Intelligent Autolanding Controller Design using Neural Networks and Fuzzy Logic S. M. B. Malaek1, Nasser Sadati2, Hojjat Izadi3, Mehrdad Pakmehr4 1
Associate Professor of Aerospace Engineering Aerospace Engineering Department, Sharif University of Technology, Azadi Ave, Tehran, I.R. IRAN, P.O. Box: 11365-8639, Email:
[email protected] 2 Associate Professor of Electrical engineering Electrical Engineering Department, Sharif university of Technology, Azadi Ave, Tehran I.R.IRAN, Email:
[email protected] 3 Graduate Student, Mechanical Engineering Department, Tarbiyat Modarres University All-e-Ahmad Highway, Tehran, Iran, Email:
[email protected] 4 Graduate Student, Mechanical Engineering Department, Concordia University, Room H-549, 1455 de Maisonneuve Blvd. West, Montreal, QC, H3G 1M8, Canada, Email:
[email protected] Abstract
U0 J0
Designing an intelligent controller for landing phase of a jet transport aircraft in presence of different wind patterns, in order to expand the flight safety envelope has been considered. There are some dangerous conditions like gusts and downbursts which may occur rarely in service life of aircraft, though, aircraft must be tested for these dangerous conditions. Then it is desired to design a controller that not only acts well in usual conditions but also has an acceptable performance in those hazardous conditions. Four different types of controllers have been designed named PID, Neuro, hybrid Neuro-PID and Anfis-PID (Adaptive Network-based Fuzzy Inference System) controllers. Simulation results show that the Anfis-PID which its inner loop is PID and outer loop is Anfis satisfies desired conditions in presence of very strong gust, however, the performance of NeuroPID is also acceptable. To evaluate the performance of controllers two level of performance have been defined named level I (desired) and level II (acceptable). Also, in comparison with JFK airport gusts two strong wind patterns named strong and very strong winds have been applied. 1 u w q T
x h h0f g ug wg
GE GT
Nomenclature
: perturbed longitudinal velocity (ft/sec.) : perturbed vertical velocity (ft/sec.) : perturbed pitch rate (deg/sec.) : perturbed pitch angle (deg.) : horizontal position of aircraft (ft) : altitude (ft) : flare initiation altitude (ft) : gravity (32.2 ft/sec2) : longitudinal wind velocity (ft/sec.) : vertical wind velocity (ft/sec.) : elevator angle setting (deg.) : throttle setting (deg.)
h0g
Ds
: normal speed (235 ft/sec.) : flight path angle (-3 deg.) : glide initiation altitude (ft) : stall angle of attack (deg.)
2
Introduction
On 24 June, 1975 in John F. Kennedy Airport a Boeing-727 aircraft had a hard crash, during its landing phase, due to a strong downburst gust (Fig. 1) and its 112 out of 124 passengers died. That was one of thousands of such crashes which have been occurred in the landing phase of the aircraft [1]. Strong downbursts such as the one shown in Fig. 1 are responsible for number of hard landing and crash each year [1]. Many research activities have been conducted on designing an automatic landing controller for different classes of aircraft, especially heavy jet transports. For example, Ref. [2] describes an automatic landing system (ALS) based on a human skill model. The model is expressed as a nonlinear I/O mapping from the aircraft state to the control command provided by a human expert; a gain adaptation technique has also been introduced for robustness. In Ref. [3], a mixed H2/ H f control technique has been employed to develop controllers for automatic landing system of a commercial airplane. In Ref. [4], H f synthesis has been applied to the problem of designing a flare mode for automatic landing for a typical transport airplane. In Ref. [5], Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) has been used to design an automatic landing controller for a typical commercial aircraft encountering a wind-shear. In Ref. [6], adaptive critic neural networks have been used to design a controller for a benchmark problem in aircraft autolanding. In Ref. [7], five different neural network structures are utilized to design intelligent autolanding controllers using linearized inverse dynamic model. In Ref.
