The aircraft equations of motion are given in the form of the decoupled state equations as follows. The flight condition assumed corresponds with Mach 2.0 at an altitude of 60,000 ft.
The longitudinal state equation is
- The Aircraft Equations Of Motion Are Given In The Form Of The Decoupled State Equations As Follows The Flight Condition 1 (27.4 KiB) Viewed 48 times
The solution tasks
(1) Set up the longitudinal output equation to include the additional variables angle of attack α and flight path angle γ. Solve the longitudinal equations of motion and obtain a full set of properly annotated transfer functions.
(2) Review the longitudinal stability properties of the aeroplane and produce response time histories to best illustrate the longitudinal stability modes. Comment on the likely requirement for stability augmentation.
(3) Set up the lateral-directional output equation, solve the lateral-directional equations of motion, and obtain a full set of properly annotated transfer functions.
(4) Review the lateral-directional stability properties of the aeroplane and produce response time histories to best illustrate the lateral-directional stability modes. Comment on the likely requirement for stability augmentation.
(5) With the aid of an appropriate root locus plot for each control axis, design three simple damping augmentation control laws. Clearly state the design decisions and the expected change to the stability modes. The root locus plots should be annotated appropriately for this purpose.
(6) Augment the open-loop longitudinal state equation to include the control law, thereby creating the closed-loop state equation. Solve the closed-loop equations of motion and obtain a full set of properly annotated transfer functions.
(7) Augment the open-loop lateral-directional state equation to include the control laws, thereby creating the closed-loop state equation. Solve the closed-loop equations of motion and obtain a full set of properly annotated transfer functions.
(8) Compare the longitudinal closed-loop stability modes with those of the basic airframe and produce time histories to best illustrate the improvements to the response properties of the aeroplane.
(9) Compare the lateral-directional closed-loop stability modes with those of the basic airframe and produce time histories to best illustrate the improvements to the response properties of the aeroplane.
(10) Summarise the flight control system design and state the main changes seen in the augmented aeroplane. Draw simple block diagrams to illustrate the structure of the stability augmentation system.
write in MATLAB in representation
SOLVE USING MATLAB
44 w -0.00871 -0.019 -135 -32.121 6.24 w -0.0117 -0.311 1931 -2.246 -89.2 9 0.000471 -0.00673 -0.182 0 9 -9.80 0 0 1 0 0 The lateral-directional state equation is -0.127 0.0698 -0.998 0.01659 -0.00498 0.0426 -2.36 - 1.02 0.103 0 28.7 5.38 8 11.1 -0.00735 -0.196 0 0.993 -6.908, 0 1 0 0 0 0 Velocities are given in fts, angular velocities in rad/s, and angles in rad (8 = 32.2 ft/s2). *18 [&:]