CN105035311B - A kind of aircraft gust alleviation adaptive feedforward control system - Google Patents

A kind of aircraft gust alleviation adaptive feedforward control system Download PDF

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CN105035311B
CN105035311B CN201510494812.0A CN201510494812A CN105035311B CN 105035311 B CN105035311 B CN 105035311B CN 201510494812 A CN201510494812 A CN 201510494812A CN 105035311 B CN105035311 B CN 105035311B
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CN105035311A (en
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王永志
李锋
吴健
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China Academy of Aerospace Aerodynamics CAAA
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Abstract

A kind of aircraft gust alleviation adaptive feedforward control system, including disturbance passage, control passage and perturbed Newton method passage;The discrete transfer function of control passage is picked out using discrimination method, perturbed Newton method passage is built based on the discrete transfer function;The disturbance picked out using perturbed Newton method passage calculates input as the feedback that feedforward controller coefficient is calculated, and design feedforward controller using FIR model, so as to increase compensating action, control efficiency is improve, the demand of aircraft gust alleviation adaptive feedforward control is met to the full extent.

Description

A kind of aircraft gust alleviation adaptive feedforward control system
Technical field
The present invention relates to a kind of aircraft gust alleviation adaptive feedforward control system, particularly a kind of aircraft fitful wind subtracts Slow adaptive feedforward control system, belongs to flying vehicles control technical field.
Background technology
In order to reduce the efficiency of influence and raising aircraft of the transporter to environment, following solution is high aspect ratio Light weight aircraft.For Altitude Long Endurance Unmanned Air Vehicle, determine that it must because high-altitude low-density and its low wing carry characteristic High aspect ratio low weight configuration must be used.The rigid motion frequency of this two classes aircraft is approached with structural elasticity vibration frequency, when The vibration of its structure will be seriously excited when running into fitful wind, this will substantially reduce riding quality (for transporter) and influence behaviour Vertical property, even results in structure destruction.
When known to the partial information of fitful wind information and system, feedforward control is better than general feedback for disturbance compensation Control.Ideally, feedforward control is completely eliminated the influence of measurable disturbance.Disturbance response and control during using feedforward control Non-time delay between compensation.
The invention of airborne laser detection sensor (Light detection and ranging, LIDAR) is with use should Gust load alleviation is carried out with feedforward controller there is provided premise.Also some other instruments, such as IntuVue tri- of Honeywell Dimension weather radar, it can also be used to carry out the collection of fitful wind information.
In existing feedforward control, as shown in figure 1, w in figuregT () is aircraft front fitful wind,For laser is visited The fitful wind signal that sensor is detected is surveyed, is wg(t) it is approximate, H be gust disturbances and aircraft response between transmission function, G be flying vehicles control actuator and its respond between accurate transmission function,It is the approximate of-G, GcIt is feedforward controller, from Adaptive filter is feedforward controller GcCoefficient is provided.U (t) and uaT () is respectively M signal, x (t) and y (t) is respectively and disturbs The output response of dynamic passage and control passage, e (t) is response error, be x (t) with y's (t) and.In adaptive feedforward control Response of the middle use aircraft under controller action, i.e. e (t) be used as feedforward controller coefficient calculating input, so before Feedback controller is to the compensation of aircraft based on closed loop response, and compensating action is less than normal.
The content of the invention
Technology solve problem of the invention is:Overcome the deficiencies in the prior art, there is provided a kind of aircraft gust alleviation is certainly Feedforward control system is adapted to, the discrete transfer function of control passage is picked out using discrimination method, based on the discrete transfer function Build perturbed Newton method passage;The disturbance picked out using perturbed Newton method passage calculates defeated as the feedback of feedforward controller coefficient Enter, and feedforward controller is designed using FIR (finite impulse response (FIR)) models, so as to increase compensating action, improve control Efficiency, meets the demand of aircraft gust alleviation adaptive feedforward control to the full extent.
Technical solution of the invention is:A kind of aircraft gust alleviation adaptive feedforward control system, including disturbance Passage, control passage and perturbed Newton method passage;
The disturbance channel reception fitful wind signal wgT (), and output disturbance response signal x (t), control passage receive fitful wind Test signalAnd output control response signal y (t);
Perturbed Newton method channel reception response error signal e (t), output disturbance response identification signalAnd as anti- Feedback signal inputs to control passage, and response error signal e (t) is that the output for disturbing passage responds x (t) and control passage Output response y (t) sum, the perturbed Newton method passage is by formula:
Be given, wherein q-1It is delay operator, q-1U (t)=u (t-1), u (t) are flying vehicles control actuator input signal, A(q-1) and B (q-1) by formula:
Be given,It is exact transfer function G between the input of flying vehicles control actuator and flying vehicles control channel response Approximate function.
