CN110471439A - A kind of calm method of rigid aircraft set time posture based on neural network estimation - Google Patents
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Abstract
A kind of calm method of rigid aircraft set time posture based on neural network estimation, concentrates probabilistic rigid aircraft posture Stabilization for having, devises set time sliding-mode surface, ensure that the set time convergence of state;It introduces neural network and approaches total uncertain function, devise neural network set time controller.The present invention realizes the control of the set time uniform ultimate bounded of aerocraft system state under external interference and the uncertain factor of rotary inertia.
Description
Technical field
The present invention relates to a kind of calm methods of the rigid aircraft set time posture based on neural network estimation, especially
There are external disturbances and the calm method of the uncertain rigid aircraft posture of moment of inertia matrix.
Background technique
Rigid aircraft attitude control system reliably plays important angle in movement in the health of rigid aircraft
Color.In complicated space environment, rigid aircraft attitude control system will receive various external disturbances and rotary inertia square
The uncertain influence of battle array.In order to effectively maintain the performance of system, need to keep it not true to external disturbance and moment of inertia matrix
Surely there is stronger robustness.Sliding mode variable structure control can be effectively improved rigidity as a kind of typical nonlinear control method
The stability and control of aircraft, and there is stronger robustness, to improve the ability of execution task.Therefore, it studies
The sliding mode variable structure control method of rigid aircraft attitude control system has a very important significance.
Sliding formwork control is considered as an effective robust control side in terms of solving systematic uncertainty and external disturbance
Method.Sliding-mode control has algorithm simple, fast response time, excellent to extraneous noise jamming and Parameter Perturbation strong robustness etc.
Point.TSM control is a kind of improvement project of traditional sliding formwork control that stability in finite time may be implemented.However, existing
Finite time technology estimation convergence time need to know the initial information of system, this is difficult to know for designer.Closely
Nian Lai, set time technology are widely used, set time control method and existing finite-time control method phase
Than, have without knowing the initial information of system, also can conservative estimation system convergence time superiority.
Neural network is middle one kind of linear parameterization approximation method, can be replaced by other arbitrary approximation methods, than
Such as RBF neural, fuzzy logic system etc..Uncertain property is approached using neural network, when being effectively combined fixed
Between sliding formwork control technology, reduce the influence to system control performance of external disturbance and system parameter uncertainty, realize that rigidity flies
The set time of row device posture controls.
Summary of the invention
In order to overcome the problems, such as unknown nonlinear existing for existing rigid aircraft attitude control system, the present invention provides one
Kind there are external disturbance and is turned based on the calm method of rigid aircraft set time posture that neural network is estimated, and in system
In the dynamic uncertain situation of inertia, the control method of the set time uniform ultimate bounded of system mode is realized.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of calm method of rigid aircraft set time posture based on neural network estimation, comprising the following steps:
Step 1, the kinematics and dynamics modeling of rigid aircraft is established, system mode and control parameter are initialized,
Process is as follows:
The kinematical equation of 1.1 rigid aircraft systems are as follows:
Wherein qv=[q1,q2,q3]TAnd q4The respectively vector section and scalar component and satisfaction of unit quaternionq1,q2,q3Respectively it is mapped in rectangular coordinate system in space x, y, the value in z-axis;It is q respectivelyvAnd q4
Derivative;For qvTransposition;Ω∈R3It is the angular speed of rigid aircraft;I3It is R3×3Unit matrix;It indicates are as follows:
The kinetics equation of 1.2 rigid aircraft systems are as follows:
