CN112678154B - Airplane anti-skid braking system control method with interference online estimation function - Google Patents

Airplane anti-skid braking system control method with interference online estimation function Download PDF

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CN112678154B
CN112678154B CN202110032703.2A CN202110032703A CN112678154B CN 112678154 B CN112678154 B CN 112678154B CN 202110032703 A CN202110032703 A CN 202110032703A CN 112678154 B CN112678154 B CN 112678154B
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braking system
skid
interference
neural network
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李繁飙
黄培铭
黄科科
阳春华
廖力清
周灿
吴政
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Central South University
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Abstract

The invention discloses a control method of an aircraft anti-skid braking system with interference online estimation, which comprises the following steps: step 1, establishing an anti-skid braking system model and performing feedback linearization treatment; step 2, introducing uncertain interference existing in the anti-skid braking system into the anti-skid braking system model after feedback linear processing, and designing an integral sliding mode surface and a controller for the anti-skid braking system; the uncertainty interference comprises external disturbance caused by time variation and internal disturbance caused by parameter variation of an unmodeled part; and 3, carrying out online estimation on the uncertain disturbance by adopting a self-adaptive RBF neural network, and introducing the estimated uncertain disturbance into a controller of the anti-skid braking system as a compensation part. The method can improve the efficiency of the airplane anti-skid brake from three aspects of anti-skid brake control law with strong robustness, accurate anti-skid brake system model and uncertain interference on-line estimation and compensation.

Description

Airplane anti-skid braking system control method with interference online estimation function
Technical Field
The invention belongs to the field of airplane brake control, and particularly relates to a control method of an airplane antiskid brake system with interference online estimation.
Background
The time spent in the takeoff and landing phases of the ground runway in the whole process of the aircraft navigation is very short, but large accidents frequently occur in the two phases, so that a safe and reliable aircraft brake control system is extremely important for the aircraft navigation.
In fact, the antiskid braking system of the airplane has serious uncertain interference, which greatly affects the control system. Common interferences are: internal disturbances caused by parameter variations, unmodeled parameters, external disturbances caused by time variations, and the like.
At present, the traditional multi-threshold speed difference plus bias voltage (PID + PBM) control brake effect which is mainstream at home and abroad is not obvious, and the brake effect is represented by large jitter, weak anti-interference capability, slow convergence speed, serious low-speed slipping and the like, and the conventional linear control design method can not meet the system characteristic requirements. In order to simplify modeling, a common aircraft brake system usually ignores a brake actuator model, a brake disc model, uncertainty interference and the like, so that the overall model is excessively simplified and ideal, and has a large error with a real brake system, thereby causing poor control effect. Therefore, the efficiency of the airplane skid brake is improved from aspects of a novel skid brake control law, an antiskid brake system model, uncertain disturbance online estimation and compensation and the like.
Disclosure of Invention
The invention provides a control method of an airplane anti-skid braking system with interference on-line estimation, which aims to solve the problem that in the prior art, an airplane anti-skid braking system model is subjected to system optimal slip rate tracking with uncertain parameters and uncertain external interference.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
an aircraft antiskid braking system control method with interference online estimation comprises the following steps:
step 1, establishing an anti-skid braking system model and performing feedback linearization treatment;
step 2, introducing uncertain interference existing in the anti-skid braking system into the anti-skid braking system model after feedback linear processing, and designing an integral sliding mode surface and a controller for the anti-skid braking system; the uncertainty interference comprises external disturbance caused by time variation and internal disturbance caused by parameter variation of an unmodeled part;
and 3, carrying out online estimation on the uncertain disturbance by adopting a self-adaptive RBF neural network, and introducing the estimated uncertain disturbance into a controller of the anti-skid braking system as a compensation part.
