a)is the aircraft stable about the equilibrium represented by the transfer function?b) Using proportional feedback,what is the range of acceptable gains for the closed loop systen to be stable?c) Design a feedback control system that allows the pilot to command a pitch angle with overshoot less than or equal to 4.15% and a natural frequency of greater than or equal to 0.99 rad/sd) Design a feedback control system that allows the pilot to command a pitch angle with the same overshoot and a natural frequency of one half the system in part c. ### Aircraft Control Design#### ProblemAn aircraft design is shown, represented by a diagram of an airplane model with axes labeled \( x \) (forward) and \( z \) (vertical). The pitch angle \( \Theta \) and elevator deflection \( \delta_e \) are given in radians.#### Transfer FunctionThe open-loop transfer function of the system is:\[\frac{\Theta(s)}{\delta_e(s)} = \frac{s - 4}{s^2 - 0.6s + 9}\]#### Questionsa) Is the aircraft at the equilibrium represented by \(\frac{\Theta(s)}{\delta_e(s)}\)?b) Using proportional feedback, what is the range of acceptable gain \( K \) for the closed-loop system to be stable?c) Design a feedback control system that allows the pilot to command a pitch angle \(\Theta\) with an overshoot less than or equal to 4.15% and a natural frequency of greater than or equal to 0.98 rad/s.d) Design a feedback control system that allows the pilot to command a pitch angle with the same overshoot and a natural frequency of the held system in part c).#### Diagram ExplanationThe diagram shows a stylized airplane with the labeled axes \( x \) and \( z \). The pitch angle \( \Theta \) indicates the rotational movement about the horizontal axis. The elevator deflection \( \delta_e \) contributes to changes in pitch, as represented in the given transfer function.

Answered: a)is the aircraft stable about the…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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a)is the aircraft stable about the equilibrium represented by the transfer function?

b) Using proportional feedback,what is the range of acceptable gains for the closed loop systen to be stable?

c) Design a feedback control system that allows the pilot to command a pitch angle with overshoot less than or equal to 4.15% and a natural frequency of greater than or equal to 0.99 rad/s

d) Design a feedback control system that allows the pilot to command a pitch angle with the same overshoot and a natural frequency of one half the system in part c.

### Aircraft Control Design

#### Problem

An aircraft design is shown, represented by a diagram of an airplane model with axes labeled \( x \) (forward) and \( z \) (vertical). The pitch angle \( \Theta \) and elevator deflection \( \delta_e \) are given in radians.

#### Transfer Function

The open-loop transfer function of the system is:

\[
\frac{\Theta(s)}{\delta_e(s)} = \frac{s - 4}{s^2 - 0.6s + 9}
\]

#### Questions

a) Is the aircraft at the equilibrium represented by \(\frac{\Theta(s)}{\delta_e(s)}\)?

b) Using proportional feedback, what is the range of acceptable gain \( K \) for the closed-loop system to be stable?

c) Design a feedback control system that allows the pilot to command a pitch angle \(\Theta\) with an overshoot less than or equal to 4.15% and a natural frequency of greater than or equal to 0.98 rad/s.

d) Design a feedback control system that allows the pilot to command a pitch angle with the same overshoot and a natural frequency of the held system in part c).

#### Diagram Explanation

The diagram shows a stylized airplane with the labeled axes \( x \) and \( z \). The pitch angle \( \Theta \) indicates the rotational movement about the horizontal axis. The elevator deflection \( \delta_e \) contributes to changes in pitch, as represented in the given transfer function.

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