CN106444368A - Near space vehicle preset performance attitude tracking control method with input nonlinearity - Google Patents
Near space vehicle preset performance attitude tracking control method with input nonlinearity Download PDFInfo
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Abstract
The invention discloses a near space vehicle (NSV) preset performance attitude tracking control method with input nonlinearity. The method comprises the following steps: (1) enabling an input nonlinearity link including a dead zone and input saturation be equivalent to an input saturation link by means of an added dead zone right inverse function, and adding the input nonlinearity to a NSV attitude model; (2) introducing preset performance limit of tracking errors, adjusting the transient performance and the steady-state error of a tracking error signal at the same time, and converting the tracking error signal constrained by preset performance into a unconstrained converted error signal by means of an error conversion function; and (3) constructing an auxiliary system and designing an adaptive neural network attitude tracking controller by means of a backstepping method. The method enables the NSV attitude model to be capable of tracking a desired attitude angle signal with parameter uncertainty, external disturbances, and input nonlinearity.
Description
Technical field
The present invention relates to a kind of Near Space Flying Vehicles default capabilities Attitude tracking control method considering unbalanced input, belong to
In Near Space Flying Vehicles technical field of flight control.
Background technology
Near Space Flying Vehicles (NSV:Near space vehicle) as a kind of new re-entry space vehicle, merge biography
The advantage of system aerospace aircraft, has a extensive future in civilian and military field, has obtained extensive concern.Simultaneously by
In its complicated characteristic, as changeable in flight environment of vehicle, mission mode is various, close coupling, non-linear etc., designs effective control
Method becomes a job that is important and having challenge.The gesture stability of NSV is the basis of its safe flight, therefore this patent
With the attitude motion model of Near Space Flying Vehicles as object of study, carry out the exploitation of its default capabilities Attitude tracking control method.
Research currently for tracking control problem is concentrated mainly in the research of steady-state behaviour, that is, ensure that tracking error is received
Hold back in bounded aggregate or asymptotic convergence to initial point, and the research to mapping is also little.In fact mapping is improving NSV
Play an important role in control system performance.For example, larger overshoot may be such that executor exceeds its amplitude and limits, from
And lead to closed loop system unstable.Therefore, need transient state and steady-state behaviour are studied simultaneously in NSV controller design.For solution
Determine this problem, introduce the concept of default capabilities.
By the selection of performance function, row constraint is entered to the mapping and steady-state behaviour of tracking error simultaneously, and pass through
Affined tracking error is converted to free signal by error switch technology, is protected by the boundedness proving this signal
The default capabilities of card tracking error limit.
Meanwhile, NSV its rudder face and motor power in practical flight can be subject to many limitations, such as amplitude, bandwidth, frequency
Deng thus executor may produce the nonlinear characteristics such as saturation, dead band, gap, showing as defeated in NSV attitude mode
Enter nonlinear characteristic.For solving the problems, such as the unbalanced input of saturation and dead band composition, the right inverse function in dead band is positioned over system
Before unbalanced input module, this two nonlinear elements are comprehensively equivalent to an input saturation element, thus using auxiliary
System approach solves the problems, such as unbalanced input.Aid system method is by constructing a stable external system, it will be entered
To in error signal, reduce or offset the impact of unbalanced input.The method is simply effective, it is easy to accomplish.
In addition, usually there will be unknown Parameter uncertainties and external disturbance in the dynamic model of NSV, this is uncertain possible
The performance of system can be affected.Neutral net (NNs:Neural network) due to its can any Approximation of Continuous Functions,
It is widely used in the design of uncertain nonlinear system.Wherein, as a kind of neutral net of linear parameterization, radially
Basic function (RBF:Radial basis function) neutral net is widely used in and approaches unknown modeling error.Therefore, adopt
With RBFNNs in system unknown uncertain approach, and compensate in virtual controlling rule and controller design.
Backstepping control strategy is a kind of nonlinear feedback, compares in actual control system
It is easier to realize in other nonlinear methods.Therefore, the Strict-feedback structure according to converting system, using backstepping
Technology carries out the design of adaptive neural network tracking control unit.
