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Questions and Answers
What information does the root locus graphically display?
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?
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?
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?
What does the root locus limit us to in terms of transient responses?
How can the flexibility in the design of a desired transient response be increased?
How can the flexibility in the design of a desired transient response be increased?
What is the goal when trying to speed up the response at a specific point on the root locus?
What is the goal when trying to speed up the response at a specific point on the root locus?
What is the purpose of compensating systems with additional poles and zeros?
What is the purpose of compensating systems with additional poles and zeros?
Where can compensating poles and zeros be added in the system?
Where can compensating poles and zeros be added in the system?
How can additional poles and zeros be generated for compensating systems?
How can additional poles and zeros be generated for compensating systems?
What is the impact of adding compensating poles and zeros on the system order?
What is the impact of adding compensating poles and zeros on the system order?
When is the proper location of additional open-loop poles and zeros determined?
When is the proper location of additional open-loop poles and zeros determined?
What type of compensator can be used to improve the steady-state error characteristics independently?
What type of compensator can be used to improve the steady-state error characteristics independently?
What technique uses a pure integrator to place an open-loop, forward-path pole at the origin?
What technique uses a pure integrator to place an open-loop, forward-path pole at the origin?
Which compensator requires an active integrator for ideal integral compensation?
Which compensator requires an active integrator for ideal integral compensation?
What does lag compensation employ in cascade compensation?
What does lag compensation employ in cascade compensation?
What type of compensator is interchangeably referred to as a proportional-plus-integral (PI) controller?
What type of compensator is interchangeably referred to as a proportional-plus-integral (PI) controller?
Which control system feeds the integral of the error?
Which control system feeds the integral of the error?
What effect does lag compensator have on the static error constant for a Type 1 system when passive networks are used?
What effect does lag compensator have on the static error constant for a Type 1 system when passive networks are used?
What is the effect of adding a lag compensator close to point P on the compensated root locus?
What is the effect of adding a lag compensator close to point P on the compensated root locus?
How does the lag compensator affect the required gain, K, for the compensated system?
How does the lag compensator affect the required gain, K, for the compensated system?
How is the improvement in the compensated system's Kv over the uncompensated system's Kv determined?
How is the improvement in the compensated system's Kv over the uncompensated system's Kv determined?
Where should the compensator's pole and zero be placed to minimize angular contribution and yield an appreciable improvement in steady-state error?
Where should the compensator's pole and zero be placed to minimize angular contribution and yield an appreciable improvement in steady-state error?
How can a lag compensator with a pole not at the origin improve the static error constant?
How can a lag compensator with a pole not at the origin improve the static error constant?
What is the requirement for circuit configurations of the lag compensator?
What is the requirement for circuit configurations of the lag compensator?
What is the transfer function of the PD controller for the ideal derivative compensator?
What is the transfer function of the PD controller for the ideal derivative compensator?
What is the predicted effect of ideal derivative compensation on settling time?
What is the predicted effect of ideal derivative compensation on settling time?
What is the relationship between compensated, dominant, closed-loop poles and the uncompensated system?
What is the relationship between compensated, dominant, closed-loop poles and the uncompensated system?
What is the effect of compensated systems on peak times compared to the uncompensated system?
What is the effect of compensated systems on peak times compared to the uncompensated system?
What is the relationship between improvement in transient response and steady-state error?
What is the relationship between improvement in transient response and steady-state error?
What is the method for designing the ideal derivative compensator?
What is the method for designing the ideal derivative compensator?
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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 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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