In a more preferred embodiment, the anti-skid braking system model is represented as:
Figure BDA0002892109720000021
in the formula, lambda is the slip ratio of the tire,
Figure BDA0002892109720000022
is a derivative of the slip ratio λ, f (λ) is a function related to the slip ratio λ, PAFor the pressure acting on the brake disc, R is the effective radius of the main wheel, kbFor the conversion coefficient of braking moment and pressure, vxFor the longitudinal sliding speed of the aircraft, JwIs the moment of inertia of the main wheel;
Figure BDA0002892109720000023
is a pressure PADerivative of cbIs the rigidity coefficient of the brake disc, L0For ball screw stroke, wmIs the rotor angular velocity;
Figure BDA0002892109720000024
is the angular speed w of the rotormDerivative of (A), JmIs the moment of inertia of the rotor, kTIs the motor torque constant, i is the armature current, BvIs a viscous damping coefficient;
the feedback linearization treatment of the anti-skid braking system model specifically comprises the following steps:
firstly, in the expression of the antiskid braking system model, lambda and PA、wmIs a system state, lambda is a system output, and i is a system input; let x1Is lambda, x2Is PA、x3Is wmAnd u is i, so that the expression of the antiskid braking system model is converted into a system nonlinear anti-radiation model form:
Figure BDA0002892109720000025
where y is the actual output of the system and x ═ x1 x2 x3]T；
Figure BDA0002892109720000026
h(x)＝[x1 0 0]T；
f(x)＝[f1(x) f2(x) f3(x)]T；
Wherein the content of the first and second substances,
Figure BDA0002892109720000027
then, based on the relative order and the order of the system being the same, performing coordinate transformation on the nonlinear anti-radiation model of the system to obtain an anti-skid braking system subjected to feedback linear processing, namely a linear standard system shown as the following formula:
Figure BDA0002892109720000031
wherein the content of the first and second substances,
Figure BDA0002892109720000032
in a more preferred embodiment, the sliding mode surface s of the integral sliding mode controller is represented as:
Figure BDA0002892109720000033
where e is the slip ratio error of tracking, and e is y-ydY is the actual output of the system, ydIs the desired output of the system; c ═ C1 c2 1]Wherein c is1 c2Normal numbers that satisfy the Hurwitz stability criterion; k is a radical ofiTo integrate the gain, satisfy ki>0; e is a vector of the systematic error vector,
Figure BDA0002892109720000034
the switching control law of the integral sliding mode controller based on the sliding mode surface is as follows:
Figure BDA0002892109720000035
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000036
sgn (. cndot.) is a sign function, and k,. epsilon.are normal numbers.
In a more preferred technical scheme, the specific process of online estimating the uncertain disturbance by adopting the self-adaptive RBF neural network comprises the following steps:
(1) the external disturbance caused by time variation and the unmodeled part is represented as d (z, t), the internal disturbance caused by parameter variation is represented as Δ a and Δ Bu, and the uncertainty disturbance d (z) is represented as:
D(z)＝△A(z)+△B(z)u+d(z,t)；
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000037
(2) assuming the presence of an unknown non-linear continuous function Dn(z) in the presence of
Figure BDA0002892109720000038
For the input of the self-adaptive RBF neural network, the self-adaptive RBF network is adopted to approximate an unknown nonlinear function Dn(z); wherein a non-linear continuous function Dn(z) satisfies:
D(z)＝Dn(z)+Dd(z)；
in the formula, | Dd(z)|≤δd，
Figure BDA0002892109720000039
Dd(z) is the influence Dn(z) interference term, δ, which is a non-linear continuous functiondIs Dd(z) boundaries of interference terms;
(3) self-adaptive RBF neural network approximation nonlinear continuous function Dn(z) actual output obtained
Figure BDA0002892109720000041
As an estimation value of the uncertainty interference of the system, and introducing the uncertainty interference into the controller as a compensation control law of the controller, namely:
Figure BDA0002892109720000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000043
for the weight of the adaptive RBF neural network, H (xi) is the input
Figure BDA0002892109720000044
The resulting radial basis vectors.
In a more optimal technical scheme, the weight updating law of the self-adaptive RBF neural network is as follows:
Figure BDA0002892109720000045
wherein γ is an adaptive gain value, and γ > 0.
In a more preferred embodiment, a Gaussian function h is selectedi(xi) as the basis function of the adaptive RBF neural network, a radial basis vector H (xi) is formed by the basis function, and the activation function of the radial basis function can be expressed as:
Figure BDA0002892109720000046
in the formula, ciFor the ith hidden of the adaptive RBF neural networkCenter of reservoir node, diThe node base width parameter is the ith hidden layer.
In a more preferable technical scheme, the controller of the anti-skid braking system comprises an equivalent control law which is stable in order to meet the final Lyapunov of the anti-skid braking system, in addition to a switching control law and a compensation control law
Figure BDA0002892109720000047
The scheme of the invention has the following beneficial effects:
1. the anti-skid brake model is subjected to feedback linearization processing for modeling, so that the problem of oscillation deviation caused by reference point linearization modeling is avoided, the nonlinear characteristic of the system is reserved, and the practicability of the model is enhanced.