The flying vehicles control actuator is input into the approximate letter with exact transfer function G between flying vehicles control channel response NumberDetailed process is:
I () manipulates control under aircraft trim condition to control actuator input test signal u (t) of aircraft Rudder face, response signal y (t) of record-setting flight device control passage;
(ii) it is input with u (t), y (t) is output, the input of identification flying vehicles control actuator and flying vehicles control passage The approximate function of exact transfer function G between response signalSpecifically by formula:Be given, wherein
The identification is completed by the tfest functions in MATLAB softwares.
Test signal u (t) is using frequency with time increased sinusoidal signal;Specifically by formula:
U (t)=u0+uA(2πft)
Be given, wherein u0It is constant value, uAIt is the amplitude of input signal, f is the instantaneous frequency of t, by formula:
F=f0t
Be given, wherein f0It is constant value.
The control passage includes laser acquisition sensor, wave filterSef-adapting filter, feedforward controller and control Actuator;
The laser acquisition sensor receives the fitful wind test signal w of inputg(t), and the fitful wind signal that will be detectedIt is sent to feedforward controller and wave filterThe wave filterWith the fitful wind signal for measuringIt is input, output Signal uaT () gives sef-adapting filter, sef-adapting filter is according to the output signal u for receivingaT () and disturbance response recognize letter NumberCalculate the coefficient of feedforward controller and export to feedforward controller, feedforward controller is according to the coefficient and battle array for receiving Wind numberProduce feed-forward control signals u (t) export actuator and perturbed Newton method passage to control, control actuator according to Feed-forward control signals u (t) for receiving carry out feedforward control.
The feedforward controller is the feedforward controller based on FIR model.
The feedforward controller discrete transfer function GcZ () is specifically by formula:
Be given, wherein BkZ () is basic function, LkFor coefficient comes from sef-adapting filter, n is previously given feedforward control Device exponent number processed, z is discrete transfer function variable;
Basic function BkZ () is by formula:
Bk(z)=z-k, k=1,2 ..., n
Be given.
The LkObtained by adaptive algorithm, try to achieve the coefficient vector L (N) of corresponding each basic function outputs of time step N =[L1(N),L2(N),...,Ln(N)] concretely comprise the following steps:
(1) initialization coefficient vector L (0)=[0,0 ..., 0], P (0)=δ-1I, wherein δ are constant, and δ is single more than 0, I Bit matrix;
(2) in time step N, the coefficient L (N) of each basic function output is calculated, specifically by formula:
Be given, wherein k (N) is gain vector, by formula:
Be given, π (N) is by formula:
π (N)=P (N-1) Φ (N)
Be given, P (N) is inverse correlation matrix, by formula:
P (N)=λ-1P(N-1)-λ-1k(N)ΦT(N)P(N-1)
Be given, λ is forgetting factor, 0<λ≤1;FIR moulds when being time step N The output of each basic function in type;
ε (N) is by formula:
ε (N)=e (N)-LT(N-1)Φ(N)
Be given, e (N) is the response of the aircraft in time step N.
Compared with the prior art, the invention has the advantages that:
System in the present invention transfers function to structure perturbed Newton method passage using control passage, and by perturbed Newton method The disturbed value that passage is recognized is logical for utilizing disturbance in the resolving of feedforward controller coefficient, with existing method as value of feedback Road response signal and control passage response signal sum, the i.e. closed loop response of aircraft are compared as value of feedback, increase compensation Effect, improves control efficiency.
