Mathematical modeling of hybrid intelligent system to longitudinal landing control design

Abstract

The purpose of this study is to integrate fuzzy sliding mode control (FSMC) into automatic landing system (ALS) to enhance aircraft safety during landing. FSMC can provide compensation signal to PID controller. The adaptive weight particle swarm optimization (AWPSO) and grey-based particle swarm optimization (GPSO) are applied to tune the matrix of controller parameters of the sliding surface. Fuzzy rules are applied to sliding mode controller to find the gain of the differential sliding function, sliding condition can be satisfied and stable control system can be achieved. PID controller is the main controller of the aircraft and it is also used for the FSMC controller in learning process. In this study, the proposed intelligent system can improve the ALS to against the wind disturbance and control aircraft landing in severe condition. Stability analysis is provided in the controller design by the use of Lyapunov theory.

Keywords

Fuzzy sliding mode control particle swarm optimization automatic landing wind disturbance

1. Introduction

Conventional automatic landing systems (ALS) work for a predefined flight envelope. If the flight conditions are outside the envelope, the ALS often cannot be used. A statistical summary of commercial jet airplane fatal accident survey [1] from 1950 to 2014 showed that weather related cases to total accidents was 12%. Most of accidents and fatalities by phase of flight are in the landing phase. From statistical summary mentioned above, it is especially important to control aircraft safety and to pay attention to the weather conditions in final approach landing phase. Thus improved ALS for aircraft to be able to operate in wind-disturbance environment is in demand. This study proposes an intelligent ALS that can reduce pilot work load and control aircraft landing in disturbance condition. Recently, many engineering applications have applied intelligent theories in control system design. A considerable number of studies have been conducted on intelligent systems, such as neural networks, fuzzy systems, genetic algorithms, and optimization schemes etc. These research results have been brought to public attention by many technical reports. Flight controller’s environmental adaptive capability is one of them [2 –9]. In here, intelligent theories are applied to the ALS controller design.

Sliding mode control (SMC) [10 –12] has been applied to many robust control systems with external disturbance. The advantages of SMC are invariant to disturbances, insensitive to variations, good transient performance, and fast response. There are two parts in SMC controller design. The first one is switching controller. It drives system states to the sliding surface. The second one is the equivalent controller. It makes system states converge to zero along the sliding surface. Some of them apply the fuzzy concept into the structure of SMC which is known as fuzzy-SMC (FSMC). The main property of fuzzy system is its fuzzy reasoning with expert knowledge. FSMC has the advantages of neural network learning ability and human like fuzzy inference. Various FSMC approaches have been proposed in the literatures [12 –17]. The approach proposed in [12] is implemented in this study.

In 1995, Kennedy and Eberhart proposed Particle swarm optimization (PSO) [18, 19], since then many researchers have applied this algorithm in real-world optimization problems [20 –22]. PSO implements social behavior of bird flocking and fish schooling into searching optimal parameters. In searching process, each particle follows personal best solution and global solution. It is a population-based iterative algorithm and can quickly converge to a reasonably good solution. But sometimes it falls in local best solution especially in multi-model functions. There are many improved PSOs have been presented on how to use each particle to find the best solution effectively. In here, we focus on choosing better inertia weight for the problems. Adaptive weight is applied that uses two different inertia weight particle swarms to test which inertia weight is better to improve both the diversity of the swarm and the range of search [23].

Besides PSO, grey system theory [24] is utilized to solve incomplete information of this study. Since Deng presented the grey system theory in 1982, it has been used in many applications such as agriculture, environment, earthquakes, and marketing. In grey system theory, one of the most used methods is the grey relational analysis or so called Deng’s Grey Incidence Analysis model. It can perform similarity measurement for finite sequences with incomplete information. Grey relational analysis has been successfully applied to cluster analysis or other applications [25]. Each particle in the PSO can be considered as a sequence in grey relational analysis, thus the relationship of the particles can be obtained by analyzing the corresponding grey relational grades [26].