2. On the basis of feedback linearization processing, a sliding mode control method based on a second-order error and an integral sliding mode surface is adopted to finally obtain a closed-loop control system, and the tracking optimal slip rate precision of the aircraft anti-skid brake system is improved.
3. The self-adaptive RBF neural network is adopted to carry out on-line estimation on the uncertain disturbance and is used as a compensation part in a control law, so that the error between the parameter value and the parameter value under the real braking condition is reduced as much as possible, and the airplane antiskid braking efficiency is improved.
Drawings
FIG. 1 is a schematic diagram of the dynamic stress situation of an aircraft body during the braking process of the aircraft.
Fig. 2 is a schematic diagram of the dynamic stress situation of a single braked wheel.
FIG. 3 is a structural diagram of feedback linearization processing and integral sliding mode control of an aircraft anti-skid braking system.
FIG. 4 is a block diagram of an aircraft anti-skid brake system feedback linearization processing and integral sliding mode control method with uncertainty interference on-line estimation.
FIG. 5 is a schematic diagram of braking efficiency calculation.
Fig. 6 is a simulation diagram of an aircraft anti-skid brake system feedback linearization processing and integral sliding mode control method with uncertain disturbance on-line estimation in a dry runway state, wherein (a) is a simulation diagram of changes of an aircraft body speed and an aircraft wheel speed with time, (b) is a simulation diagram of changes of an actual slip ratio and an expected slip ratio with time, (c) is a simulation diagram of changes of an actual combination coefficient and an expected combination coefficient with time, (d) is a simulation diagram of changes of a brake pressure with time, (e) is a simulation diagram of changes of a vertical load of a single main wheel with time, and (f) is a simulation diagram of changes of a longitudinal sliding distance with time.
Fig. 7 is a simulation diagram of the comparison of the interference of the actual braking process and the output estimation value of the adaptive RBF neural network, which is assumed to introduce a sinusoidal curve with gaussian noise.
Detailed Description
The invention provides a control method of an airplane anti-skid brake system with uncertain interference on-line estimation, which aims at the problems of uncertain model parameters and tracking of the optimal slip rate of the airplane anti-skid brake system subjected to uncertain external interference, and solves the adverse effect of the uncertain model parameters and the external interference on the control effect by adopting an integral sliding mode control method and combining self-adaptive Radial Basis Function (RBF) neural network on-line estimation on the basis of input and output feedback linearization treatment of the original anti-skid brake system. On one hand, the uncertainty model parameters are estimated on line by using a self-adaptive RBF neural network technology and are used as a compensation part in a control law, so that the error between the uncertainty model parameters and the parameter values under the real braking condition is reduced as much as possible, on the other hand, the external interference is weakened by using an integral sliding mode control technology, the system is quickly converged and stably, and the buffeting is reduced.
The invention is described in detail below with reference to the drawings and simulation and experimental examples. The specific implementation steps of the embodiment are as follows:
1. modeling of aircraft anti-skid braking system
(1) Aircraft body dynamics model
The aircraft body model mainly describes the dynamics of the aircraft, and the stress analysis is performed on the aircraft body model in the landing and running process, as shown in fig. 1.
Before analyzing the airplane brake dynamics model, the following assumptions are made: considering the airplane as an ideal rigid body, simplifying the airplane body into concentrated mass without considering elastic deformation, and keeping the quality of the airplane constant in the whole braking process; secondly, only longitudinal movement is considered on the assumption that no crosswind exists when the ground of the airplane lands and runs; the front wheel is not braked, so that the front wheel is rolling friction force, and the magnitude is small and can be ignored; and fourthly, assuming that the braking mechanisms of all the braked wheels have consistent performance and are synchronously controlled, simplifying the braking control of all the wheels into the control of a single-wheel single-channel wheel.
