Ideal Derivative Compensation Techniques Quiz
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Questions and Answers

What information does the root locus graphically display?

  • Frequency response
  • Phase margin and gain margin
  • Steady-state response
  • Transient response and stability information (correct)

    • What does the root locus allow us to choose?

  • The proper loop gain to meet a transient response specification (correct)
  • The settling time of the system
  • The type of controller to use
  • The sampling frequency

    • What happens as the gain is varied in the root locus?

  • The settling time decreases
  • We move through different regions of response (correct)
  • The overshoot increases
  • The system becomes more stable

    • What does the root locus limit us to in terms of transient responses?

    <p>Responses that exist along the root locus</p> Signup and view all the answers

    How can the flexibility in the design of a desired transient response be increased?

    <p>By designing for transient responses that are not on the root locus</p> Signup and view all the answers

    What is the goal when trying to speed up the response at a specific point on the root locus?

    <p>To achieve the desired transient response without affecting the percent overshoot</p> Signup and view all the answers

    What is the purpose of compensating systems with additional poles and zeros?

    <p>To achieve the desired response without changing the existing system</p> Signup and view all the answers

    Where can compensating poles and zeros be added in the system?

    <p>At the low-power end of the system before the plant</p> Signup and view all the answers

    How can additional poles and zeros be generated for compensating systems?

    <p>With a passive or an active network</p> Signup and view all the answers

    What is the impact of adding compensating poles and zeros on the system order?

    <p>It may increase the system order</p> Signup and view all the answers

    When is the proper location of additional open-loop poles and zeros determined?

    <p>At the beginning of the design process</p> Signup and view all the answers

    What type of compensator can be used to improve the steady-state error characteristics independently?

    <p>Compensators</p> Signup and view all the answers

    What technique uses a pure integrator to place an open-loop, forward-path pole at the origin?

    <p>Ideal integral compensation</p> Signup and view all the answers

    Which compensator requires an active integrator for ideal integral compensation?

    <p>Ideal integral compensation</p> Signup and view all the answers

    What does lag compensation employ in cascade compensation?

    <p>Pure integration</p> Signup and view all the answers

    What type of compensator is interchangeably referred to as a proportional-plus-integral (PI) controller?

    <p>Ideal integral compensation</p> Signup and view all the answers

    Which control system feeds the integral of the error?

    <p>Integral control</p> Signup and view all the answers

    What effect does lag compensator have on the static error constant for a Type 1 system when passive networks are used?

    <p>Decreases the static error constant</p> Signup and view all the answers

    What is the effect of adding a lag compensator close to point P on the compensated root locus?

    <p>It has minimal angular contribution and does not significantly alter the location of point P.</p> Signup and view all the answers

    How does the lag compensator affect the required gain, K, for the compensated system?

    <p>It remains virtually the same for both uncompensated and compensated systems after inserting the compensator.</p> Signup and view all the answers

    How is the improvement in the compensated system's Kv over the uncompensated system's Kv determined?

    <p>By the ratio of the compensator zero to the compensator pole.</p> Signup and view all the answers

    Where should the compensator's pole and zero be placed to minimize angular contribution and yield an appreciable improvement in steady-state error?

    <p>Close to each other, preferably close to the origin.</p> Signup and view all the answers

    How can a lag compensator with a pole not at the origin improve the static error constant?

    <p>By a factor equal to the ratio of the zero to the pole.</p> Signup and view all the answers

    What is the requirement for circuit configurations of the lag compensator?

    <p>They can be obtained with passive networks, requiring no active amplifiers or additional power supplies.</p> Signup and view all the answers

    What is the transfer function of the PD controller for the ideal derivative compensator?

    <p>$\frac{K2s}{K1 G(s) + K2}$</p> Signup and view all the answers

    What is the predicted effect of ideal derivative compensation on settling time?

    <p>Shortened settling time</p> Signup and view all the answers

    What is the relationship between compensated, dominant, closed-loop poles and the uncompensated system?

    <p>More negative real parts in compensated poles predict shorter settling times</p> Signup and view all the answers

    What is the effect of compensated systems on peak times compared to the uncompensated system?

    <p>All compensated systems will have smaller peak times than the uncompensated system</p> Signup and view all the answers

    What is the relationship between improvement in transient response and steady-state error?

    <p>Improvement in transient response doesn't always yield an improvement in steady-state error</p> Signup and view all the answers

    What is the method for designing the ideal derivative compensator?

    <p>Evaluating the sum of angles from open-loop poles and zeros to a design point</p> Signup and view all the answers

    Study Notes

    Ideal Derivative Compensation and Design Techniques

    • Compensated system with damping ratio of 0.4 achieved by adding compensating zero at different positions in Figures 9.15(b), (c), and (d)
    • Dominant, second-order poles in compensated cases are farther out along the 0.4 damping ratio line than the uncompensated system
    • Compensated cases have dominant poles with the same damping ratio as the uncompensated case, predicting the same percent overshoot
    • Compensated, dominant, closed-loop poles have more negative real parts than the uncompensated, predicting shorter settling times
    • System in Figure 9.15(b) is predicted to have the shortest settling time
    • All compensated systems will have smaller peak times than the uncompensated system
    • Ideal derivative compensation shortened the response time in each case while keeping the percent overshoot the same
    • Steady-state error of the compensated system is at least one-third that of the uncompensated system
    • Improvement in transient response doesn't always yield an improvement in steady-state error
    • The compensated responses are faster and exhibit less error than the uncompensated response
    • Designing ideal derivative compensator involves evaluating the sum of angles from open-loop poles and zeros to a design point
    • Ideal derivative compensator is implemented with a proportional-plus-derivative (PD) controller, and the transfer function is K Gc…s†ˆK2s‡K1 ˆK2 s‡ 1 …9.17† K2 R(s) + ++ C(s) PD controller K2s K1 G(s) – FIGURE 9.23

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    Description

    Test your knowledge of ideal derivative compensation and design techniques with this quiz. Explore the impact of adding compensating zero at different positions, the effect on dominant poles, settling times, peak times, and steady-state error. Understand the implementation of ideal derivative compensator with a proportional-plus-derivative (PD) controller.

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