2. System description

In landing phase, the aircraft descends from the cruising altitude to approximate 1200 feet above ground. The pilots then adjust the airplane towards the runway centerline. At 4 nautical miles away from the runway, there is the outer airport marker and the aircraft receives the glide path signal (as shown in Fig. 1). Along the glide path, the aircraft maintains a constant speed, descending rate (10 ft/sec), and pitch angle (between –5 to +5 degrees). When the aircraft approaches to 20 to 70 feet above the ground, it will switch the control process from glide path control to the flare maneuver control. In the flair path, the aircraft change its pitch angle to 0 to 5 degrees and decreases its descending rate to 2 ft/sec so that the landing gear may be able to absorb the energy of the impact at landing and allows a soft touchdown on the runway surface [6].

Fig. 1.

Glide and flare paths.

This study applied a simplified commercial aircraft model in the automatic landing control simulations [5]. Only the horizontal and vertical planes are considered in the control system. Equations (1 to 5) describe the incremental dynamics of aircraft on horizontal and vertical motion. Inputs of the aircraft control system are the elevator command δ_E and throttle command δ_T. External disturbance (u_g, w_g) is also considered in the simulations. $\begin{matrix} Δ \dot{u} & = & X_{u} (Δ u - u_{g}) + X_{w} (Δ w - w_{g}) + X_{q} Δ q \\ - g (\frac{π}{180}) cos (γ_{0}) Δ θ + X_{E} δ_{E} + X_{T} δ_{T} \end{matrix}$ (1)

$\begin{matrix} Δ \dot{w} & = & Z_{u} (Δ u - u_{g}) + Z_{w} (Δ w - w_{g}) \\ + (Z_{q} - \frac{π}{180} U_{0}) Δ q - g (\frac{π}{180}) sin (γ_{0}) Δ θ \\ + Z_{E} δ_{E} + Z_{T} δ_{T} \end{matrix}$ (2)

$\begin{matrix} Δ \dot{q} & = & M_{u} (Δ u - u_{g}) + M_{w} (Δ w - w_{g}) + M_{q} Δ q \\ + M_{E} δ_{E} + M_{T} δ_{T} \end{matrix}$ (3) $Δ \dot{θ} = Δ q$ (4) $Δ \dot{h} = - Δ w + \frac{π}{180} U_{0} Δ θ$ (5)

Δu is the incremental horizontal velocity, Δw is the incremental descending velocity, u_g is the horizontal disturbance velocity, w_g is the vertical disturbance velocity, Δq is the incremental pitch rate, Δθ is the incremental pitch angle, h is the altitude of the aircraft, δ_E is the incremental elevator angle setting, δ_T is the incremental throttle setting [6].

Automatic landing system consists of several subsystem, they are the localizer, the glide path coupler, the automatic flare control system, the attitude control system, and the airspeed control system. As the purpose of this paper is concerned, it is not necessary to discuss the ALS in detail. We will limit the discussion on the basic elements combinations of automatic landing system. It includes a reference signal, aircraft dynamics, flight control system, and external wind model as shown in Fig. 2. In Fig. 2, equations of aircraft model are described in Equations (1 to 5). Equation of wind model is from [5] and is added in Equations (1 to 3). A simplified structure of the traditional PID controller is shown in Fig. 3, where its typical parameters are: θpitch = 4°, $k \dot{h} = 0.3$ , kh = 0.25, wh = 0.1. At the same time, the supervisor’s role that controller is acted in the intelligent controller is trained. Inputs of the PID controller are aircraft altitude, aircraft altitude rate, command of aircraft altitude, and command of aircraft altitude rate. Output of the PID controller is the pitch command θ_c. The pitch command is the input of the pitch autopilot. Aircraft is controlled by the pitch autopilot so that it can follow the predefined landing path. The pitch autopilot is shown in Fig. 4. Detail description is given in [6].

Fig. 2.

Automatic landing system architecture.

Fig. 3.

Conventional PID controller architecture.