According to Newton's second law and dynamics analysis, an airplane body dynamics model is established:
Figure BDA0002892109720000061
where m is the aircraft mass, vxFor the longitudinal running speed of the aircraft, FxIs windward resistance, n is the number of braked main wheels, FfFor friction between a single main wheel and the ground, TvAs engine thrust, FyFor aircraft lift, N1For single main wheel vertical load, N2Is the vertical load of the front wheel, g is the gravitational acceleration, a is the horizontal distance between the center of the front wheel and the center of gravity of the airplane, b is the horizontal distance between the center of the main wheel and the center of gravity of the airplane, h is the vertical height between the center of gravity of the airplane and the groundtIs the vertical height of the thrust point of the engine and the gravity center of the airplane, mu (lambda) is the combination coefficient between the main wheel and the ground, lambda is the slip ratio of the tire, TintFor residual engine thrust, kvCoefficient of engine residual thrust to aircraft longitudinal speed, kxIs the coefficient of air resistance in the horizontal direction, kyAir resistance coefficient in vertical direction, ρ is air density, CdIs the aerodynamic drag coefficient of the aircraft, SwIs the total area of the wing, CLThe coefficient of lift when the airplane runs.
(2) Dynamic model of single braked wheel
During the landing of the airplane and the contact of the airplane wheels with the ground, the main wheels are mainly subjected to the following forces: the friction force generated between the ground and the tire, the vertical load given to the aircraft by the ground, and the braking force applied between the brake disks by the brake device. The friction force generated by the contact of the wheel and the ground is related to the combination coefficient and the vertical load of the wheel, and the mutual correlation and the mutual restriction between the combination coefficient and the vertical load of the wheel, so that the brake system is a strong nonlinear and strong coupling system, and the decoupling solution of the brake system is difficult to realize through a simple control strategy. The single wheel is stressed in the braking condition as shown in figure 2.
According to Newton's second law and dynamic analysis, a dynamic model of a single braked wheel is established:
Figure BDA0002892109720000062
in the formula, JwIs the rotational inertia of the main wheel, w is the angular velocity of the wheel, R is the effective radius of the main wheel, TbFor braking moment, kbFor the conversion coefficient of braking torque and pressure, PAIs the pressure acting on the brake disc.
(3) Binding coefficient model
The weight of the airplane is almost unchanged in the braking process, the binding force is determined by the binding coefficient, and the Magic Formula with high fitting degree with experimental data is selected as a relation model of the binding coefficient and the slip ratio:
μ(λ)＝Dsin(Carctan(Bλ)) (3)
in the formula, D is a peak value factor, C is a rigidity factor, B is a curve shape factor, and lambda is the slip ratio of the tire.
When the speed of the airplane is constant, a relation model of the combination coefficient mu and the slip ratio lambda under the dry runway condition, the wet runway condition and the ice runway condition is established. The peak factor, stiffness factor and curve shape factor values obtained from the comparison of the test data and reference to the relevant references are shown in table 1 for the dry, wet and ice runway conditions.
TABLE 1 values of factors of Magic Formula model under different runway conditions
Runway conditions Crest factor D Stiffness factor C Curve shape factor B Maximum slip ratio lambda*
Dry matter 0.8 1.5344 14.0326 0.117
Wet 0.4 2.0192 8.2098 0.12
Ice 0.2 2.0875 7.201788 0.13
During braking, regardless of the braking pressure PAWhether the effect is on or not, the v is always more than or equal to Rw, so that the slip ratio lambda is defined as:
Figure BDA0002892109720000071
according to the planeThe machine body dynamic model, the single braked machine wheel dynamic model and the combination coefficient model are used for solving the derivation of the formula (4) and then combining the (1) and the (2) to obtain the change rate of the slip rate
Figure BDA0002892109720000072
The formula of (a):
Figure BDA0002892109720000073
(4) full electric brake actuator model
According to the brushless direct current motor all-electric brake actuator model, the pressure change rate acting on the brake disc can be obtained
Figure BDA0002892109720000074
And rate of change of angular velocity of rotor
Figure BDA0002892109720000075
The formula of (1) is:
Figure BDA0002892109720000076
in the formula, cbIs the stiffness coefficient of the brake disc, L0For ball screw stroke, wmIs the rotor angular velocity.
Figure BDA0002892109720000081
In the formula, JmIs the moment of inertia of the rotor, kTIs the motor torque constant, i is the armature current, BvIs a viscous damping coefficient.