[8], a Radial Basis Function Neural Network (RBFN) has been used in the control scheme to aid a conventional controller for aircraft autolanding procedure. In Ref. [9], a controller based on fuzzy logic methodology has been designed for a flight vehicle that enables it to track a predetermined flight path trajectory for safe landing. All of these works suffer from the point that they lack sufficient generality for a flight phase as landing phase is. Landing as a flight phase could vary considerably, due to its vicinity to the ground and existence of unknown pattern of wind and gust during the year and finally, the buildings surrounding an airport. Therefore, it is very desirable to develop a control system that can handle different climatic conditions in this regard, and neuro based control systems could be a solution. Statistics show that landing phase of aircraft normally has the highest percentage of accidents and/or incident, hence this stage, is considered to be the most critical phase of a mission [10]. These accidents are normally due to several reasons that could be categorized into two different sets. The first set of reasons is related to the human errors such as error to estimate the altitude, runway condition and orientation. The second reason is due to the sudden changes in atmospheric conditions. To prevent the first set of errors, we need controllers as well as pilots with the accumulated knowledge but without the usual human approximation. To prevent the second set of problems, we need an adaptive controller with the ability to adapt its parameters with regard to the changes in parameters during landing. Solving problems such as this, requires a flexible controller based on human knowledge. PID controller, on the other hand, has good capabilities to control the aircraft through out the landing phase of a flight. However, these types of controllers need precise information about system dynamics. Knowing, that approximations in system dynamical model as well as its output parameters are inevitable, the primary objective of this paper is to present a methodology to practically, omit the need for switching between glide and flare modes with the help of neural networks technique by integrating the glide and flare controllers. The main objective of this paper is to design a controller with outstanding performance and stability during landing phase of flight in presence of very strong winds. At the end, classical, neural based and fuzzy based controllers will be compared to show that our goal has been achieved. The procedure has four major steps as follows: a- First a PID controller is designed for a known trajectory, with dynamic of aircraft linearized in the vertical plane. b- Then a neuro-controller is designed to control the aircraft through-out the glide and flare modes. c- Then a hybrid neuro-PID controller has been designed to handle the aircraft in Very Strong wind pattern. In this controller the inner loop is PID based and the outer loop is neural based. d- Finally a hybrid Anfis-PID controller has been designed. In this controller the inner loop is PID based and the outer loop is Anfis-based.
In this approach, the data and outputs generated by the PID controller are used to train the neuro-controller. Obviously, the PID controller is deigned only for a single known trajectory in a specific set of conditions. However, it could be used for a wide range of flight conditions, based on the characteristics of neural networks. Omission of the switching mechanism between the glide and flare modes leaves out the selection of proper point to flare. In this way, uncertainties due to the so called "sensor errors" are no longer a concern. Different simulation conducted shows that with the help of hybrid neuro-PID technique acceptable landing performance & with Anfis-PID desired landing performance in severe atmospheric conditions are possible. 3
Problem Definition and Objectives