Brief description of the drawings
Fig. 1 is existing feedforward control block diagram;
Fig. 2 is gust alleviation control block diagram of the present invention;
Fig. 3 is the FIR controller model schematic diagrames that the present invention is used;
Fig. 4 is the dimensional airfoil illustraton of model in the embodiment of the present invention;
Fig. 5 is sinusoidal signal schematic diagram in the embodiment of the present invention;
Fig. 6 is the response schematic diagram of aerofoil profile in the embodiment of the present invention;
Fig. 7 is " 1-cos " fitful wind schematic diagram in the embodiment of the present invention;
Fig. 8 is the controller response schematic diagram under " 1-cos " fitful wind;
Fig. 9 is the deflection schematic diagram of control rudder face under " 1-cos " fitful wind;
Figure 10 is Von K á rm á n fitful wind schematic diagrames in the embodiment of the present invention;
Figure 11 is Von K á rm á n fitful winds Airfoil pitching open-loop responses and the controller control using FIR_e modellings Under response schematic diagram;
Figure 12 is the controller under Von K á rm á n fitful winds using FIR_e modellings and the control of FIR_x modellings Device aerofoil profile responds contrast schematic diagram;
Figure 13 be Von K á rm á n fitful winds under, the control of controller and FIR_x modellings based on FIR_e modellings The control control surface deflection schematic diagram of device.
Specific embodiment
Specific embodiment of the invention is further described in detail below in conjunction with the accompanying drawings.
The gust alleviation control block diagram that the present invention is used is as shown in Fig. 2 as can be seen from Figure 2, the system in the present invention includes disturbing Dynamic passage, control passage and perturbed Newton method passage;
The disturbance channel reception fitful wind signal wgT (), and output disturbance response signal x (t), control passage receive fitful wind Test signalAnd output control response signal y (t);
Perturbed Newton method channel reception response error signal e (t), output disturbance response identification signalAnd as anti- Feedback signal inputs to control passage, and response error signal e (t) is that the output for disturbing passage responds x (t) and control passage Output response y (t) sum, the perturbed Newton method passage is by formula:
Be given, wherein q-1It is delay operator, q-1U (t)=u (t-1), u (t) are flying vehicles control actuator input signal, A(q-1) and B (q-1) by formula:
Be given,It is exact transfer function G between the input of flying vehicles control actuator and flying vehicles control channel response Approximate function.
The control passage includes laser acquisition sensor, wave filterSef-adapting filter, feedforward controller and control Actuator;
The laser acquisition sensor receives the fitful wind test signal w of inputg(t), and the fitful wind signal that will be detectedIt is sent to feedforward controller and wave filterThe wave filterWith the fitful wind signal for measuringIt is input, output Signal uaT () gives sef-adapting filter, sef-adapting filter is according to the output signal u for receivingaT () and disturbance response recognize letter NumberProduce the coefficient of feedforward controller and export to feedforward controller, feedforward controller is according to the coefficient and battle array for receiving Wind test signalProduce feed-forward control signals u (t) to export and give control actuator and perturbed Newton method passage, control actuator Feedforward control is carried out according to feed-forward control signals u (t) for receiving.Using feedforward control, can be carried in aircraft encounter fitful wind Before carry out responsive corrections.
Common feed forward control method be using e (t) as sef-adapting filter input, this will reduce feedforward compensation effect Really.Perturbed Newton method passage is increased on the basis of hereinbefore adaptive feedforward control method, the approximate disturbance for coming will be picked outAs the input of sef-adapting filter.
For preferable feedforward controller
But be typically difficult to obtain the exact transfer function of controlled device in practice in engineering, typically take following side Method.
1st, algorithmic derivation
First, in control actuator input test signal u (t), obtain corresponding aircraft and respond y (t), believed according to input Number with output response go out transmission function G's using the linear dimensions identification model tfest Function identifications in business software MATLAB Approximate functionWherein
q-1It is delay operator, wherein algorithm is x (t)=q-1X (t-1), x (t) are the response at t sample point moment, x (t-1) Be the t-1 moment, i.e., the response at next sample point moment.
Relation in control block diagram can be obtained
With
X (t)=H (q-1)wg(t) (4)
Can be drawn by formula (2), (3), (4) simultaneous
The coefficient that thus be accordingly used in system feedforward control can be by with uaT () is input, x (t) is calculated for output using self adaptation Method is calculated.
In actual applications, because response error e (t) is easy to be measured by sensor, frequently with e (t) as adaptive The input of wave filter is answered, i.e., using equation below
Carry out the coefficient of computing controller, whereinIt is approximate using FIR model in the present invention.Due to e (t) generally Differ larger with disturbance response x (t), this will influence control efficiency.This method is obtained approximately by increasing perturbed Newton method passage DisturbanceIts derivation is as follows
E (t)=x (t)+y (t) (7)
Z (t)=A (q-1)e(t)-q-dB(q-1)u(t)≈A(q-1)x(t) (9)
Can be drawn by formula (7), (8), (9) simultaneous
2nd, controller
Controller G is thought in this methodcIt is linear time invariant system, is built based on FIR model, its discrete transfer function Gc Z () can be write as
Wherein BkZ () is basic function, LkCome from the sef-adapting filter in control block diagram for coefficient, n is previously given The exponent number of controller, z is discrete transfer function variable.
