynamic response • Pure time delay: polynomial approximation to • Approximation of higher order transfer functions : Half Rule • Interacting and non-interacting processes

  20. Pole and zero and their effects on dynamic response

  21. Pole and zero and their effects on dynamic response (continued)

  22. Pole and zero and their effects on dynamic response (continued)

  23. Pole and zero and their effects on dynamic response (continued) See Page 138

  24. Pure time delay y(t) x(t)

  25. Polynomial approximation

  26. Approximation of higher order transfer functions

  27. Approximation of higher order transfer functions---Half rule • Half of the largest neglected time constant to the existing time delay (if any) • The other half is added to the smallest retained time constant • Time constants smaller than the largest neglected time constant are approximated as time delay by:

  28. Half rule: Examples Neglected time constants: 3, 0.5, -0.1 Approximation:

  29. Half rule: Example 2 Approximation: Neglected time constants: 0.2, 0.05

  30. 100oC T 20oC 0% [ T ] 100% T- 20 = 80 x { [T]/100}

  31. Scaling: T- 20 = 80 x { [T]/100} Ts-20 = 80 x { [Ts]/100} G = 80/100 [G] = ST/100 [G] M = Sm/100 [M]

  32. Y(s) M(s) 100% 0%

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