During complex maneuvers, such as landing and take-off; the dynamics of the aircraft is changing rapidly which leads to a complex design procedure as far as conventional controllers are concerned. The problem can become even more complex, while gusts and other natural climatic conditions are present. Two major modes of landing phase studied here are glide-slope hold and intercept and flare and touch down with regard to [14]. The following characteristics are usually observed, during landing phase of a flight: 1. A suitable altitude should be selected for the aircraft autopilot to start to glide mode or glide mode initiation. 2. At a height of about 15 meters (45 ft) AGL, the flare maneuver is started which results in nose being lifted, reducing the vertical speed of the aircraft and allowing the main gear to touch the ground firstly and smoothly. During this limited time interval the control law has to be adjusted continuously. 3. Through continuous decrease in the aircraft altitude, the ground effect starts to play a major role and the aircraft dynamics becomes affected accordingly. 4. Gust and downburst, which have an inevitable influence on the aircraft dynamics, do not follow a well-known pattern. Based on design performance outlined in [11] and [13] and to evaluate the controllers' performance, we consider two level of performance named level 1 and level 2. In level 1, the controllers should satisfy the following conditions in any gust: (I) h d 17 fps
D d 7 deg
(II)
In level 2, the necessary conditions are as follows: h d 20 fps
(III)
D d10 deg
(IV)
It is desired that the controllers achieve the level 1 of performance; however, Level 2 is also acceptable. It is further assumed that glide mode begins at 500 ft AGL and finishes at 45 ft AGL, which is the start point of flare
mode [14] (Fig. 2). The flare mode continues until a smooth touch down is achieved. During a glide-slope mode, an automatic landing system guides the aircraft along a straight line with a constant slope (with a constant glide angle, J ). Autopilot also attempts to prevent any changes in aircraft vertical and horizontal speeds, that is, during glide mode the sink rate is constant. As flare mode starts, autopilot starts to nose up the aircraft by changing the glide angle to prepare aircraft for a smooth touchdown. The trajectory of aircraft during this mode is estimated by an exponential function. Through this mode the sink rate is reduced to the desired value of -1.5 fps. Longitudinal control surfaces such as elevator in addition to the throttle are the usual controls during these modes. 4
Aircraft Equations of Motion and Turbulence Model
In this work, 3-DOF equations of motion in the vertical plane known as longitudinal dynamics have been used to design the controller, however, the procedure is very well extendable to a complete 6-DOF equations of motion. Based on [14], these equations are given by (1) through (9). u X u (u u g ) X w ( w w g ) X q q (1) g( w
S 180
) cos( J 0 )T X E G
E
X TGT
Z u (u u g ) Z w ( w w g ) ( Z q ( g(
q
S 180
M M
u q
S 180
)U 0 ) q
(2)
) sin( J 0 )T Z E G E Z T G T
(u u g ) M
w
(w w g )
G E M TGT T q x u cosT w sin T h u sin T w cosT
q M
(3)
E
(4) (5) (6)
wg
u g1
Vw
ug=ug1+ugc a w ( a w w g1
2 a u N 1 a u u g1
(13)
w g2
(14)
N 2 a 2w w g1 2 a w w g 2
(15)
0 .2 | u g c |
g1 w g2 w
3w g2 )
(11) (12)
Where
U /(100 3 h ) au® 0 ¯ U 0 / 600
; h ! 230 ; h d 230
(16)
aw= U0 /h Vw
(17)
0 . 2 | u gc |; ® ¯ 0 . 2 | u gc | ( 0 . 5 0 . 00098 h );
h ! 500 h d 500
(18)
And N1 and N2 are the Gaussian Random Noises with mean zero and different variances. In this approach, wind patterns with different velocities and intensities can be generated. 5
Autoland Controller Design
As previously mentioned, a conventional PID controller, a modern neuro-controller and also a hybrid neuro-PID controller are designed to show the effectiveness of a hybrid system. To design a PID controller to train the Neurocontroller, longitudinal controls are throttle and elevator. Throttle is used in such a way that the aircraft speed during landing phase remains constant [2]. So:
T
K T (u c u ) K T Z T
³
t
( u c u ) dt
(19) In this case: uc= 0, kT= 3, wT= 0.1 The function of elevator is to control the pitch angle and pitch rate during landing phase, so: (20) E K T (T c T ) K q q 0
And it is further assumed that, the desired pitch angle is a
function of error in h and h , so t
The initial conditions are assumed as: u(0)=w(0)=q(0)= T (0) =0 h(0)=500 ft, x(0)=h(0)/tag J 0
x (0) U0
(7) (8) (9)
Wind disturbance, which are shown by (ug, wg) consists of two components: constant velocity (ugc, 0) and turbulence (ug1,wg). It is further assumed that the constant velocity component exists only in the horizontal direction, given by (10),
u gc
u 0 (1 Ln(h / 510) / Ln51) h t 10 ® 0 h 10 (10) ¯
Here u0 is the wind speed at altitude 510 ft and its typical value is 20 ft/sec. Turbulence is represented by [2].