Basic function B in this methodkZ () uses following formula:
Bk(z)=z-k, k=1,2 ..., n, (12)
The basic function is FIR model.Using the controller model G of FIR modelcIt is illustrated in fig. 3 shown below,
3rd, adaptive algorithm
The corresponding real-time adjustment of response magnitude controls rudder face amplitude to slow down when adaptive algorithm can meet with fitful wind according to flight Gust response, adaptive algorithm returns least-squares algorithm using index weight, using the method come in calculating formula (11) and Fig. 3 Coefficient Lk(k=1,2 ..., n).A cost function is defined first
Wherein N is the quantity of time step, and λ is forgetting factor,It is the response of aircraftWith the output r of FIR model The error of (i) in time step i, i.e.,
It is wherein vectorialIt is the output of each basic function in i time step FIR models, L (N)=[L1(N),L2(N),...,Ln(N)] be corresponding each basic function of N time steps coefficient, or for tap-weights to Amount.Adaptive algorithm is comprised the following steps:
(1) initialize, initialization coefficient vector L (0)=[0,0 ..., 0], P (0)=δ-1I, wherein δ are constant, and δ is more than 0, I is unit matrix;
(2) iteration, in time step N, calculates the coefficient L (N) of each basic function output, specifically by formula:
Be given, wherein k (N) is gain vector, by formula:
Be given, π (N) is by formula:
π (N)=P (N-1) Φ (N)
Be given, P (N) is inverse correlation matrix, by formula:
P (N)=λ-1P(N-1)-λ-1k(N)ΦT(N)P(N-1)
Be given, λ is forgetting factor, 0<λ≤1;Φ (N)=[ua1(N),ua2(N),...,uan(N)] FIR when being time step N The output of each basic function in model;
ε (N) is by formula:
ε (N)=e (N)-LT(N-1)Φ(N)
Be given, e (N) is the response of the aircraft in time step N.
Specific embodiment
The step of describing to carry out aircraft gust alleviation using the method by taking the gust alleviation of dimensional airfoil as an example to control And effect.
The model of dimensional airfoil is illustrated in fig. 4 shown below, the chord lengths of b half in Fig. 4, and cb is distance of the chord length midpoint to rudder face rotating shaft, E.a. it is aerofoil profile elasticity shaft position, c.g. is aerofoil profile position of centre of gravity, ahIt is chord length midpoint to aerofoil profile elastic shaft distance and the ratio of b Value, xαTo the distance of aerofoil profile center of gravity and the ratio of b, α is aerofoil profile luffing angle to aerofoil profile elastic shaft, and h is aerofoil profile sink-float distance, and δ is Aerofoil profile control surface deflection angle, KαAnd KξRespectively aerofoil profile sink-float rigidity and relative resilient axle torsional rigidity.The aerofoil profile has sink-float With two frees degree of pitching.
The case study on implementation is using its pitch freedom of controller major control in the present invention.Relevant parameter in the implementation case As shown in table 1:
Table 1
Variable Numerical value
B (rice) 0.175
-0.3333
0.09
It is the control effect of controller in the test present invention, fitful wind model considers " 1-cos " and two kinds of Von K á rm á n.It is first Multicycle " 1-cos " fitful wind is first tested, free speed of incoming flow is 8 meter per seconds.
(1) the input δ of rudder face is controlled as aerofoil profile using sinusoidal signal u (t), G is recognized,
Test signal u (t) is using frequency with time increased sinusoidal signal;Specifically by formula:
U (t)=u0+uA(2πft)
Be given, wherein u0It is constant value, uAIt is the amplitude of input signal, f is the instantaneous frequency of t, by formula:
F=f0t
Be given, wherein f0It is constant value, f needs covering frequency range interested.
u0Take 0, uAThe scope for taking 1, f is 0-8Hz.The schematic diagram of sinusoidal signal is as shown in figure 5, in above-mentioned battle array wind action Under, the response of aerofoil profile is as shown in fig. 6, from fig. 6, it can be seen that pitching mode is fully energized.