Fig. 4.

Pitch autopilot.

Aircraft is influenced by environment while flying in the sky. Disturbance wind model presented by Dryden is used in this study [5]. Figure 5 shows a wind profile at the strength of 30 ft/s.

Fig. 5.

Turbulence profile.

In this study, successful touchdown conditions are: descending rate (vertical speed) is in between –3 ft/sec and –1 ft/sec, touchdown position is between 300 ft and 1000 ft, forward speed is 200 ft/sec to 270 ft/sec, pitch angle is –10 deg to 5 deg.

3. Control scheme

Control scheme of the proposed intelligent ALS is shown in Fig. 6. Aircraft altitude, Aircraft altitude rate, Aircraft altitude command, and Aircraft altitude rate command are the inputs of the control scheme. They are also inputs of the PID and FSMC controllers. Outputs of the PID and FSMC controllers, U_PID and U_FSMC, are added to be the input of the pitch autopilot, U. In most of the aircraft control systems, the conventional PID controller is the main controller. It provides necessary control signals to the aircraft. In here, the PID also provides information to the FSMC controller in learning process. The FSMC controller can provides compensation to the aircraft in severe disturbance conditions. The PID control gains were from the reference [5] by the use of Ziegler and Nichols rule. The C matrix of the SMC is adjusted by using advanced PSO to adjust parameters of the FSMC.

Fig. 6.

Control scheme.

At each sampling instant k, aircraft dynamic model is Y (k). Y_d (k + 1) is the desired model at instant k + 1, as shown in Fig. 7. In the recall process, U_FSMC and U_PID are integrated to obtain the control signal U. Figure 8 shows the learning process. U_FSMC is from the recall process and is used as the desired output. By applying optimal searching, convergence of system error can be obtained and the FSMC system can play as a compensator to the PID controller.

Fig. 7.

The control process of intelligent system.

Fig. 8.

The learning process of FSMC system.

4. Fuzzy sliding mode control

SMC was confirmed for a system of nonlinear systems and interference with good performance [10 –12]. The advantages of the SMC are good transient performance, fast response, and insensitive to disturbances. SMC has been successfully applied to systems with external disturbances and bounded parameter uncertainties. The SMC involves following two steps. First, reform Equations (1 to 5) in state space model: $\dot{x} = Ax + Bu + D$ (6)

Step 1. Choose a sliding surface.

Define the sliding surface as $s = Ce$ (7)

$x \in ℝ^{5 \times 1}$ is the state vector, $u \in ℝ^{2 \times 1}$ is the input vector. $C \in ℝ^{2 \times 5}$ is the parameter matrix of the controller which is obtained from optimization algorithms. D ∈ R^5×1 is the disturbance matrix. $e \in ℝ^{5 \times 1}$ is the tracking error vector. Given external disturbance and system function, we can obtain optimal equivalent control signal u_eq as follows [10].

Let $\dot{s} | u = u_{e q} = 0$ (8)

Thus, Equations (7) becomes $\begin{matrix} \dot{s} = C \dot{e} \\ = C ({\dot{x}}_{d} - \dot{x}) \\ = C {\dot{x}}_{d} - CAx - {CBu}_{eq} - CD = 0 \end{matrix}$ (9)

By solving (9), u_eq is $u_{eq} = (CB)^{- 1} (C {\dot{x}}_{d} - CAx - CD)$ (10)

Choose switching control u_sw as $u_{sw} = (CB)^{- 1} k sgn (s)$ (11)

Where sgn (s) is $sgn (s) = {\begin{matrix} + 1, & s > 0 \\ 0, & s = 0 \\ - 1, & s < 0 \end{matrix}$ (12)

Step 2. Design the control law u. $\begin{matrix} u = u_{eq} + u_{sw} \\ = (CB)^{- 1} (C {\dot{x}}_{d} - CAx - CD) + (CB)^{- 1} k sgn (s) \end{matrix}$ (13)