Tc kh(hc h) khZh ³ (hc h)dtkh (hc h) Tp 0
(21)
Where Kh=0.3, Wh=0.1, K h
0 .3
At Glide KT 3 , Kq=3, T p 0 mode: At Flare KT 12 , Kq=6.0, T p 0.0698 mode: The PID controller gains are estimated by applying the Linear Matrix Inequality (LMI) method, which is normally used to design PID controllers for MIMO systems. This method guarantees the stability of the designed system [15]. However, to achieve the desired performance one needs to optimize the gains through a trial and error process. hc and hc for each mode are obtained from their trajectories in glide and flare modes. As we know in glide mode the aircraft moves along a constant slope path characterized by (22):
hc x
tgJ 0
hc
x tgJ 0
(22)
At the flare mode the controller is applied to aircraft so that
h is reduced smoothly to a desired value of -1.5 fps. It is assumed that the flare mode begins at t=t0 and h0f=h(t0)=45 ft and it ends at the main gear touch down point where t=T and h(T)=0, then:
h0 (h0 e ( x x0 )W hTD ) h0 hT
hc
performance; however, in this controller the outer loop is fuzzy based, using a mixed type of adaptive networks & fuzzy systems named ANFIS. In other words, Anfis acts like fuzzy systems and structurally is similar to adaptive networks (or Perceptron Neural Networks). Firstly, consider the following Sugno Type Fuzzy System, in which x and y are inputs of system and f is its output: Rule 1: if x is A1 and y is B1, then f1=P1x+Q1y+r1 Rule 2: if x is A2 and y is B2, then f2=P2x+Q2y+r2
(23) And
w1 f 1 w 2 f 2 w1 w 2
f
Where
hTD
h(W )
(24) 1.5( ft / sec) (25) W [ h 0 x ( t 0 )] /( h 0 hT ) Results of different simulations conducted by the authors show that setting the throttle command to zero results in much better trajectories. Therefore, the rest of the simulations, once the throttle setting was selected it was treated as a constant throughout the simulation. 6
( T , q , h and h ). The output of elevatornet is the elevator setting. The hidden layer has 7 neurons (N4,7,1). In this neural network, tangent-sigmoid function is used in input and hidden layers and pure-linear function is used in output layers. To train the network classical error back propagation method (Levenberg-Marquardt back propagation) is used. This method updates weight and bias values according to Levenberg-Marquardt optimization [16]. 7
Equivalent Anfis system for above fuzzy system is shown in Fig. 3 [17]. Layer 1 is membership layer in which the membership degree of x relative to Ai computes the output of layer 1 as follows: (27) O ' P ( x) i
Hybrid Neuro-PID Controller Design
Ai
where P is membership function of Ai. In layer 2, input signals are multiplied: (28)
P A ( x) P B ( y )
wi
Neuro-Controller Design
One neural network is designed for Elevator control. As previously mentioned the outputs of PID controller are used to train the neural network. The neural network used for Elevator control is a Multi Layer Perceptron (MLP) with the name of elevatornet, which has 3 layers and 4 inputs
(26)
i
i
That expresses the firing strength of each fuzzy rule. The output of each node in layer 3 is:
w
wi w1 w 2
(29)
which is named normalized firing strength. Each node in layer 4 is a square node with node function: (30) O 4 w f w (P x Q y r ) i
2
t
z
z
z
z
Therefore, network acting like Sugno Type fuzzy system is provided by using the concept of adaptive (Perceptron) networks. The {Pi, Qi, ri} parameters and parameters of membership functions are defined by training process, which is usually based on steepest descent method or least square error method. As mentioned previously, in this controller the inner loop is designed by classic PID tuning method, the outer loop is designed by using Anfis. To train the Anfis Network, two error parameters are defined as follows: (31) e h h & e h h
To achieve a better performance in the presence of very strong winds and gusts a new controller has been proposed. In this controller inner loop that provides stability of the system, is designed with the aid of classic methods (such as root locus plot), in other words, according to equations for elevator setting (20), we tune KT and Kq by classical
These two parameters ( e h & e h ) are inputs to Anfis
methods. The outer loop ( T c ) is estimated by a type of
estimates the desired pitch angle ( T c ) for compensation and
neural networks named General Regression Neural Networks (GRNN). A GRNN is often used for function approximation and has a radial basis layer as it hidden layer and a special linear layer as its output layer. [16]