It is input with u (t), with u (t) for input, y (t) they are to export the tfest Function identification G using in MATLAB softwares, Number of poles is taken as 7, and zero point quantity is taken as 6.It is hereby achieved thatFor
(2) structure of perturbed Newton method passage
Previous step has picked out the Approximation Discrete transmission function of control passage, can obtain:
A(z-1)=1-6.7760z-1+19.6600z-2-31.6800z-3+30.6100z-4-17.7300z-5+5.7000z-6- 0.7849z-7
B(z-1)=0.0040z-1-0.0231z-2+0.0560z-3-0.0725z-4+0.0528z-5-0.0205z-6+ 0.0033z-7
D=0
Using A (z-1)、B(z-1) and d build perturbed Newton method passage.
(3) construction basic function BkZ () and design controller, basic function B is constructed using the method in formula (12)k(z), Controller is designed according to Fig. 3.
Gust alleviation effect
(1) " 1-cos " fitful wind
Test the effect that slows down of " 1-cos " fitful wind, fitful wind schematic diagram as shown in fig. 7, wherein fitful wind intensity is 1m/ first S, fitful wind length is 1.75m.Hereinafter, represent to use with FIR_e and calculated by sef-adapting filter of the closed loop response of aerofoil profile The controller of the 20 rank FIR models design of input, controller of the present invention is represented with FIR_x, i.e., pick out what is come to recognize passage Disturb the controller that the 20 rank FIR models design of input is calculated for sef-adapting filter.Under the effect of above-mentioned fitful wind, aerofoil profile pitching Open-loop response and the pitching response in the case where two kinds of controllers are controlled are as shown in figure 8, solid line open loop ring for aerofoil profile open loop pitching Should.By be can be seen that in Fig. 8 using after two kinds of controllers, aerofoil profile pitching response amplitude is reduced, using FIR_x of the present invention Controller is become apparent than the gust alleviation effect using FIR_e controllers, and gust response amplitude is significantly less than using FIR_e controls The gust response amplitude of device processed.The deflection of corresponding control rudder face is as shown in Figure 9.
(2) Von K á rm á n fitful winds
The effect that slows down of Von K á rm á n fitful winds is tested, as shown in Figure 10, peak gust speed is 0.7m/ to fitful wind schematic diagram s.Under fitful wind effect, the pitching under aerofoil profile pitching open-loop response and the control of FIR_e and FIR_x controllers is responded such as Figure 11 institutes Show, solid line open loop are responded for aerofoil profile open loop pitching.By be can be seen that in Figure 11 using after FIR_e controllers, aerofoil profile is bowed Response amplitude is faced upward to reduce.Responded to such as Figure 12 institutes using the fitful wind pitching of FIR_e controllers and FIR_x controllers of the present invention Show, be can be seen that from the point of view of whole structure by Figure 12, FIR_x adaptive feedforwards controller of the present invention is than FIR_e controller Gust alleviation effect will get well.Open loop is as shown in table 3 with the standard deviation of controller action Airfoil response, from the standard deviation of table 3 below In can also draw the conclusion, using FIR_e controllers make gust response amplitude standard deviation reduction by 29.2%, use the present invention control Device processed makes gust response amplitude standard deviation reduction by 34.3%.
Table 3
Open loop or controller type Standard deviation [deg]
Open loop 0.2165
FIR_e controllers 0.1533
FIR_x controllers 0.1357
As shown in figure 13, solid line is the control surface deflection of FIR_x controllers, short stroke to corresponding controller control surface deflection in the figure Line is the control surface deflection of FIR_e controllers of the present invention.
The content not being described in detail in description of the invention belongs to the known technology of professional and technical personnel in the field.

Claims (8)

1. a kind of aircraft gust alleviation adaptive feedforward control system, it is characterised in that:Including disturbance passage, control passage and Perturbed Newton method passage;
The disturbance channel reception fitful wind signal wgT (), and output disturbance response signal x (t), control passage receive fitful wind test SignalAnd output control response signal y (t);
Perturbed Newton method channel reception response error signal e (t), output disturbance response identification signalAnd as feedback letter Number input to control passage, response error signal e (t) be disturb passage output disturbance response signal x (t) and control it is logical Control response signal y (t) sum of road output, the perturbed Newton method passage is by formula:
x ^ ( t ) = 1 A ( q - 1 ) ( A ( q - 1 ) e ( t ) - q - d B ( q - 1 ) u ( t ) )
Be given, wherein q-1It is delay operator, q-1U (t)=u (t-1), u (t) are flying vehicles control actuator input signal, A (q-1) and B (q-1) by formula:
G ^ ( q - 1 ) = q - d B ( q - 1 ) A ( q - 1 )
Be given,For flying vehicles control actuator input between flying vehicles control channel response exact transfer function G it is approximate Function.
2. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 1, it is characterised in that:It is described Flying vehicles control actuator is input into the approximate function of the exact transfer function G and flying vehicles control channel response betweenSpecific mistake Cheng Wei:
(2-1) is input into flying vehicles control actuator input signal u under aircraft trim condition to the control actuator of aircraft T () manipulates control rudder face, response signal y (t) of record-setting flight device control passage;
(2-2) is input with u (t), and y (t) is output, the input of identification flying vehicles control actuator and flying vehicles control channel response Between exact transfer function G approximate functionSpecifically by formula:Be given, wherein
3. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 2, it is characterised in that:It is described Identification is completed by the tfest functions in MATLAB softwares.
4. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 1 and 2, it is characterised in that: Input signal u (t) is using frequency with time increased sinusoidal signal;Specifically by formula:
U (t)=u0+uA(2πft)
Be given, wherein u0It is constant value, uAIt is the amplitude of input signal, f is the instantaneous frequency of t, by formula:
F=f0t
Be given, wherein f0It is constant value.
5. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 1 and 2, it is characterised in that: The control passage includes laser acquisition sensor, the first wave filter, sef-adapting filter, feedforward controller and control start Device;
The laser acquisition sensor receives the fitful wind test signal of inputAnd the fitful wind signal w that will be detectedgT () is sent out Give feedforward controller and the first wave filter, fitful wind signal w of first wave filter to measuregT () is input, output signal uaT () gives sef-adapting filter, sef-adapting filter is according to the output signal u for receivinga(t) and disturbance response identification signalCalculate the coefficient of feedforward controller and export to feedforward controller, feedforward controller is according to the coefficient and fitful wind for receiving Signal wg(t), produce feed-forward control signals as flying vehicles control actuator input signal u (t) export actuator to control and Perturbed Newton method passage, control actuator carries out feedforward control according to flying vehicles control actuator input signal u (t) for receiving.
6. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 5, it is characterised in that:It is described Feedforward controller is the feedforward controller based on FIR model.
7. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 6, it is characterised in that:It is described The discrete transfer function G of feedforward controllercZ () is specifically by formula:
G c ( z ) = &Sigma; k = 1 n L k B k ( z )
Be given, wherein BkZ () is basic function, LkFor coefficient comes from sef-adapting filter, n is previously given feedforward controller Exponent number, z is discrete transfer function variable;
Basic function BkZ () is by formula:
Bk(z)=z-k, k=1,2 ..., n
Be given.
8. a kind of aircraft gust alleviation adaptive feedforward control system according to claim 7, it is characterised in that:It is described LkObtained by adaptive algorithm, try to achieve coefficient vector L (N)=[L of corresponding each basic function outputs of time step N1(N),L2 (N),...,Ln(N)] concretely comprise the following steps:
(8-1) initialization coefficient vector L (0)=[0,0 ..., 0], P (0)=δ-1I, wherein δ are constant, and δ is unit more than 0, I Matrix;
(8-2) calculates the coefficient L (N) of each basic function output, specifically by formula in time step N:
L ( N ) = L ( N - 1 ) + k ( N ) &epsiv; &OverBar; ( N )
Be given, wherein k (N) is gain vector, by formula:
k ( N ) = &pi; ( N ) &lambda; + &Phi; T ( N ) &pi; ( N )
Be given, π (N) is by formula:
π (N)=P (N-1) Φ (N)
Be given, P (N) is inverse correlation matrix, by formula:
P (N)=λ-1P(N-1)-λ-1k(N)ΦT(N)P(N-1)
Be given, λ is forgetting factor, 0<λ≤1;It is each in FIR model when being time step N The output of individual basic function;
ε (N) is by formula:
ε (N)=e (N)-LT(N-1)Φ(N)
Be given, e (N) is the response of the aircraft in time step N.
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