Content of the invention
For above-mentioned the deficiencies in the prior art, it is an object of the invention to provide a kind of near space with unbalanced input flies
Row device default capabilities Attitude tracking control method, enables to NSV attitude mode having Parameter uncertainties, external disturbance and defeated
Enter nonlinear in the case of can follow the tracks of desired attitude angle signal.
For achieving the above object, the present invention employs the following technical solutions：
A kind of Near Space Flying Vehicles default capabilities Attitude tracking control method with unbalanced input, walks including following
Suddenly：
(1) pass through the right inverse function in dead band adding, the unbalanced input link comprising dead band and input saturation is equivalent to
Input saturation element, this unbalanced input is added in NSV attitude mode；
(2) default capabilities introducing tracking error limit, and the mapping to tracking error signal and steady-state error are simultaneously
It is adjusted, and by error transfer function, the tracking error signal being constrained by default capabilities is converted to free conversion
Error signal；
(3) construct aid system, unbalanced input impact to control system performance is reduced or eliminated, according to NSV attitude
The feature of model, control system speed loop respectively does not know to approach using RBF neural is unknown to system, profit
With adaptive technique, composite interference is processed, carry out the design of Attitude tracking control device by backstepping method.
In described step (1),
Unbalanced input linkIt is expressed as tandem structure, including asymmetrical input saturation element and dead band
Link, wherein McFor preferable control input,For actual control input；
Saturation function sat () is expressed as：
Wherein Mc max i,Mc min iRepresent the bound of i-th control input, viFor saturation element output；
Dead zone Db() is expressed as：
Wherein bri>0,bli<0 is that known dead band is interval, mri>0,mli>0 is dead band Slope Parameters；
Introduce Dead zone DbThe right inverse function of ()This function meetsIt is defined as：
By above-mentioned functionBefore being placed on unbalanced input link, produce new Cascading Nonlinearity link, whereinControl law for design；
Above-mentioned control law has following several situation：
Situation 1：
According to saturation function sat () and right inverse functionDefinition obtain：
Know againTherefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 2：
Similar with situation 1, according to saturation function sat () and right inverse functionDefinition obtain：
Understand simultaneouslyTherefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 3：
In the case of being somebody's turn to do,ThusTherefore
Consider above-mentioned three kinds of situations, can obtain：
The equation meansI.e. all of nonlinear element can overall seeing as
New saturation element；Therefore, the right inverse function of Dead zone is positioned over before system unbalanced input link it becomes possible to adopt one
As constrained control method processing unbalanced input problem；
Above-mentioned unbalanced input link is added in NSV attitude mode and obtains：
Wherein Ω=[α, β, μ]TFor attitude angle vector, represent the angle of attack, yaw angle and flight path inclination angle respectively；ω=[p,
q,r]TFor attitude angle roll angle velocity vectors, represent rolling angular speed, pitch rate and yawrate respectively；F1∈R3,
F2∈R3For known function of state vector, G1∈R3×3,G2∈R3×3Control gain matrix for known system；△F1∈R3,△
F2∈R3For unknown smooth function, represent system modelling error；d1∈R3,d2∈R3For unknown external disturbance；satb() is
New saturation function, it is as defined above shown.