correction. Each input ( eh & eh ) has three bell-shaped
8
Hybrid Anfis-PID Controller Design
Similar to the neuro-PID controller, the hybrid Anfis-PID controller has been designed to achieve a better
h
c
h
c
network and output of Anfis is T c . In other words, Anfis network, based on these two error values ( eh & eh ),
membership function. Linguistic variables for these membership functions are Low, Medium and High. Consequently after 20 epochs training of Anfis, nine fuzzy laws are generated as follows [18]: 1. If (eh is low) and (eh-dot is Low) then (theta_c is Very-Low)
2. If then 3. If then 4. If then 5. If then 6. If then 7. If then 8. If then 9. If then
(eh is low) and (theta_c is Very-Low) (eh is low) and (theta_c is Low) (eh is Medium) and (theta_c is Low-Medium) (eh is Medium) and (theta_c is Medium) (eh is Medium) and (theta_c is High-Medium) (eh is High) and (theta_c is High) (eh is High) and (theta_c is Very-High) (eh is High) and (theta_c is Very-Very-High) 9
(eh-dot is Medium) (eh-dot is High) (eh-dot is Low) (eh-dot is Medium) (eh-dot is High) (eh-dot is Low) (eh-dot is Medium) (eh-dot is High)
Case Studies and Simulation Results
To train the networks, the M-files and Neural Networks Toolbox [16] of Matlab software have been used, and to simulate the system, Simulink Toolbox [19] of Matlab software has been used; also, suitable links between the Mfiles and Simulink environment have been provided. The initial conditions for all of the aforementioned controllers have been introduced in Equations (7) to (9). According to the Federal Aviation Administration (FAA) regulations (FAR 25) [20], environmental conditions considered in the determination of dispersion limits are: headwinds up to 25 knots (42.23 fps); tailwinds up to 10 knots (16.9 fps). The simulation result of the designed hybrid controller was found to be robust enough to properly handle all of the imposed turbulences proposed by the FAA in landing phase of flight. Fig. 4 to 7, show the horizontal and vertical components of Strong and Very Strong winds applied to the controllers. With applying these wind patterns, the performance of the controllers have been discussed. Simulation results have been presented in two sections. In the first section, simulation results of the three controllers in presence of Strong wind and in the second section, the results in presence of Very Strong wind have been presented. The profile of strong wind is depicted in Fig. 4 and 5. It can be compared with JFK gust, a strong Downburst, depicted in Fig. 1. Simulation results for applying Strong wind have been shown in Fig. 8 to 15. Followed and command trajectories of aircraft for all of four controllers are shown in Fig. 8 to 11. It is shown that for all of controllers, range of errors are acceptable. The sink rate variations for the controllers are shown in Fig. 12 to 15, which all of them satisfy the necessary conditions for level 2; moreover, the Anfis controller satisfy conditions for level 1. Variations of angle of attack during the landing phase of the aircraft, for the controllers, are not shown here, but its variations for all of the cases are in the acceptable range,
with regard to angle of attack limitation (Stall angle, D s ). Consequently, all of the controllers- PID, Neuro, NeuroPID and Anfis-PID controller- have good capabilities to guide the aircraft throughout the landing phase in presence of Strong wind. To evaluate limitations of flight safety envelope, in the next section, we will discuss the aircraft performance with applying Very Strong wind. Horizontal and vertical components of Very Strong wind have been depicted in Fig.6 and 7. Comparing these figures with JFK Airport Downburst, Fig. 1, it is seen that the wind named Very Strong wind is stronger than the JFK Airport Downburst. Since, JFK wind is known as a strong Downburst, if our controllers, in presence of Very Strong wind, show acceptable performance, our objective, which was the extension of flight safety envelope, have been achieved. Fig. 16 to 23, show simulation results of the controllers in presence of Very Strong wind. Followed and command trajectories for the controllers, in presence of Very Strong wind, have been shown in Fig. 16 to 19. Fig. 16 shows that the classic controller follows the command trajectory well, but according to Fig. 17, the neuro controller hasn’t an acceptable behavior in following the command trajectory. Fig. 18 shows that the neuro-PID controller has a relative better performance. Fig. 19 shows that the