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7-7 Effects of Adding Poles and Zeros to Transfer Functions

7-7 Effects of Adding Poles and Zeros to Transfer Functions. Adding of a Pole to the Forward-Path Transfer Function : Unity-Feedback System Adding of A Pole to the Closed-Loop Transfer Function Addition of a Zero to the Closed-Loop Transfer Function

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7-7 Effects of Adding Poles and Zeros to Transfer Functions

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  1. 7-7 Effects of Adding Poles and Zeros to Transfer Functions • Adding of a Pole to the Forward-Path Transfer Function : Unity-Feedback System • Adding of A Pole to the Closed-Loop Transfer Function • Addition of a Zero to the Closed-Loop Transfer Function • Adding of a Zero to the Forward-Pth Transfer Function : Unity-Feedback System

  2. 7-7-1 Adding of a Pole to the Forward-Path Transfer Function : Unity-Feedback System Figure 7-30 Unit-step responses of the system with the closed-loop transfer function in eq. (7-145)

  3. The addition of a pole to the forward-path transfer function generally has the effect of increasing the maximum overshoot of the closed-loop system.

  4. 7-7-2 Adding of A Pole to the Closed-Loop Transfer Function Figure 7-31 Unit-step responses of the system with the closed-loop transfer function in Eq. (7-145)

  5. Figure 7-32 Unit-step responses of the system with the colsed-loop transfer function in Eq. (7-146) As for as the overshoot is concerned, adding a pole to the closed-loop transfer function has just the opposite effect to that of adding a pole to the forward-path transfer function.

  6. 7-7-3 Addition of a Zero to the Closed- Loop Transfer Function Figure 7-33 Unit-step responses of the system with the closed-loop transfer function in Eq. (7-147)

  7. adding a zero to the closed-loop transfer function decreases the rise time and increases the maximum overshoot of the step response.

  8. 7-7-4 Adding of a Zero to the Forward-Path Transfer Function : Unity-Feedback System Figure 7-34 Unit-step responses showing the effect of adding a zero to the closed-loop transfer function.

  9. although the characteristic equation roots are generally used to study the relative damping and relative stability of linear control systems, the zeros of the transfer function should not be overlooked in their effects on the transient performance of the system. Figure 7-35 Unit-step responses of the system with the closed-loop transfer function in Eq. (7-151)

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