In described step (2),
Tracking error meets following default capabilities and limits：
el(t)≤e(t)≤eu(t)
Wherein e (t)=[e1(t),e2(t),e3(t)],With
For the bound function up and down of default capabilities function, and meetThe overshoot of tracking error signal is maintained atIn interval, maximum allowable steady-state error must is fulfilled forTherefore, the default wink of tracking error
State property can be realized by selecting suitable performance function with steady-state behaviour；
Limit for realizing default capabilities, introduce transfer function and default capabilities restriction is converted to free signal, should
Function is designed as：
Wherein σ=[σ1,σ2,σ3]TFor transformed error signal；
Definition according to transfer function：
In addition, trying to achieve tracking error eiWith regard to σiPartial derivative be：
Above formula shows tracking error eiWith transformed error σiFor strictly increasing relation；Therefore, if transformed error σiBounded,
Tracking error default capabilities limit and always set up, and that is, the boundedness of transformed error σ ensure that the default capabilities limit of tracking error e
System；
In addition, trying to achieve transformed error σiWith regard to tracking error eiPartial derivative be：
Defined function M (e, eu,el) be：
Therefore, M (e, eu,el) inverse be constantly present；
Transformed error σ is obtained with regard to time derivation：
WhereinTransformed error is dynamically substituted in system equation and obtain new error system
For：
In described step (3),
Step a, system control loop are divided into speed loop, are that attitude angle loop is analyzed to slow loop first：Construction
Aid system, using backstepping control strategy design virtual controlling rule, adopts radial basis function neural network pair simultaneously
In slow loop unknown uncertain approached, using adaptive approach, composite interference is processed, specially：
A-1, the impact for unbalanced input is reduced or eliminated, construct the aid system of following form：
Wherein ξ1∈R3,ξ2∈R3For aid system state variable, matrixDesign meets：For actually entering the difference with preferable input；
A-2, using radial base neural net approximation system unknown uncertain △ F1, it most preferably approaches and is written as：
It is wherein W1 *∈Rq×3Neutral net best initial weights matrix, utilizesIt is approached, its adaptive law designs
For：
Wherein P1=P1 T>0,τ1>0 is design parameter or matrix；S (Ω)=[S (Ω)1,S(Ω)2,…,S(Ω)q]TFor
RBF, is typically chosen in the form of Gaussian function, that is,d1kFor neutral net kth
The center vector of individual node, b1kFor the sound stage width parameter of k-th node of neutral net, k=1,2 ..., q；In addition,
For approximate error, and
A-3, RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D1||≤δ1, wherein δ1>0；Using variableThe upper bound to composite interference
δ1Approached, its adaptive law is designed as：
Wherein M (e, eu,el)=diag { M11,M22,M33, β1>0 is design parameter；
A-4, the aid system signal xi according to construction in step a-11, in step a-2, RBF neural is to uncertain
Estimated valueAnd in step a-3 the composite interference upper bound parameter update lawUsing backstepping control design case
Method, obtains virtual controlling rule：
WhereinFor design
Feedback matrix, z1=σ-ξ1,Follow the tracks of the first derivative of signal for expectation,
Step b, it is that attitude angular rate loop is analyzed to fast loop, design control using backstepping control strategy
Device processed, does not know to approach to unknown in fast loop using RBF neural, using adaptive approach to composite interference simultaneously
Processed, specially：
B-1, using RBF neural approximation system unknown uncertain △ F2, it most preferably approaches and is written as：
WhereinFor neutral net best initial weights matrix, utilizeIt is approached, its adaptive law designs
For：
WhereinIt is design parameter or matrix；S (Ω, ω)=[S (Ω, ω)1,S(Ω,ω)2,…,S
(Ω,ω)q]TFor RBF, it is typically chosen in the form of Gaussian function, that is,
d2kFor the center vector of k-th node of neutral net, b2kFor the sound stage width parameter of k-th node of neutral net, k=1,2 ...,
q；In addition,For approximate error, and
B-2, RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D2||≤δ2, wherein δ2>0.Using variableUpper to composite interference
Boundary δ2Approached, its adaptive law is designed as：
Wherein β2>0 is design parameter；
B-3, the aid system signal xi according to construction in step a-12, in step b-1, RBF neural is to uncertain
Estimated valueAnd in step b-2 the composite interference upper bound parameter update lawControlled using backstepping and set
Meter method, obtaining control law is：
Wherein z2=ω-α1-ξ2,For designing square
Battle array.
The invention has the beneficial effects as follows：
The present invention compared with prior art, has following significant advantage：The present invention passes through the right inverse function in dead band adding,
Unbalanced input is equivalent to input saturation element, construction auxiliary system processes input saturation, simple and easy to do.It is simultaneously introduced tracking
The default capabilities of error, and by error transfer function, the tracking error being constrained by default capabilities is converted to free
Transformed error signal.Consider the kinetic characteristic of NSV attitude system, control system is divided into speed loop, using RBF neural
System is not known to approach, using adaptive technique, composite interference is processed, by backstepping side simultaneously
Method carries out the design of Attitude tracking control device.Designed controller make NSV attitude system exist unknown uncertain, outside
Realization in the case of interference and unbalanced input is preset tracking performance and is limited.