Anfis controller has a good performance. Desired and actual sink rates for the controllers have been shown in Fig. 20 to 23. Actual sink rate of classic controller (Fig. 20) exceeds -20 fps and doesn’t satisfy the conditions. The neuro controller also doesn’t satisfy the limitations in this case (Fig. 21). Sink rate of the aircraft with hybrid neuro-PID controller (Fig. 22) in presence of Very Strong wind doesn’t exceed -20 fps limitation and satisfies the necessary conditions for level 2 of performance and Fig. 23 shows that the actual sink rate with Anfis-PID controller in presence of Very Strong wind doesn't exceed 17 fps and then satisfies the necessary conditions for Level 1 of performance. Angle of Attack variations for the controllers have not been shown here. But, variations of angle of attack with neuro controller were not acceptable at all. Angle of attack of the aircraft in presence of Very Strong wind, with applying the PID and neuro-PID controllers, didn’t exceed the stall angle limitation, during the landing phase of flight, but Anfis-PID controller has a relative better performance. The aforementioned results have been showed briefly in Table 1: Table 1: Performance of the controllers in presence of different wind patterns controller wind pattern Strong Wind Very Strong Wind
PID Controller
Neuro Controller
NeuroPID Controller
Anfis-PID Controller
Level 2
Level 2
Level 2
Level 1
Unacceptable
Unacceptable
Level 2
Level 1
[7] Jih-Gau Juang, Hao-Hsiang Chang, Kai-Chung Cheng,
10 Discussion and Conclusion Four different types of controllers (Classic, Neuro, NeuroPID and Anfis-PID) have been designed and simulated. To evaluate performance of the controllers, two different wind patterns have been introduced, named Strong and Very Strong winds, also 2 level of performance have been considered named Level 1 and Level 2. Strong wind is weaker than the JFK Downburst and Very Strong wind is stronger than it. Results show that performance of controllers in presence of Strong wind satisfy necessary conditions for Level 2(acceptable), and only Anfis–PID controller satisfies Level 1(desired) of performance. Simulations of applying Very Strong wind, shows that only Anfis-PID controller satisfies the necessary conditions for Level 1 performance and only Neuro-PID controller satisfies the necessary conditions for Level 2 performance. So, only with applying the hybrid neuro-PID and Anfis-PID controllers we can extend the flight envelop of the aircraft. Block diagrams of the PID, neuro, neuro-PID and AnfisPID controllers have been shown consequently in Fig. 24 to 27. As it is obvious, T , q, h and h are the inputs of the controllers, so the number of required sensors for all of the controllers is equal. On the other hand, the neuro-controller has a good ability to estimate the system parameters in a condition that had not been trained before, and it is capable to extend the performance range of the system. In other words by this technique, the flight safety envelope of the aircraft can be extended in a wide range and this make the landing system operate more safely in presence of sudden and unpredicted conditions. Moreover; it is possible to decrease the number of flight tests with this controller. In overall, a mixed Neuro-Classic or Fuzzy-classic controller has a better performance in comparison with the controllers which are based only on classic methods or only on neural networks methods. References
[8]
[9] [10] [11]
[12]
[13]
[14] [15]
[16] [17] [18] [19]
[1] J. Shen, E. K. Park, R. E. Bach, "Comprehensive Analysis of [2]
[3]
[4]
Two Downburst-Related Aircraft Accidents", Journal of Aircraft, Vol. 33, No. 5, PP. 924-930, 1996. Youji Iiguni, Hideo Akiyoshi, Norihiko Adachi, "An Intelligent Landing System Based on a Human Skill Model", IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No.3, July 1998. Shgh – Pyng Shue, Ramesh K. Agrawal, "Design of Automatic Landing Using Mixed H2/ H f Control", Journal of Guidance, Control & Dynamics, Vol. 22, No.1, JanuaryFebruary 1999. Issac Kaminer, Pramod P. Khargonekar, "Design of the f
[5] [6]
Flare Control Law for longitudinal Autopilot Using H Synthesis", Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawell, IEEE 1990. Mounir Ben Ghalia, Ali T. Alouani, "Robust Control Design of an Autolanding System", IEEE Conference, 1993. Gaurav Saini, S. N. Balakrishnan, "Adaptive Critic Based Neuro-Controller for Autolanding of Aircraft", Proceedings of the American Control Conference, Albuquerque, New Mexico, June 1997.