Equation (13) is then used in sliding surface, we obtain $\begin{matrix} \dot{s} = C {\dot{x}}_{d} - CAx - CBu + CD \\ = C {\dot{x}}_{d} - CAx - CB [(CB)^{- 1} (C {\dot{x}}_{d} - CAx - CD) \\ + (CB)^{- 1} k sgn (s)] + CD \\ = - k sgn (s) + 2 CD \end{matrix}$ (14)

Define a Lyapunov function candidate as follow: $V = \frac{1}{2} s^{T} s$ (15)

The sliding condition is $\dot{V} = \frac{1}{2} (s^{T} \dot{s} + {\dot{s}}^{T} s) = s^{T} \dot{s} < 0$ (16)

From (14) and (16), we can obtain $\begin{matrix} \dot{V} = s^{T} \dot{s} = - k | s^{T} | sgn (s) + 2 s^{T} CD \\ \leq - k ∥ s^{T} ∥ + 2 s^{T} CD \leq 0 \end{matrix}$ (17)

If we select the control gain $k \geq \frac{2 s^{T} CD}{∥ s^{T} ∥}$ , then the sliding condition (16) can be satisfied, stability of the control system is guaranteed. Comparison chart is shown in Fig. 9.

Fig. 9.

The select k compare with results of $\frac{2 s^{T} CD}{∥ s^{T} ∥}$ .

Since the SMC has chattering phenomenon along the sliding surface, how to eliminate this problem is considered in this study. The sgn (s) function is replaced by the function $sat (\frac{s}{ɛ})$ , which is defined as: $sat (\frac{s}{ɛ}) = {\begin{matrix} + 1, & s > ɛ \\ \frac{s}{ɛ}, & - ɛ \leq s ⩽ ɛ \\ - 1, & s < - ɛ \end{matrix}$ (18) where ɛ is a positive constant.

To ensure differentiation of Lyapunov function is less than zero and to reduce the error on the sliding surface [12 –14], this study applies fuzzy system to obtain the control gain k of the SMC. The SMC is then becomes fuzzy SMC or FSMC. In the FSMC, the gain k is updated online and the sliding condition (17) can be satisfied. The control system can be kept in stable condition. In here, inputs of the fuzzy system are s and $\dot{s}$ , output of the fuzzy system is the gain k. The fuzzy control rules of two inputs and one output are given in Table 1. N means negative. NS means negative small. S means small. M means median. B means big. VB means very big. The fuzzy sets of inputs and outputs are shown in Figs. 10 to 12.

Table 1

Fuzzy rules for the control gain k

$\dot{s}$ S	NS	S	M	B	VB
N	VS	VS	MS	S	M
S	VS	MS	S	M	B
M	MS	S	M	B	MB
B	S	M	B	MB	VB
VB	M	B	MB	VB	VB

Fig. 10.

Fuzzy membership functions of the inputs s and $\dot{s}$ .

Fig. 11.

Fuzzy membership functions of the output gain k.

Fig. 12.

Fuzzy output function with respect to inputs.

5. Advanced PSO

The PSO methods are used to tune the parameters in $C$ matrix of Equation (7). Fitness function consists of desired successful touchdown conditions of pitch angle, altitude rate, and landing position. During searching process, parameters of $C$ matrix are obtained through PSO searching process. The best set of parameters is determined by a fitness function that counts the maximal wind speed allowed for a safe landing. In this paper, we apply two PSO methods to find the optimal $C$ matrix.