Brief description
Fig. 1 is unbalanced input φ (M of the present inventionc) tandem structure chart；
Fig. 2 is input saturation function sat () schematic diagram；
Fig. 3 is Dead zone Db() schematic diagram；
Fig. 4 be unbalanced input φ () withThe structure chart combining；
Fig. 5 is the overall control block diagram of NSV attitude control system.
Specific embodiment
Below in conjunction with the accompanying drawings the present invention is further described.
The Near Space Flying Vehicles default capabilities Attitude tracking control method with unbalanced input of the present invention, including following
Step：
Step 1. passes through the right inverse function in dead band adding, will be equivalent for the unbalanced input link comprising dead band and input saturation
For inputting saturation element, this unbalanced input is added in NSV attitude mode；
The default capabilities that step 2. introduces tracking error limit, and the mapping to tracking error signal and steady-state error are same
When be adjusted, and by error transfer function, the tracking error signal being constrained by default capabilities is converted to free turn
Change error signal；
Step 3. constructs aid system, unbalanced input impact to control system performance is reduced or eliminated, according to NSV appearance
The feature of states model, control system speed loop respectively does not know to approach using RBF neural is unknown to system,
Using adaptive technique, composite interference is processed, by backstepping method carry out adaptive neural network attitude with
The design of track controller.
Wherein, the NSV attitude mode of step 1 can be expressed as：
Wherein Ω=[α, β, μ]TFor attitude angle vector, represent the angle of attack, yaw angle and flight path inclination angle respectively.ω=[p,
q,r]TFor attitude angle roll angle velocity vectors, represent rolling angular speed, pitch rate and yawrate respectively.Mc=[lc,
mc,nc]TFor control moment vector, represent rolling, pitching and yawing respectively.F1∈R3,F2∈R3For known function of state
Vector, G1∈R3×3,G2∈R3×3Control gain matrix for known system.△F1∈R3,△F2∈R3For unknown smooth letter
Number, represents system modelling error, d1∈R3,d2∈R3For unknown external disturbance.
Unbalanced input linkTandem structure can be expressed as, as shown in figure 1,
Including asymmetrical input saturation element and dead band link, wherein McFor preferable control input, McFor actual control input.
Can be seen by Fig. 2, saturation function sat () can be expressed as：
Wherein Mc max i,Mc min iRepresent the bound of i-th control input, viFor saturation element output.
Can be obtained by Fig. 3, Dead zone Db() can be expressed as
Wherein bri>0,bli<0 is that known dead band is interval, mri>0,mli>0 is dead band Slope Parameters.
According to the definition of unbalanced input, it is understood that this nonlinear characteristic is more complicated and very difficult direct process.Therefore,
For solving this problem, introduce Dead zone DbThe right inverse function of ()This function meetsIt is defined as：
By above-mentioned functionBefore being placed on unbalanced input link, produce new Cascading Nonlinearity link, as Fig. 4 institute
Show, whereinControl law for design.Below, according to different situations, labor is carried out to this link.
Needed to do hypothesis below before analyzing：
Assume 1：For the unbalanced input link of NSV attitude mode, its saturation is far longer than deadband boundaries, that is,
Mc max i>bri,Mc min i<bli, i=1,2,3.
Situation 1：
According to saturation function sat () and right inverse functionDefinition can obtain：
Again from hypothesis 1Therefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 2：
Similar with situation 1, according to saturation function sat () and right inverse functionDefinition can obtain：
Simultaneously according to hypothesis 1Therefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 3：
In the case of being somebody's turn to do,ThusTherefore
Consider above-mentioned three kinds of situations, can obtain：
The equation meansI.e. all of nonlinear element can overall seeing as
New saturation element.Therefore, if as shown in figure 4, the right inverse function of Dead zone is positioned over system unbalanced input link
Front it is possible to unbalanced input problem is processed using general constrained control method.
Above-mentioned unbalanced input link is added in NSV attitude mode and can obtain：
Wherein satb() is new saturation function, and its definition is as shown in formula (11).