2. Feedback linearization processing of airplane antiskid brake system
Integrating the formulas (5), (6) and (7) into a complete airplane antiskid brake model:
Figure BDA0002892109720000082
at λ, PA、wmIn the system state, λ is the system output, and i is the system input. Suppose x1Is lambda, x2Is PA、x3Is wmU is i, the model (8) is rewritten into the system nonlinear affine model form:
Figure BDA0002892109720000083
the correlation vector parameters and output functions in the system (9) are:
x＝[x1 x2 x3]T；
Figure BDA0002892109720000084
h(x)＝[x1 0 0]T；
f(x)＝[f1(x) f2(x) f3(x)]T；
wherein the content of the first and second substances,
Figure BDA0002892109720000085
to accurately feed back the linearization to the nonlinear aircraft brake system, it is necessary to ensure that the relative order of the system is equal to the system order, so that the relative order of the system is judged:
zeroth order:
Figure BDA0002892109720000086
first order:
Figure BDA0002892109720000087
second order:
Figure BDA0002892109720000091
Figure BDA0002892109720000092
third order:
Figure BDA0002892109720000093
Figure BDA0002892109720000094
because of the fact that
Figure BDA0002892109720000095
The relative order of the braking system is 3, which is equal to the order of the system, so the system can perform feedback linearization processing.
And (3) carrying out coordinate transformation on the nonlinear system model to obtain the following linear standard system:
Figure BDA0002892109720000096
wherein z is1＝h(x),z2＝Lfh(x),
Figure BDA0002892109720000097
3. Sliding mode control method design based on integral sliding mode surface
Considering the existence of uncertain disturbances in the actual anti-skid braking system, such as external disturbances d (z, t) caused by time variation and unmodeled parts and internal disturbances Δ A and Δ Bu caused by parameter variation, the model (10) is rewritten as:
Figure BDA0002892109720000098
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000099
let the actual output of the system be y and the desired output be ydThen the tracking error e of the system is:
e＝y-yd (12)
let the systematic error vector be
Figure BDA0002892109720000101
Then:
Figure BDA0002892109720000102
rate of change of systematic error vector
Figure BDA0002892109720000103
Comprises the following steps:
Figure BDA0002892109720000104
designing a sliding mode switching surface by combining a linear state space equation to obtain an integral sliding mode surface s as follows:
Figure BDA0002892109720000105
wherein C ═ C1 c2 1]Wherein c is1 c2Normal number, k, to satisfy the Hurwitz stability criterioniTo integrate the gain, satisfy ki>0。
The control law is composed of equivalent control terms ueqAnd a switching control item uswThe two parts are as follows:
u＝ueq+usw (16)
Figure BDA0002892109720000106
Figure BDA0002892109720000107
in the formula, sgn (. cndot.) is a sign function, and k and ε are normal numbers. A structural block diagram of the feedback linearization processing and integral sliding mode control of the aircraft anti-skid brake system is shown in fig. 3.
4. Self-adaptive RBF neural network uncertainty interference on-line estimation
(1) Adaptive RBF neural network design
In fact, the antiskid braking system of the airplane has serious nonlinearity and complexity, and has uncertain interference, thereby causing great influence on a control system. In order to enable the robustness of control to be better, the self-adaptive RBF neural network is adopted to estimate uncertainty interference on line and is introduced into an integral sliding mode controller as a compensation part to be processed, and the interference is well inhibited.
The self-adaptive RBF neural network adopted by the invention has 4 neurons as an input layer and 1 neuron as an output layer. And selecting the number of hidden layers of the neural network and corresponding control parameters by adopting a k-means clustering algorithm, and finally determining that the number of neurons of the hidden layers is 7.
For the model (11), let d (z) be the interference parameter uncertainty term, satisfying the following expression:
D(z)＝△A(z)+△B(z)u+d(z,t) (19)
assuming the presence of an unknown non-linear continuous function Dn(z), namely:
D(z)＝Dn(z)+Dd(z) (20)
in the formula, | Dd(z)|≤δd，
Figure BDA0002892109720000111
Dd(z) is the influence Dn(z) interference term, δ, which is a non-linear continuous functiondIs Dd(z) boundaries of interference terms.
Approximation of unknown nonlinear function D by adaptive RBF networkn(z), an approximation of the actual output may be expressed as:
Figure BDA0002892109720000112
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000113
the estimated values of d and W are obtained.