5.1. Grey-based PSO

In this study, we combine grey relational analysis and PSO to find optimal controller parameter matrix. For partial information sequences, the grey relational analysis can be used for similarity measurement [24]. Given a reference sequence x = (x₁, x₂, x₃, …, x_n) and the comparative sequences y_j = (y_j1, y_j2, …, y_jn), where j is 1 to m. At kth data, between x and y_j, the factor of grey relation is $r (x_{k}, y_{jk}) = \frac{Δ_{min} + ξ \cdot Δ_{max}}{Δ_{jk} + ξ \cdot Δ_{max}}$ (19)

Δ_jk = |x_k - y_jk|, $Δ_{max} = max_{j} max_{k} Δ_{jk}$ , Δ_min $= min_{j} min_{k} Δ_{jk}$ . Resolution between Δ_max and Δ_min can be controlled by a factor ξ ∈ (0, 1]. The grade of grey relation between x and y_j is $g (x, y_{i}) = \sum_{k = 1}^{n} [α_{k} \cdot r (x_{k}, y_{jk})]$ (20)

The greater the grade is, the better the comparative sequence is. α_k is a weight of r (x_k, y_jk) and $\sum_{k = 1}^{n} α_{k} = 1$ . The weight represents the importance of the data. Normally we choose α_k = 1/n. Reference sequence is the fittest particle. Comparative sequences are other particles. Grey relational analysis can be used to obtain the similarity between them. The relational grade is applied to acquire particle’s inertia weight and acceleration factor. For different generations, the analysis results could be different, thus the factors are varying [26]. From (19), the factor of grey relation between the fittest particle and the ith particle is $r_{id} = r (gbest, x_{id}) = \frac{Δ_{min} + ξ \cdot Δ_{max}}{Δ_{id} + ξ \cdot Δ_{max}}$ (21) where gbest is the fittest particle and Xi is the ith particle, $\underset{id}{Δ} = | {gbest}_{d} - x_{id} |$ , $Δ_{max} = max_{i} max_{d} Δ_{id}$ , $Δ_{min} = min_{i} min_{d} Δ_{id}$ , and ξ ∈ (0, 1]. The grade can be obtained by $g_{i} = g (gbest, x_{i}) = \sum_{d = 1}^{D} r_{id} / D$ (22)

From (22) we can obtain r_id ∈ [ξ/(1 + ξ), 1] and g_i ∈ [ξ/(1 + ξ), 1].

An improved PSO was proposed in [27] that the authors used varying inertia weight in different generations. By varying the inertia weight from 0.9 at the beginning to 0.4 at the end of search, optimal solution can be obtained. If a particle is far away from the fittest particle its relational grade g_i is also small. Thus we should give a larger inertia weight w_i to that particle. If a particle is in the exploitation state, then a small weight should be assigned to that particle. Since g_i ∈ [ξ/(1 + ξ), 1] and w ∈ [0.4, 0.9], we can obtain a function of g_i and w_i as: $w_{i} = - 0.7 (1 + ξ) g_{i} + (0.9 + 0.3 ξ)$ (23)

To simplify the time-varying process, the acceleration factor can be obtained by the following nonlinear transformation. $C_{1 i} = 0.5 cos [f (g_{i}) π] + 2$ (24) $C_{2 i} = 4 - C_{1 i}$ (25) where f (g_i) =1.5 (1 + ξ) g_i + 1.5 (1 - ξ) g_i. Figure 13 shows the case when ξ = 1 [24].

Fig. 13.

Relationship between grey relational grade and acceleration coefficients for ξ = 1.

From (24) and (25) we know, in the evolution, every particle has the fact that C_1i + C_2i = 4.0. In the exploration state, a small C₂ and a large C₁ are assigned to a particle which can help the swarm to explore local optimums and maintain diversity. If the particle is in the exploitation state, a large C₂ and a small C₁ will help the particle converging to global optimum [24].

5.2. Adaptive weight PSO

In this method the outset particles were randomly divided into two groups each given inertial weight 0.9 and 0.4. And then let the two groups independently search, determine the function characteristic that is through the two groups fitness to compare, then merge the two groups suitable for the inertia weights of characteristics continued to search for half of the total time. Finally, go back to linear decreasing way for the rest of the time to improve the accuracy [23]. Time plan is given in Fig. 14. These improvement algorithm’s steps are:

Fig. 14.

Time plan.

Particles were randomly divided into two groups, a group using inertial weight of 0.9 speed search, another using inertial weight of 0.4 speed search.