The default capabilities of step 2：
In order to without loss of generality, tracking error meets following default capabilities and limits：
el(t)≤e(t)≤eu(t) (13)
Wherein e (t)=[e1(t),e2(t),e3(t)],WithFor
The bound function up and down of default capabilities function, and meetIt can clearly be seen that tracking error signal
Overshoot is maintained atIn interval, maximum allowable steady-state error must is fulfilled forTherefore, with
The default mapping of track error and steady-state behaviour can be realized by selecting suitable performance function.
Limit for realizing default capabilities, introduce transfer function and default capabilities restriction is converted to free signal, should
Function is designed as：
Wherein σ=[σ1,σ2,σ3]TFor transformed error signal.
Definition according to transfer function：
Furthermore it is possible to obtain tracking error eiWith regard to σiPartial derivative:
Above formula shows tracking error eiWith transformed error σiFor strictly increasing relation.Therefore, if transformed error σiBounded,
Inequality (13) is always set up, and that is, the boundedness of transformed error σ can ensure that the default capabilities of tracking error e limit.
In addition, can be in the hope of transformed error σ according to formula (14)iWith regard to tracking error eiPartial derivative be：
Defined function M (e, eu,el) be：
Therefore, M (e, eu,el) inverse be constantly present.
Transformed error σ can be obtained with regard to time derivation：
WhereinTransformed error is dynamically substituted into the error that can obtain in system equation (12) newly
System：
The controller design of step 3 is：
Step a. system entirety control structure, as shown in figure 5, system control loop is divided into speed loop, is returned to slow first
Road is that attitude angle loop is analyzed, and constructs aid system, using backstepping control strategy design virtual controlling rule, same
Shi Caiyong radial basis function neural network does not know to approach to unknown in slow loop, using adaptive approach to composite interference
Processed, specially：
A-1. it is the impact that unbalanced input is reduced or eliminated, construct the aid system of following form：
Wherein ξ1∈R3,ξ2∈R3For aid system state variable, matrixDesign meets：For actually entering the difference with preferable input.
A-2. utilize the unknown uncertain △ F of RBF neural approximation system1, it most preferably approaches and can be written as：
It is wherein W1 *∈Rq×3Neutral net best initial weights matrix, utilizesIt is approached, its adaptive law designs
For：
Wherein P1=P1 T>0,τ1>0 is design parameter or matrix.S (Ω)=[S (Ω)1,S(Ω)2,…,S(Ω)q]TFor
RBF, is typically chosen in the form of Gaussian function, that is,d1kFor neutral net kth
The center vector of individual node, b1kFor the sound stage width parameter of k-th node, k=1,2 ..., q.In addition,For approaching by mistake
Difference, and
A-3. RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D1||≤δ1, wherein δ1>0.Using variableUpper to composite interference
Boundary δ1Approached, its adaptive law is designed as：
Wherein M (e, eu,el)=diag { M11,M22,M33, β1>0 is design parameter.
A-4. the aid system signal xi according to construction in a-11, in a-2, RBF neural is to uncertain estimated valueAnd in a3 the composite interference upper bound parameter update lawUsing backstepping control design case method, obtain void
Intend control law：
WhereinFor design
Feedback matrix, z1=σ-ξ1,Follow the tracks of the first derivative of signal for expectation.
Step b. is that attitude angular rate loop is analyzed to fast loop, designs control using backstepping control strategy
Device processed, does not know to approach to unknown in fast loop using RBF neural, using adaptive approach to composite interference simultaneously
Processed, specially：
B-1. utilize the unknown uncertain △ F of RBF neural approximation system2, it most preferably approaches and can be written as：
WhereinFor neutral net best initial weights matrix, utilizeIt is approached, its adaptive law designs
For：
WhereinIt is design parameter or matrix.S (Ω, ω)=[S (Ω, ω)1,S(Ω,ω)2,…,S
(Ω,ω)q]TFor RBF, it is typically chosen in the form of Gaussian function, that is,
d2kFor the center vector of k-th node of neutral net, b2kFor the sound stage width parameter of k-th node, k=1,2 ..., q.In addition,For approximate error, and
B-2. RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D2||≤δ2, wherein δ2>0.Using variableUpper to composite interference
Boundary δ2Approached, its adaptive law is designed as：
Wherein β2>0 is design parameter.
