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ак 67 4 Figure 1: Figur 1: Roll of an airplane An autopilot is to be made that regulates the roll motion of an aircraft. The goal is for the aircraft's roll motion, o, to follow a reference, pref, affected by disturbances on the aircraft. The angle is measured with a gyroscope and compared to the reference Pref. The difference, - Oref, is the input signal to a regulator with the transfer function hR(S). The output signal from the regulator, u(t), controls an electrohydraulic servosystem that adjusts the aileron angle, 0. The electrohydraulic system is described by the equation: ȧ(t) = k₁ (u(t) – k20(t)) The aileron provides a rolling moment on the aircraft as: Mr = k30(t) This moment will cause the aircraft to rotate, changing the roll angle. The following values are given: k₁ = 5, k21, k3 10,000 Gyroscope measurement constant: hm = 140 [V/rad] Aircraft moment of inertia around the roll axis: J = 50,000 [kgm²] The aircraft's friction constant against the air in roll motion is: B = 50,000 [kgm²/s] a) A moment balance around the aircraft's longitudinal axis gives us the differential equation that describes the aircraft's roll motion. Write down the differential equations that are part of this dynamic system.

ак 67 4 Figure 1: Figur 1: Roll of an airplane An autopilot is to be made that regulates the roll motion of an aircraft. The goal is for the aircraft's roll motion, o, to follow a reference, pref, affected by disturbances on the aircraft. The angle is measured with a gyroscope and compared to the reference Pref. The difference, - Oref, is the input signal to a regulator with the transfer function hR(S). The output signal from the regulator, u(t), controls an electrohydraulic servosystem that adjusts the aileron angle, 0. The electrohydraulic system is described by the equation: ȧ(t) = k₁ (u(t) – k20(t)) The aileron provides a rolling moment on the aircraft as: Mr = k30(t) This moment will cause the aircraft to rotate, changing the roll angle. The following values are given: k₁ = 5, k21, k3 10,000 Gyroscope measurement constant: hm = 140 [V/rad] Aircraft moment of inertia around the roll axis: J = 50,000 [kgm²] The aircraft's friction constant against the air in roll motion is: B = 50,000 [kgm²/s] a) A moment balance around the aircraft's longitudinal axis gives us the differential equation that describes the aircraft's roll motion. Write down the differential equations that are part of this dynamic system.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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ак 67 4 Figure 1: Figur 1: Roll of an airplane An autopilot is to be made that regulates the roll motion of an aircraft. The goal is for the aircraft's roll motion, o, to follow a reference, pref, affected by disturbances on the aircraft. The angle is measured with a gyroscope and compared to the reference Pref. The difference, - Oref, is the input signal to a regulator with the transfer function hR(S). The output signal from the regulator, u(t), controls an electrohydraulic servosystem that adjusts the aileron angle, 0. The electrohydraulic system is described by the equation: ȧ(t) = k₁ (u(t) – k20(t)) The aileron provides a rolling moment on the aircraft as: Mr = k30(t) This moment will cause the aircraft to rotate, changing the roll angle. The following values are given: k₁ = 5, k21, k3 10,000 Gyroscope measurement constant: hm = 140 [V/rad] Aircraft moment of inertia around the roll axis: J = 50,000 [kgm²] The aircraft's friction constant against the air in roll motion is: B = 50,000 [kgm²/s] a) A moment balance around the aircraft's longitudinal axis gives us the differential equation that describes the aircraft's roll motion. Write down the differential equations that are part of this dynamic system.
Transcribed Image Text:ак 67 4 Figure 1: Figur 1: Roll of an airplane An autopilot is to be made that regulates the roll motion of an aircraft. The goal is for the aircraft's roll motion, o, to follow a reference, pref, affected by disturbances on the aircraft. The angle is measured with a gyroscope and compared to the reference Pref. The difference, - Oref, is the input signal to a regulator with the transfer function hR(S). The output signal from the regulator, u(t), controls an electrohydraulic servosystem that adjusts the aileron angle, 0. The electrohydraulic system is described by the equation: ȧ(t) = k₁ (u(t) – k20(t)) The aileron provides a rolling moment on the aircraft as: Mr = k30(t) This moment will cause the aircraft to rotate, changing the roll angle. The following values are given: k₁ = 5, k21, k3 10,000 Gyroscope measurement constant: hm = 140 [V/rad] Aircraft moment of inertia around the roll axis: J = 50,000 [kgm²] The aircraft's friction constant against the air in roll motion is: B = 50,000 [kgm²/s] a) A moment balance around the aircraft's longitudinal axis gives us the differential equation that describes the aircraft's roll motion. Write down the differential equations that are part of this dynamic system.
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