[20]
"Intelligent Landing Control Using Linearized Inverse Aircraft Model", American Control Conference, Vol. 4, 2001, PP 3269-3274. L. Yan, N. Sundararajan, P. Saratchandran, “An Investigation of a Neuro-Controller in Automatic Landing”, can be downloaded from: http://www.mindef.gov.sg/rsaf/ats2002/uav/Uv4.pdf P. E. Kee, L. Dong, “Fuzzy-Logic Based Autoland Controller”, can be downloaded from: http://www.mindef.gov.sg/rsaf/ats2002/uav/Uv3.pdf Jeppesen Sanderson Inc., Private Pilot Manual, 1992. Richard M. Hueschen, "Implementation and flight tests for the Digital Integrated Automatic Landing System (DIALS), Part 1", NASA-TM-87632-PT-1, NASA National Aeronautics and Space Administration, Langley Research Center, July 1986. Richard M. Hueschen, "Implementation and flight tests for the Digital Integrated Automatic Landing System (DIALS), Part 2", NASA-TM-87632-PT-2, NASA National Aeronautics and Space Administration, Langley Research Center, July 1986. R. K. Heffley, T. M. Schulman, W. F. Clement, "An Analysis of Airline Landing Flare Data Based on Flight and Training Simulator Measurements", NASA-CR-166404, NASA National Aeronautics and Space Administration, Ames Research Center, August 1982. J. Roskam., Airplane Flight Dynamics and Automatic Flight Control, Roskam Publishing Incorp., 1979 (Part I & II). Feng Zheng, Qing-Guo Wang, Tong Heng Lee, "Brief Paper on the Design of Multivariable PID Controllers via LMI Approach", Journal of Automatica, Vol. 38, 2002, PP 517526. H. Demuth, M. Beale, Neural Networks Toolbox (For Use with Matlab) User's Guide, Version 4, Mathworks Inc., 2000. J. Shine, R. Jang, "Anfis: Adaptive Network-based Fuzzy Inference System", IEEE Transactions on Systems, MAN and Cybernetics, Vol 23, NO.3, May/June 1993. Fuzzy Logic Toolbox (For Use with Matlab) User's Guide, Version 2, Mathworks Inc., 2002. Simulink Toolbox of Matlab (Model-Based and SystemBased Design) User's Guide, Version 4, Mathworks Inc., 2000. Federal Aviation Administration (FAA), "Automatic Landing Systems", AC 20-57A, Jan. 1971.
N=300, u
gc
=30(ft/sec)
g
u (ft/sec)
100
50
10 knots -Tailw ind Limit with Regard to FAR 25 (AC 20-57A)
0
-50 25 knots -Headw ind Limit w ith Regard to FAR 25 (AC 20-57A)
-100
0
5
10
15
20
25
30
35
40
45
50
55
t(sec)
Fig. 1: JFK Airport Downburst
Fig. 6: Very Strong wind pattern, Variation of ug with h, N=300 N=250
W (ft/sec)
60
g
40
20
0
-20
-40
Fig. 2: Typical trajectory in landing 1 2
-60
5
10
15
20
25
30
35
40
45
50
55
t(sec)
4
3
0
Fig. 7: Very Strong wind Pattern, Variation of wg with h, N=250 5
A
500 Followed Trajectory Command Trajectory c
h,h (ft)
X A
400
f 300
B
Y
B
200
2
100
0
Fig. 3: Anfis equivalent of Sugno Type fuzzy
-100 -10000
-8000
-6000
-4000
-2000
0
2000
4000
X(ft)
N=200
Fig. 8: Trajectory for PID controller with Strong wind
10 Knots - Tailwind limit with regards to FAR 25 (AC 20-57 A)
20
g
u (ft/sec)
30
10 500 Followed Trajectory Command Trajectory
450
c
h,h (ft)
0 -10
400 350
-20 300
-30
250 200
-40
150
25 Knots - Headwind limit with regards to FAR 25 (AC 20-57 A) -50
100
-60 -70
50 0 -10000
0
10
20
30
40
50
t(sec)
-6000
-4000
-2000
0
2000
4000 X(ft)
Fig. 9: Trajectory for Neuro controller with Strong wind
Fig. 4: Strong wind pattern, Variation of ug with h, N=200
500
N=100
Followed Trajectory Command Trajectory
h(ft)
30
400