B-3. the aid system signal xi according to construction in a-12, in b-1, RBF neural is to uncertain estimated valueAnd in b-2 the composite interference upper bound parameter update lawUsing backstepping control design case method, obtain
To control law it is：
Wherein z2=ω-α1-ξ2,For designing square
Battle array.
The controller design of the present invention：
Before being controlled device design, hypothesis below and lemma need to be provided：
Assume 2：For NSV nonlinear attitude model (1), matrix G1,G2All reversible, and there is unknown arithmetic number
So thatSet up.
Assume 3：For outside time-varying unknown disturbance diT (), has unknown arithmetic number ηiSo thatBecome
Vertical.
Assume 4：Follow the tracks of signal y for expectationd, its i order derivative exist and bounded, that is,Wherein ζi>0, i=0,
1,2.
Assume 5：For the difference actually entering with preferable inputThere is unknown arithmetic number ρ to makeBecome
Vertical.
Lemma 1：For arbitrary variableWith constant b>0, inequality below is always set up：
Carry out the design of adaptive neural network Attitude tracking control device below with backstepping technology
1st step：Define error variance：
Wherein α1For virtual controlling rule.
According to formula (20), variable z1Derivative with regard to the time is：
Unknown uncertain △ F is approached using RBF neural1, its best approximation is：
WhereinFor approximate error, and
Formula (35) is brought into (34) can obtain：
WhereinFor composite interference.From hypothesis 1, composite interference D1Norm-bounded, that is, | | D1||≤δ1, its
Middle δ1>0.
Virtual controlling restrains α1It is designed as：
WhereinFor design
Feedback matrix, M (e, eu,el)=diag { M11,M22,M33}.For W1 *Approach value.For δ1Approach value, its adaptive law
It is designed as：
Wherein β1>0 is design parameter.
Define approximate errorVirtual controlling is restrained α1Bring formula (36) into can obtain：
Choose Lyapunov function：
Wherein P1=P1 T>0.Define estimation differenceAnd according to formula (39) and lemma 1, to Lyapunov function
Can obtain with regard to time derivation：
Understand again：
Adaptive lawIt is designed as：
Wherein τ1>0 is design parameter.
Formula (42) and (43) are brought into formula (41) can obtain：
Wherein
In addition we know:
Therefore, formula (44) can be rewritten as：
2nd step：According to formula (20) and (33), to variable z2Can obtain with regard to time derivation：
Similar with the 1st step, unknown uncertain △ F is approached using RBF neural2, its best approximation can be written as：
WhereinFor approximate error, and
Formula (48) is brought into formula (47) can obtain：
WhereinSimilar with the 1st step, disturb D2Meet | | D2||≤δ2, wherein δ2>0.
Control lawIt is designed as：
WhereinFor design matrix.For's
Approach value.For δ2Approach value, its adaptive law is designed as：
Wherein β2>0 is design parameter.
Define approximate errorControl law by designBring formula (49) into can obtain：
Select Lyapunov function be：
WhereinDefine estimation differenceAnd according to formula (52) and lemma 1, to Lyapunov function
Can obtain with regard to time derivation：
According to assuming 2 and 5, can obtain：
Adaptive lawIt is designed as：
Wherein τ2>0 is design parameter.
Therefore, formula (55) and (56) are brought into (54) can obtain：
According to such as lower inequality：
Simultaneously according to formula (46), formula (57) can be rewritten as：
Wherein
Therefore, according to Lyapunov Theory of Stability, all of closed loop system signal all half globally uniformly bounded, i.e. variable
z1,z2, disturb Estimation of Upper-Bound errorAid system variable ξ1,ξ2With neural network parameter approximate errorAll bounded.
Thus can obtainAgain by variable z1Definition substantially can obtain：
Therefore, transformed error signal σ bounded.According to the analysis of conversion performance (15) and (16), in the control of design
Under device effect, the boundedness of transformed error σ can ensure that the default capabilities of tracking error e limit (13), thus realizing controlling mesh
Mark.
