Study of a neural network-based system for stability augmentation of an airplane

77 Pages·2013·3.54 MB·English

by  Roger Isanta

Study of a neural network-based system
for stability augmentation of an airplane
Author: Roger Isanta Navarro

Report

Supervisors: Oriol Lizandra Dalmases
Fatiha Nejjari Akhi-Elarab
Aeronautical Engineering
September 2013
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Contents
1 Aim of the study .................................................................................................... 1
2 Scope .................................................................................................................... 2
3 Justification ........................................................................................................... 3
4 State of the art ...................................................................................................... 4
5 Background ........................................................................................................... 7
5.1 Airplane dynamics .............................................................................................. 7
5.2 Fuzzy Logic, Neural networks and ANFIS ............................................................ 9
5.3 Optimal control and dynamic programming .................................................... 14
6 Neural network structure .................................................................................... 17
6.1 Structure .......................................................................................................... 17
6.2 Behavior ........................................................................................................... 18
6.3 Implementation ................................................................................................ 20
6.4 Code validation ................................................................................................ 20
7 Numerical simulation .......................................................................................... 27
7.1 Fourth order Runge-Kutta method ................................................................... 27
7.2 Implementation ................................................................................................ 27
7.3 Code validation ................................................................................................ 28
8 Stability augmentation system proposal ............................................................. 35
8.1 Optimal control algorithm for offline training .................................................. 35
8.2 Simulation results for offline control ................................................................ 36
8.3 Simulation results for offline control with unstable aircraft............................. 44
8.4 Integration in phugoid PID controller ............................................................... 50
9 Viability of online critic-adaptive stability augmentation system ........................ 55
9.1 Online stability augmentation system proposal ............................................... 55
9.2 Viability of the proposal ................................................................................... 56
10 Conclusions and further work ............................................................................. 58
11 Environmental effects ......................................................................................... 61
12 Budget ................................................................................................................. 62
12.1 Work hours ....................................................................................................... 62
12.2 Used software .................................................................................................. 62
12.3 Used hardware ................................................................................................. 62
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13 Source codes ....................................................................................................... 63
14 References .......................................................................................................... 64