When one-quarter generation are determined that suitable for 0.9 or 0.4 (decision table is shown in Table 2), and then merge two groups using suitable inertia weights in calculation until half generation are done.

Back to linear decreasing mode.

Table 2

Inertia weight decision rules

	Frist stage	Situation Assessment	Second stage
Situation one	Weight of 0.4 is better	More suitable for 0.4	Weight fixed 0.4
Situation two	Weight of 0.9 is better	More suitable for 0.9	Weight fixed 0.9
Situation three	Both have same performance	Maintain linear decreasing mode	0.9-0.4 mode

Map of concept is given in Figs. 15 to 17.

Fig. 15.

When one-quarter generation are determined that suitable for 0.4.

Fig. 16.

When one-quarter generation are determined that suitable for 0.9.

Fig. 17.

When one-quarter generation find 0.9 and 0.4 have same performance.

Because inertia weight is small, the particles will converge rapidly, but this does not guarantee a good result. It may be premature convergence (local optimal solution). In a limit searching time, the initials rapidly converge to near the area of minimum, and revert to the faster speed that is helpful to improve accuracy and convergence rate. Figure 18 shows the operation of adaptive weight particle swarm optimization.

Fig. 18.

Flowchart of adaptive weight particle swarm optimization.

6. Simulations

According to the conditions of safe landing, the simulation results under conventional pitch autopilot with original control gains show that the PID controller can guide the aircraft landing safely only up to 30 ft/sec of initial turbulence strength. If the wind speed is greater than 30 ft/sec, the ALS is unable to provide safe landing [5]. The performance of the PID and FSMC compensator with AWPSO is shown in Table 3 and the searched $C$ matrix is also given. Parameters of $C$ matrix are obtained through PSO searching process. The best set of parameters is determined by a fitness function that counts the maximal wind speed allowed for a safe landing. The simulations show that the situations at wind turbulence 138 ft/sec are: pitch angle 2.8897 degrees, descending speed –1.8264 ft/sec, horizontal velocity 234.6779 ft/sec, touchdown position 914.3339 ft. Turbulence profile, aircraft altitude, and commanded elevator angle are shown in Figs. 19 to 21, respectively. In Fig. 20, there are two peaks of vertical disturbance component at time 2 sec and 13 sec. This phenomenon causes aircraft vertical velocity changes rapidly and makes the altitude of aircraft drop.

Table 3
The results from using FSMC-PID with AWPSO $c = [\begin{matrix} 0.1761 & 0.1852 & 0.2003 & 0.1923 & 0.3604 \\ 0.1676 & 0.1936 & 0.1777 & 0.0931 & 0.0583 \end{matrix}]$

Wind speed Landing position (ft) Descending speed (ft/sec) Pitch angle (degree)

0 973.0033 –2.1504 –1.1735

10 890.8661 –2.02875 –0.8054

20 867.3983 –2.0151 –0.4150

30 890.8661 –1.9266 –0.2165

40 914.3339 –1.8640 –0.1727

50 867.3983 –1.9450 0.5502

60 832.1966 –1.9888 0.8959

70 843.9305 –1.9950 1.3513

80 855.6644 –1.9626 1.6798

90 937.8017 –1.7462 0.9201

100 855.6644 –1.9710 2.5231

110 785.2610 –2.1337 3.0186

120 867.3983 –1.9152 2.3959

130 444.9780 –2.8302 3.8802

135 843.9305 –1.9683 3.2494

136 491.9136 –2.7962 4.1348

138 914.3339 –1.8264 2.8897

Wind speed	Landing position (ft)	Descending speed (ft/sec)	Pitch angle (degree)
0	973.0033	–2.1504	–1.1735
10	890.8661	–2.02875	–0.8054
20	867.3983	–2.0151	–0.4150
30	890.8661	–1.9266	–0.2165
40	914.3339	–1.8640	–0.1727
50	867.3983	–1.9450	0.5502
60	832.1966	–1.9888	0.8959
70	843.9305	–1.9950	1.3513
80	855.6644	–1.9626	1.6798
90	937.8017	–1.7462	0.9201
100	855.6644	–1.9710	2.5231
110	785.2610	–2.1337	3.0186
120	867.3983	–1.9152	2.3959
130	444.9780	–2.8302	3.8802
135	843.9305	–1.9683	3.2494
136	491.9136	–2.7962	4.1348
138	914.3339	–1.8264	2.8897

Fig. 19.