The above is only the preferred embodiment of the present invention it is noted that ordinary skill people for the art
For member, some improvement can also be made under the premise without departing from the principles of the invention, these improvement also should be regarded as the present invention's
Protection domain.
Claims (4)
1. a kind of Near Space Flying Vehicles default capabilities Attitude tracking control method with unbalanced input it is characterised in that：Bag
Include following steps：
(1) pass through the right inverse function in dead band adding, the unbalanced input link comprising dead band and input saturation is equivalent to input
Saturation element, this unbalanced input is added in NSV attitude mode；
(2) default capabilities introducing tracking error limit, and the mapping to tracking error signal and steady-state error are carried out simultaneously
Adjust, and by error transfer function, the tracking error signal being constrained by default capabilities is converted to free transformed error
Signal；
(3) construct aid system, unbalanced input impact to control system performance is reduced or eliminated, according to NSV attitude mode
Feature, control system respectively speed loop uncertain is carried out using RBF (RBF) neutral net is unknown to system
Approach, using adaptive technique, composite interference is processed, carry out adaptive neural network by backstepping method
The design of tracking control unit.
2. there is the Near Space Flying Vehicles default capabilities Attitude tracking control method of unbalanced input as claimed in claim 1,
It is characterized in that：In described step (1),
Unbalanced input linkIt is expressed as tandem structure, it includes asymmetrical input saturation element and dead band ring
Section, wherein McFor preferable control input,For actual control input；
Saturation function sat () is expressed as：
Wherein Mcmaxi,McminiRepresent the bound of i-th control input, viFor saturation element output；
Dead zone Db() is expressed as：
Wherein bri>0,bli<0 is that known dead band is interval, mri>0,mli>0 is dead band Slope Parameters；
Introduce Dead zone DbThe right inverse function of ()This function meetsIt is defined as：
By above-mentioned functionBefore being placed on unbalanced input link, produce new Cascading Nonlinearity link, whereinControl law for design；
Above-mentioned control law has following several situation：
Situation 1：
According to saturation function sat () and right inverse functionDefinition obtain：
Know againTherefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 2：
Similar with situation 1, according to saturation function sat () and right inverse functionDefinition obtain：
Understand simultaneouslyTherefore, according to Dead zone DbThe definition of () understands：
Above-mentioned equation can be rewritten as：
Situation 3：
In the case of being somebody's turn to do,ThusTherefore
Consider above-mentioned three kinds of situations, can obtain：
The equation meansSeeing as that i.e. all of nonlinear element can be overall is new
Saturation element；Therefore, the right inverse function of Dead zone is positioned over before system unbalanced input link it becomes possible to adopt general
Constrained control method is processing unbalanced input problem；
Above-mentioned unbalanced input link is added in NSV attitude mode and obtains：
Wherein Ω=[α, β, μ]TFor attitude angle vector, represent the angle of attack, yaw angle and flight path inclination angle respectively；ω=[p, q, r]T
For attitude angle roll angle velocity vectors, represent rolling angular speed, pitch rate and yawrate respectively；F1∈R3,F2∈R3
For known function of state vector, G1∈R3×3,G2∈R3×3Control gain matrix for known system；ΔF1∈R3,ΔF2∈R3
For unknown smooth function, represent system modelling error； d1∈R3,d2∈R3For unknown external disturbance；satb() is new satisfying
And function, it is as defined above shown.