20
g
w (ft/sec)
-8000
60
300
10
0
200
-10
100
-20
0
-30
-40
-100 -10000
0
10
20
30
40
50
60 t(sec)
Fig. 5: Strong wind Pattern, Variation of wg with h, N=100
-8000
-6000
-4000
-2000
0
X(ft)
2000
Fig.10: Trajectory for Neuro-PID controller with Strong wind
500 h,h (ft)
Followed Trajectory Command Trajectory
c
450
500 Followed Trajectory Desired Trajectory
400
350
400
h,h (ft)
c
300
250
300 200
150
200 100
50
100 0 -10000
-8000
-6000
-4000
-2000
0
2000 X(ft)
Fig. 11 Trajectory for Anfis-PID controller with Strong wind
0
-100 -10000
-8000
-6000
-4000
-2000
0
2000
4000
X(ft)
(ft/sec)
0
dot
-2
Actual Sink Rate Command Sink Rate
h
-4
Fig. 16: Trajectory for PID controller with Very Strong wind
-6 -8 -10
500
-12
Followed Trajectory Command Trajectory
h,h (ft)
c
-14
400
-16 -18 -20 0
300 5
10
15
20
25
30
35
40
45
50
55
t(sec)
200
100
0
0 Followed Sink Rate Command Sink Rate
-2
dot
h (ft/sec)
Fig. 12: Sink rate variations for PID controller with Strong wind
-4
-100 -10000
-6
-8000
-6000
-4000
-2000
0
2000
4000 X(ft)
-8 -10
Fig. 17: Trajectory for Neuro controller with Very Strong wind
-12 -14 -16
500
-18
Followed Trajectory Desired Trajectory
-20 0
5
10
15
20
25
30
35
40
45
450
50
t(sec)
h,h (ft)
400
c
350
300
0
250
Followed Sink Rate Command Sink Rate
-2
dot
h (ft/sec)
Fig. 13: Sink rate variations for Neuro controller with Strong wind
200
-4
150
-6
100
-8 50
-10 0 -10000
-8000
-6000
-4000
-2000
0
2000
-12
4000 X(ft)
-14
Fig. 18: Trajectory for Neuro-PID controller with Very Strong wind
-16 -18 -20
0
5
10
15
20
25
30
35
40
45
50
t(sec) h,h (ft)
500
c
Fig. 14: Sink rate variations for Neuro-PID controller with Strong wind
Actual Trajectory Command Treajectory 450
400
350 0 (ft/sec)
-4
dot
h
300 -2
250 Actual Sink Rate Command Sink Rate
200
-6
150 -8
100 -10
50 -12
0 -10000
-14
-8000
-6000
-4000
-2000
0
2000 X(ft)
-16
-18
0
5
10
15
20
25
30
35
40
45
50 t(sec)
Fig. 15: Sink rate variations for Anfis-PID controller with Strong wind
55
Fig. 19: Trajectory for Anfis-PID controller with Very Strong wind
Aircraft
h
dot
(ft/sec)
0
-5
T,q
h , h
E
-10
hc
-15
Tc
-20 Actual Sink Rate Command Sink Rate
-25 0
5
10
15
20
25
30
35
40
45
50
hc
Fig. 24: PID Controller block diagram
55
t(sec)
T , q, h, h
Fig. 20: Sink rate variations for PID controller with Very Strong wind dot
(ft/sc)
30
h
Elevator
+
Training Procedure
Actual Sink Rate Command Sink Rate
20
Neuro Controller (MLP)
Data for Training
hc hc
10
0
Aircraft
Elevator
PID
T , q, h , h
-10
-20
Fig. 25: Neuro Controller block diagram (with training procedure)
-30
-40 0
10
20
30
40
50
60
E
t(sec)
Aircraft
Fig. 21: Sink rate variations for Neuro controller with Very Strong wind (ft/sec)
Tc
Actual Sink Rate Command Sink Rate
-2
dot
T,q
Tc
0
hc
-4
h
h , h
hc
-6
-8
T , q, h , h
Tc
+
-10
-12
-14
-
-16
Fig. 26: Neuro-PID Controller block diagram (with training procedure)
-18
-20
0
10
20
30
40
50
Neural Network Estimator (GRNN)
60 t(sec)
Fig. 22: Sink rate variations for Neuro-PID controller with Very Strong wind T,q
E
-2
dot
(ft/sec)
0
Elevator
Aircraft
h
Actual Sink Rate Command Sink Rate
-4
-6
Tc
-8
Tc
h , h
hc
-10
+
-12
Tc
-14
-16
0
10
20
30
40
50
hc
T , q, h , h
60 t(sec)
Fig. 23: Sink rate variations for Anfis-PID controller with Very Strong wind
Anfis Estimator -
Fig. 27: Anfis-PID Controller block diagram (with training procedure)