Assuming that an ideal RBF neural network weight W exists, the following expression is satisfied:
Dn(z)＝WTH(ξ)+δ (22)
in the formula (I), the compound is shown in the specification,
Figure BDA0002892109720000114
for the input vector of the adaptive RBF neural network, H (xi) ═ H1(ξ) H2(ξ) … Hi(ξ)]TIs a radial basis vector of the neural network, delta is an approximation error of the neural network, and the approximation error delta is bounded, namely | delta | is less than or equal to delta |m。
Selecting a Gaussian function hi(xi) as a basis function, the radial basis vector H (xi) formed by it, and thus the activation function of the radial basis function can be expressed as:
Figure BDA0002892109720000115
in the formula, ciIs the ith hidden layer node center, diThe node base width parameter is the ith hidden layer.
Designing a weight updating law of the self-adaptive RBF neural network as follows:
Figure BDA0002892109720000116
wherein γ is an adaptive gain value, and γ > 0.
Combining the formulas (17) and (18) to obtain the final control law which is composed of an equivalent control term ueqSwitching control item uswAnd a compensation control term unnThe three parts are as follows:
u＝ueq+usw+unn (25)
Figure BDA0002892109720000121
after the feedback linearization processing and the integral sliding mode control of the airplane antiskid braking system, the self-adaptive RBF neural network on-line estimation combined with uncertain disturbance is used as a compensation part in the control law, the tracking control effect on the expected slip rate under the influence of uncertain disturbance can be well shown, the self-adaptive capacity and the robustness are high, and the comprehensive control strategy diagram is shown in figure 4.
(2) Stability and Convergence analysis
Self-adaptive RBF neural network weight estimation error
Figure BDA0002892109720000122
Figure BDA0002892109720000123
Since W changes slowly, the derivation of equation (27) yields:
Figure BDA0002892109720000124
the simultaneous formulas (11), (19), (20), (21), (22), (25) and (27) can obtain:
Figure BDA0002892109720000125
to ensure the stability of the control law, the Lyapunov function is defined as:
Figure BDA0002892109720000126
the derivation of equation (30) and the combination of (24), (27), (28), (29) yields:
Figure BDA0002892109720000127
ensure epsilon>δm+δdThen, then
Figure BDA0002892109720000128
The convergence speed of the tracking error can be adjusted by the value of k. When in use
Figure BDA0002892109720000129
S ≡ 0, the closed-loop system becomes progressively stable according to the LaSalle invariant set principle, and t → ∞ time, s → 0, and thus e → 0.
Therefore, the airplane antiskid brake system (8) can ensure the final stable convergence of the system under the action of the designed sliding mode control law (25) and the self-adaptive updating law (24).
5. Simulation verification and result analysis
(1) Slip control performance index
Braking efficiency is generally an important measure of system performance, and includes pressure efficiency, torque efficiency, and coupling coefficient efficiency. The braking efficiency is high or low, which often determines the quality of the control strategy. For the calculation of the braking efficiency, the area method is most commonly used, such as the curve shown in fig. 5, and the calculation formula is:
Figure BDA0002892109720000131
in the formula, eta is braking efficiency; a is the area enclosed by the solid line; a. the0The area enclosed by the dotted line (as shown by the shaded portion in fig. 5).
The other performance index of the antiskid brake is the brake distance, and under the same condition, the brake distance can be shortened, so that the utilization rate of the runway can be greatly improved, and the occupied area of the runway is saved.
(2) Model simulation verification and analysis
In the whole simulation test process, after the aircraft lands, the speed of a brake wheel is consistent with the speed of the aircraft, and the start speed condition of braking is met, until the speed of the aircraft reaches the failure speed (5 m/s) of a brake system, the anti-skid brake system stops working, and the operation is finished.
The initial aircraft speed of the aircraft antiskid braking system is vx(0) The initial wheel angular velocity w (0) is 160rad/s, 72 m/s. The simulation was run in a dry runway state, corresponding to an expected slip rate of 0.117. The simulation results of the anti-skid braking model under dry runway conditions are shown in fig. 6.