3. there is the Near Space Flying Vehicles default capabilities Attitude tracking control method of unbalanced input as claimed in claim 1,
It is characterized in that：In described step (2),
Tracking error meets following default capabilities and limits：
el(t)≤e(t)≤eu(t)
Wherein e (t)=[e1(t),e2(t),e3(t)],WithIt is default
The bound function up and down of performance function, and meetThe overshoot of tracking error signal is maintained atIn interval, maximum allowable steady-state error must is fulfilled forTherefore, tracking error is default
Mapping and steady-state behaviour can be realized by selecting suitable performance function；
For realizing default capabilities, introduce transfer function and default capabilities restriction is converted to free signal, this function designs
For：
Wherein σ=[σ1,σ2,σ3]TFor transformed error signal；
Definition according to transfer function：
In addition, trying to achieve tracking error eiWith regard to σiPartial derivative be：
Above formula shows tracking error eiWith transformed error σiFor strictly increasing relation；Therefore, if transformed error σiBounded, follows the tracks of
Error default capabilities limit and always set up, and that is, the boundedness of transformed error σ ensure that the default capabilities of tracking error e limit；
In addition, trying to achieve transformed error σiWith regard to tracking error eiPartial derivative be：
Defined function M (e, eu,el) be：
Therefore, M (e, eu,el) inverse be constantly present；
Transformed error σ is obtained with regard to time derivation：
WhereinTransformed error is dynamically substituted in system equation and obtain new error system and be：
4. there is the Near Space Flying Vehicles default capabilities Attitude tracking control method of unbalanced input as claimed in claim 1,
It is characterized in that：Described step (3) comprises the following steps：
Step a, system control loop are divided into speed loop, are that attitude angle loop is analyzed to slow loop first：Construction auxiliary
System, using backstepping control strategy design virtual controlling rule, adopts radial basis function neural network to return to slow simultaneously
In road unknown uncertain approached, using adaptive approach, composite interference is processed, specially：
A-1, the impact for unbalanced input is reduced or eliminated, construct the aid system of following form：
Wherein ξ1∈R3,ξ2∈R3For aid system state variable, matrixDesign meets：For actually entering the difference with preferable input；
A-2, using RBF neural approximation system unknown uncertain Δ F1, it most preferably approaches and is written as：
It is whereinNeutral net best initial weights matrix, utilizesIt is approached, its adaptive law is designed as：
Wherein P1=P1 T>0,τ1>0 is design parameter or matrix；S (Ω)=[S (Ω)1,S(Ω)2,…,S(Ω)q]TFor radially
Basic function, is typically chosen in the form of Gaussian function, that is,d1kSave for k-th for neutral net
The center vector of point, b1kFor the sound stage width parameter of k-th node of neutral net, k=1,2 ..., q；In addition,For forcing
Nearly error, and
A-3, RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D1||≤δ1, wherein δ1>0；Using variableUpper bound δ to composite interference1Enter
Row approaches, and its adaptive law is designed as：
Wherein M (e, eu,el)=diag { M11,M22,M33, β1>0 is design parameter；
A-4, the aid system signal xi according to construction in step a-11, in step a-2, RBF neural is to uncertain estimated valueAnd in step a-3 the composite interference upper bound parameter update lawUsing backstepping control design case method,
Obtain virtual controlling rule：
Wherein For design of feedback square
Battle array, z1=σ-ξ1,Follow the tracks of the first derivative of signal for expectation,
Step b, it is that attitude angular rate loop is analyzed to fast loop, designed using backstepping control strategy and control
Device, is not known to approach to unknown in fast loop using RBF neural simultaneously, using adaptive approach, composite interference is entered
Row is processed, specially：
B-1, using RBF neural approximation system unknown uncertain Δ F2, it most preferably approaches and is written as：
WhereinFor neutral net best initial weights matrix, utilizeIt is approached, its adaptive law is designed as：
Wherein P2=P2 T>0,τ2>0 is design parameter or matrix；S (Ω, ω)=[S (Ω, ω)1,S(Ω,ω)2,…,S
(Ω,ω)q]TFor RBF, it is typically chosen in the form of Gaussian function, that is,
d2kFor the center vector of k-th node of neutral net, b2kFor the sound stage width parameter of k-th node of neutral net, k=1,2 ...,
q；In addition,For approximate error, and
B-2, RBF neural approximate error is considered with unknown external disturbance, be equivalent to composite interference：
This composite interference meets norm-bounded, that is, | | D2||≤δ2, wherein δ2>0；Using variableUpper bound δ to composite interference2Enter
Row approaches, and its adaptive law is designed as：
Wherein β2>0 is design parameter；
B-3, the aid system signal xi according to construction in step a-12, in step b-1, RBF neural is to uncertain estimated valueAnd in step b-2 the composite interference upper bound parameter update lawUsing backstepping control design case side
Method, obtaining control law is：
Wherein For design matrix.
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