ii
List of figures
Figure ‎4.1 Example of pitch damper stability augmentation system .............................. 4
Figure ‎5.1 Artificial neuron model [2] ............................................................................. 9
Figure ‎5.2 Membership evaluation of traditional logic ................................................. 10
Figure ‎5.3 Membership evaluation of fuzzy logic using bell functions ......................... 11
Figure ‎5.4 Membership evaluation of fuzzy logic using linear functions ...................... 11
Figure ‎5.5 Diagram representation of a 3-inputs 3-rules ANFIS network ..................... 12
Figure ‎5.6 Example of optimal path from to .......................................................... 15
Figure ‎5.7 Backwards dynamic programming example to find optimal path from to
......................................................................................................................................... 15
Figure ‎6.1 Diagram representation of a 2-inputs 2-rules network................................ 17
Figure ‎6.2 Example of partial activation of network paths ........................................... 19
Figure ‎6.3 Test approximation to single-variable function using linear membership
functions .......................................................................................................................... 21
Figure ‎6.4 Mean Square Error vs. number of membership functions in test
approximation to single variable function using linear membership functions ............... 21
Figure ‎6.5 Training time vs. number of membership functions in test approximation to
single variable function using linear membership functions ............................................ 22
Figure ‎6.6 Two-variable test approximation function................................................... 23
Figure ‎6.7 Test approximation to two-variable function using 5 linear membership
functions per input ........................................................................................................... 23
Figure ‎6.8 Test approximation to two-variable function using 9 linear membership
functions per input ........................................................................................................... 24
Figure ‎6.9 Test approximation to two-variable function using 25 linear membership
functions per input ........................................................................................................... 24
Figure ‎6.10 Two-variable test approximation function for online training ................... 25
Figure ‎6.11 Online training test approximation to two-variable function using 25 linear
membership functions per input ..................................................................................... 26
Figure ‎7.1 Phugoid oscillation for evaluation of numerical integration method .......... 29
Figure ‎7.2 Short period oscillation for evaluation of numerical integration method ... 30
Figure ‎7.3 response to elevator ( ) ............................................................. 31
Figure ‎7.4 Theoretical response to elevator ( ) .......................................... 31
Figure ‎7.5 response to elevator ( ) ............................................................. 32
Figure ‎7.6 Theoretical response to elevator ( ) .......................................... 32
Figure ‎7.7 response to elevator ( ) ............................................................... 33
Figure ‎7.8 Theoretical response to elevator ( ) ............................................. 33
Figure ‎7.9 response to elevator ( ) ............................................................... 34
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Figure ‎7.10 Theoretical response to elevator ( ) ........................................... 34
Figure ‎8.1 Discretization example and optimal control algorithm behavior ................. 36
Figure ‎8.2 Block diagram of offline stability augmentation system (training phase) .... 37
Figure ‎8.3 Block diagram of offline stability augmentation system (application phase)
......................................................................................................................................... 37
Figure ‎8.4 Simulation results of short period offline stabilization augmentation system
for Boeing 747. Response to initial vertical speed ( ) ( ). ........... 38
Figure ‎8.5 Simulation results of short period offline stabilization augmentation system
for Boeing 747. Response to initial vertical speed ( ) Variation of R. ( ). .. 39
Figure ‎8.6 Simulation results of short period offline stabilization augmentation system
for Boeing 747. Response to commanded ( ) ( ). ............. 40
Figure ‎8.7 Full system simulation results of short period offline stabilization
augmentation system for Boeing 747. Response to commanded ( )
( ). Short time simulation. ................................................................... 42
Figure ‎8.8 Full system simulation results of short period offline stabilization
augmentation system for Boeing 747. Response to commanded ( )
( ). Large time simulation. ................................................................... 44
Figure ‎8.9 Unstable behavior of modified Boeing 747 with no control action. ............ 45
Figure ‎8.10 Simulation results of short period offline stabilization augmentation
system for Boeing 747. Response to initial vertical speed ( ) ( ).
......................................................................................................................................... 46
Figure ‎8.11 Simulation results of short period offline stabilization augmentation
system for unstable Boeing 747. Response to commanded ( ) (
). ................................................................................................................. 47
Figure ‎8.12 System simulation results of short period offline stabilization
augmentation system for unstable Boeing 747. Response to commanded ( )
( ). ....................................................................................................... 49
Figure ‎8.13 Block diagram of offline stability augmentation system integrated with a
PID controller. (Application phase) .................................................................................. 50
Figure ‎8.14 Full system simulation results of short period offline stabilization
augmentation system for unstable Boeing 747 with phugoid PID control. Response to
commanded ( ) ( ). Short time simulation ....................... 52
Figure ‎8.15 Full system simulation results of short period offline stabilization
augmentation system for unstable Boeing 747 with phugoid PID control. Response to
commanded ( ) ( ). Large time simulation. ...................... 54
Figure ‎9.1 Block diagram representation of a critic-adaptive control system .............. 55
Figure ‎9.2 Block diagram of offline training phase in online stability augmentation
system .............................................................................................................................. 56
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Figure ‎9.3 Block diagram of online stability augmentation system application ............ 56

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List of tables
Table ‎7.1 Validation data for numerical integration method [1] .................................. 29
Table ‎12.1 Budget breakdown ...................................................................................... 62

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List of abbreviations
Airplane dynamics:
State matrix
Input matrix
Wing span
̅ Mean aerodynamic chord
Drag coefficient

Lift coefficient

Elevator deflection

Throttle position

Pitch angle
Longitudinal speed variation
Moments of inertia

Products of inertia

Moments in body axes
Aircraft mass
Balance rate
Pitch rate
Yaw rate
Wing area
Subscript Refers to lineal speed
Subscript Refers to lineal speed
Subscript Refers to linear speed
Subscript Refers to angular speed
Subscript Refers to angular speed
Subscript Refers to angular speed
Subscript Refers to control action
Subscript Refers to elevator deflection

Subscript Refers to throttle position

Longitudinal speed
Control vector
Lateral speed
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Vertical speed
Aircraft weight
State vector
Forces in body axes

Neural networks:
Premise parameters
Refers to consequence parameters
Mean Squared Error
Minimum acceptable error
ANFIS fourth layer output (when multiplied by ̅)
Membership function
ANFIS first layer output
Sum on ANFIS third layer
Output of layer

Number of paths
Refers to premise parameters
Product on ANFIS second layer
Consequence parameters
Time
Threshold value
Input
( ) Neural network output
Algebraic sum of input-weight products
ANFIS second layer output
̅ ANFIS third layer output
Synaptic weight

Optimal control:
Cost function
Cost from to

Optimal cost from to

State vector to cost matrix at end time
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