Fig. 6(a) shows the comparison waveform of the airplane speed and the wheel speed, and it can be seen that the deceleration of the airplane speed and the wheel speed is smooth, and the phenomena of large fluctuation and deep wheel slip do not occur. The slip ratio simulation result under the dry runway condition is shown in fig. 6(b), and it can be seen that the tracking performance of the actual slip ratio is basically consistent with the expected slip ratio, the actual slip ratio is always on the left side of the optimal slip ratio, the work is in a stable area, the error convergence of the slip ratio is fast, and the optimal slip ratio is tracked by the anti-skid braking system all the time. As shown in fig. 6(c) and (e), at a certain speed, the coupling coefficient and the slip ratio reach the maximum value, and the optimal coupling torque is ensured, so that the ideal braking efficiency is obtained. In addition, the load is small in the initial braking stage due to the fact that the speed of the airplane is high and the lifting force effect is obvious. When the speed of the airplane is reduced, the lift force of the airplane is reduced, the vertical load acting on the airplane wheel is larger and larger, and the combined moment is larger and larger. Also, when the braking torque reaches the maximum value of the coupling torque, the slip ratio can be stabilized around the optimum slip ratio. In fig. 6(d), it is found that the braking pressure is smooth and stable throughout the braking process, has small jitter, and has a similar waveform with the binding coefficient. In wet runway conditions, brake pressure is greatly dithered, but quickly restored. As can be seen in fig. 6(f), the dry runway aircraft braking time is 12.2s, the roll distance is 471.3m, and the braking efficiency is 96.3%.
The test is carried out by adopting a traditional multi-threshold speed difference plus bias voltage (PID + PBM) control mode, the braking time of the dry runway airplane is 13.7s, the sliding distance is 498.7m, and the braking efficiency is 92.7%. Compared with the traditional PID + PBM control strategy, the control method adopted by the invention has the advantages of higher braking efficiency, stronger anti-interference performance, reduced braking time, shortened sliding distance and better anti-sliding braking effect.
In order to test the error estimation effect of the adaptive RBF neural network on the uncertain disturbance, it is assumed that a sine curve with gaussian noise is introduced as the disturbance in the actual braking process, and as can be seen from fig. 7, the error between the estimated value output by the neural network and the actual disturbance curve is small, and a certain filtering effect is achieved.
In conclusion, the invention provides an airplane anti-skid brake system feedback linearization processing and integral sliding mode control method with uncertain disturbance online estimation. An accurate airplane anti-skid brake system model is established, then feedback linearization processing is carried out on an original system, and a system with strong complexity, strong nonlinearity and strong coupling is simplified into a linear system, so that the model is optimized to a great extent, and a control method depending on the accurate model obtains a good basic premise. And then, the slip ratio is subjected to closed-loop control by adopting a slip form control method of an integral slip form surface, so that the slip ratio can be ensured to rapidly and stably work in a stable area near the optimal slip ratio, a good inhibition effect can be achieved when large interference occurs, and buffeting is eliminated and weakened by introducing integral. And finally, the uncertainty interference on-line estimation is carried out by combining the self-adaptive RBF neural network, and a corresponding compensator is designed, so that the robustness and the self-adaptive capacity of the whole system are improved, and the simulation result is very close to the real airplane run-off condition.
While the foregoing is directed to the preferred embodiment of the present invention, it will be appreciated by those skilled in the art that various changes and modifications may be made therein without departing from the principles of the invention as set forth in the appended claims.

Claims (4)

1. An aircraft antiskid braking system control method with interference online estimation is characterized by comprising the following steps:
step 1, establishing an anti-skid braking system model and performing feedback linearization treatment;
the antiskid braking system model is expressed as:
Figure FDA0003657710380000011
in the formula, lambda is the slip ratio of the tire,
Figure FDA0003657710380000012
is a derivative of the slip ratio λ, f (λ) is a function related to the slip ratio λ, PAFor the pressure acting on the brake disc, R is the effective radius of the main wheel, kbFor the conversion coefficient of braking moment and pressure, vxFor the longitudinal sliding speed of the aircraft, JwIs the moment of inertia of the main wheel;
Figure FDA0003657710380000013
is a pressure PADerivative of cbIs the rigidity coefficient of the brake disc, L0For ball screw stroke, wmIs the rotor angular velocity;
Figure FDA0003657710380000014