Turbulence profile (initial strength 138 ft/sec).

Fig. 20.

Aircraft altitude and command at wind speed 138 ft/sec.

Fig. 21.

Commanded elevator angle at wind speed 138 ft/sec.

The FSMC-PID with GPSO control scheme can successfully control the aircraft to overcome wind speed of 145 ft/sec, as shown in Table 4. The situations at wind turbulence 145 ft/sec are: pitch angle 3.7208 degrees, descending speed –2.5110 ft/sec, horizontal velocity 234.6779 ft/sec, touchdown position 562.3170 ft, as shown in Figs. 22 to 24.

Compare to previous studies [5 , 28], as shown in Table 5, the proposed FSMC-PID with advanced PSOs have better performance than conventional PID controller, feedforward neural network (NN), resource allocating network (RAN), and recurrent neural network (RNN).

Table 4

The results from using FSMC-PID and GPSO $c = [\begin{matrix} 0.1722 & 0.1681 & 0.1927 & 0.1664 & 0.3353 \\ 0.1534 & 0.1747 & 0.1581 & 0.0377 & 0.0222 \end{matrix}]$

Wind speed	Landing position (ft)	Descending speed (ft/sec)	Pitch angle (degree)
0	914.3339	–2.3225	–1.2277
10	867.3983	–2.0089	–0.7687
20	832.1966	–1.9700	–0.5454
30	820.4627	–1.9404	–0.0370
40	808.7288	–1.9741	0.0816
50	785.2610	–1.9999	0.1790
60	726.5915	–2.1639	1.0502
70	703.1237	–2.1919	1.2729
80	750.0593	–2.0632	1.5288
90	726.5915	–2.1250	1.79500
100	644.4542	–2.3318	3.3847
110	620.9864	–2.4012	3.0250
120	750.0593	–1.9803	2.5831
130	632.7203	–2.3675	2.9759
140	644.4542	–2.2069	3.7488
145	562.3170	–2.5110	3.7208

Fig. 22.

Turbulence profile (initial strength145 ft/sec).

Fig. 23.

Aircraft altitude and command at wind speed 145 ft/sec.

Fig. 24.

commanded elevator angle at wind speed 145 ft/sec.

Table 5

Comparison of PID, NN, RNN, RAN, and FSMC controllers

Controller	Maximal turbulence (ft/sec)
PID	30
NN	40
RNN	65
RNN+GA	90
RAN	70
Adaptive RAN	75
FSMC+AWPSO	138
FSMC+GPSO	145

7. Conclusion

This paper presents application of fuzzy sliding mode control to aircraft automatic landing system. Modified optimization algorithms are applied to improve the performance of the flight control system under wind disturbance environment. Fuzzy sliding mode controller with advanced PSO can compensate for PID controller and guide an aircraft to a safe landing. The PSO is regarded as an improvement calculation method. In turbulence condition, the proposed controllers improve the robustness of automatic landing controller to 145 ft/sec of turbulence strength. The fuzzy sliding mode controller and modified optimization algorithms can effectively improve the intelligent system to against external disturbance. In addition, we utilize the Lyapunov theorem to analyze stability and select optimal updating rule for the proposed controller. In the intelligent system concept that we used, descending path tracking and environmental adaptive capability are demonstrated in software simulations. Obviously, this attempt carries out a good substitute scheme for conventional controller. This paper only presents longitudinal plane control. In real flight control system it also needs lateral plane control which is the next phase of our project. After that the real flight control system will be considered.

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