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 (B)</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 (A)</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 (A)</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 (B)</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 (B)</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 (C)</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 (C)</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 (B)</p> Signup and view all the answers

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

<p>Compensators (D)</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 (D)</p> Signup and view all the answers

Which compensator requires an active integrator for ideal integral compensation?

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

What does lag compensation employ in cascade compensation?

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

Which control system feeds the integral of the error?

<p>Integral control (C)</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 (B)</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. (B)</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. (D)</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. (B)</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. (D)</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. (A)</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. (B)</p> Signup and view all the answers

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

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

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

<p>Shortened settling time (B)</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 (B)</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 (C)</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 (C)</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 (B)</p> Signup and view all the answers

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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 GcÂ…s†ˆK2s‡K1 ˆK2 s‡ 1 Â…9.17† K2 R(s) + ++ C(s) PD controller K2s K1 G(s) – FIGURE 9.23

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