is the angular speed w of the rotormDerivative of (A), JmIs the moment of inertia of the rotor, kTIs the motor torque constant, i is the armature current, BvIs a viscous damping coefficient;
the feedback linearization treatment of the anti-skid braking system model specifically comprises the following steps:
firstly, in the expression of the antiskid braking system model, lambda and PA、wmIs a system state, lambda is a system output, and i is a system input; let x1Is lambda, x2Is PA、x3Is wmAnd u is i, so that the expression of the antiskid braking system model is converted into a system nonlinear anti-radiation model form:
Figure FDA0003657710380000015
where y is the actual output of the system and x is [ x ]1 x2 x3]T；
Figure FDA0003657710380000016
h(x)＝[x1 0 0]T；
f(x)＝[f1(x) f2(x) f3(x)]T；
Wherein the content of the first and second substances,
Figure FDA0003657710380000017
then, based on the relative order and the order of the system being the same, performing coordinate transformation on the nonlinear anti-radiation model of the system to obtain an anti-skid braking system subjected to feedback linear processing, namely a linear standard system shown as the following formula:
Figure FDA0003657710380000021
wherein the content of the first and second substances,
Figure FDA0003657710380000022
step 2, introducing uncertain interference existing in the anti-skid braking system into the anti-skid braking system model after feedback linear processing, and designing an integral sliding mode surface and an integral sliding mode controller for the anti-skid braking system; the uncertainty interference comprises external disturbance caused by time variation and internal disturbance caused by parameter variation of an unmodeled part;
the sliding mode surface s of the integral sliding mode controller is expressed as:
Figure FDA0003657710380000023
wherein e is slip rate error of trackingA difference of e ═ y-ydY is the actual output of the system, ydIs the desired output of the system; c ═ C1 c2 1]Wherein c is1And c2Normal numbers that satisfy the Hurwitz stability criterion; k is a radical ofiTo integrate the gain, satisfy kiIs greater than 0; e is a vector of the systematic error vector,
Figure FDA0003657710380000024
the switching control law of the integral sliding mode controller based on the sliding mode surface is as follows:
Figure FDA0003657710380000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003657710380000026
sgn (·) is a sign function, and k and epsilon are normal numbers;
step 3, carrying out online estimation on the uncertain disturbance by adopting a self-adaptive RBF neural network, and introducing the estimated uncertain disturbance into a controller of an anti-skid brake system as a compensation part;
the specific process of adopting the self-adaptive RBF neural network to carry out on-line estimation on the uncertain disturbance comprises the following steps:
(1) when the external disturbances caused by time variation and the unmodeled part are represented as d (z, t), the internal disturbances caused by parameter variation are represented as Δ a and Δ Bu, and the uncertainty interference d (z) is represented as:
D(z)＝ΔA(z)+ΔB(z)u+d(z,t)；
in the formula (I), the compound is shown in the specification,
Figure FDA0003657710380000027
(2) assuming the presence of an unknown non-linear continuous function Dn(z) in order
Figure FDA0003657710380000028
For the input of the self-adaptive RBF neural network, the self-adaptive RBF network is adopted to approach the neural networkKnowing the non-linear function Dn(z); wherein a non-linear continuous function Dn(z) satisfies:
D(z)＝Dn(z)+Dd(z)；
wherein, | Dd(z)|≤δd，
Figure FDA0003657710380000031
Dd(z) is the influence Dn(z) interference term, δ, which is a non-linear continuous functiondIs Dd(z) boundaries of interference terms;
(3) self-adaptive RBF neural network approximation nonlinear continuous function Dn(z) actual output obtained
Figure FDA0003657710380000032
As an estimation value of the uncertainty interference of the system, and introducing the uncertainty interference into the controller as a compensation control law of the controller, namely:
Figure FDA0003657710380000033
in the formula (I), the compound is shown in the specification,
Figure FDA0003657710380000034
for the weight of the adaptive RBF neural network, H (xi) is the input
Figure FDA0003657710380000035
The resulting radial basis vectors.
2. The method of claim 1, wherein the adaptive RBF neural network weight update law is:
Figure FDA0003657710380000036
wherein gamma is an adaptive gain value, and gamma > 0.
3. Method according to claim 1, characterized in that a gaussian function h is choseni(xi) as a basis function of the adaptive RBF neural network, a radial basis vector H (xi) is formed by the base function, and an activation function of the radial basis function is expressed as:
Figure FDA0003657710380000037
in the formula, ciFor the ith hidden layer node center of the adaptive RBF neural network, diThe node base width parameter is the ith hidden layer.
4. The method according to claim 1, wherein the anti-skid brake system controller includes, in addition to the switching control law and the compensation control law, an equivalent control law for satisfying a final Lyapunov stabilization of the anti-skid brake system as
Figure FDA0003657710380000038
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