Wherein J ∈ R3×3It is the rotator inertia matrix of aircraft;It is the angular acceleration of aircraft;u∈R3With d ∈
R3It is control moment and external disturbance;Ω×It indicates are as follows:
1.3 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain portion
Point, then formula (4) is write as again:
Further obtain:
1.4 pairs of formulas (1) carry out differential, obtain:
WhereinFor total uncertain set;ΩT
For the transposition of Ω;For qvSecond dervative;For J0It is inverse;It indicates are as follows:
Respectively q1,q2,q3Derivative;
Step 2, for external disturbance and the uncertain rigid aircraft system of rotary inertia, the sliding-mode surface of design,
Process is as follows:
Select set time sliding-mode surface are as follows:
Wherein,sgn
(qi),With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qi
Derivative, i=1,2,3;
Define S=[S1,S2,S3]T, to S derivation, obtain:
Formula (8) are substituted into (11), are obtained:
Step 3, neural network set time controller is designed, process is as follows:
3.1 define neural network are as follows:
Gi(Xi)=Wi *TΦ(Xi)+εi (13)
WhereinFor input vector, Φi(Xi)∈R4For Base Function, Wi *∈
R4For ideal weighted vector, is defined as:
Wherein Wi∈R4For weighted vector, εiFor approximate error, meet | εi|≤εN, i=1,2,3, εNFor the normal of very little
Number;Arg min { } is Wi *The set for taking its minimum value all;
3.2 consideration set time controllers are designed to:
WhereinFor 3 × 3 symmetrical diagonal matrix,For WiEstimated value Φ (X)=
[Φ(X1),Φ(X2),Φ(X3)]T,L=[L1,L2,L3]T,
Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix,0 < r1< 1, r2> 1, K1=diag (k11,k12,k13)∈R3×3It is symmetrical diagonal for 3 × 3
Matrix;K2=diag (k21,k22,k23)∈R3×3For 3 × 3 symmetrical diagonal matrix;K3=diag (k31,k32,k33)∈R3×3It is 3
× 3 symmetrical diagonal matrix;For WiEstimation;
3.2 design updates rule are as follows:
Wherein γi> 0, pi> 0,ForDerivative, i=1,2,3;Φ(Xi) it is selected as sigmoid function below:
Wherein l1,l2,l3And l4For approximation parameters, Φ (Xi) meet 0 < Φ (Xi) < Φ0, and
Step 4, set time stability proves that process is as follows:
4.1 prove that all signals of rigid aircraft system are all uniform ultimate boundeds, and design liapunov function is such as
Lower form:
WhereinSTIt is the transposition of S;It isTransposition;
Derivation is carried out to formula (18), is obtained:
Wherein min { } indicates minimum value; | | | | two norms of expression value;
Then determine that all signals of rigid aircraft system are all uniform ultimate boundeds;
4.2 prove set time convergence, and design liapunov function is following form:
Derivation is carried out to formula (20), is obtained:
Wherein
υ2It is greater than zero upper dividing value for one;
Based on the above analysis, rigid aircraft system mode is in set time uniform ultimate bounded.
The present invention is flown under external interference and the uncertain factor of rotary inertia with the rigidity estimated based on neural network
Row device set time posture is calmed method, realizes system stability contorting, guarantees that system mode realizes that the set time unanimously finally has
Boundary.Technical concept of the invention are as follows: for external disturbance and the uncertain rigid aircraft system of rotary inertia is contained, utilize sliding formwork
Control method devises neural network set time controller in conjunction with neural network.The design of set time sliding-mode surface guarantees
The set time of system mode restrains.The present invention, there are under external interference and the uncertain situation of rotary inertia, is realized in system
The control method of the set time uniform ultimate bounded of system mode.
The invention has the benefit that realizing system there are under external interference and the uncertain situation of rotary inertia in system
The set time uniform ultimate bounded of system state, and convergence time is unrelated with the original state of system.
Detailed description of the invention
Fig. 1 is rigid aircraft attitude quaternion schematic diagram of the invention;
Fig. 2 is rigid aircraft angular speed schematic diagram of the invention;
Fig. 3 is rigid aircraft sliding-mode surface schematic diagram of the invention;
Fig. 4 is rigid aircraft control moment schematic diagram of the invention;
Fig. 5 is rigid aircraft parameter Estimation schematic diagram of the invention;
Fig. 6 is control flow schematic diagram of the invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
- Fig. 6 referring to Fig.1, a kind of calm method of rigid aircraft set time posture based on neural network estimation are described
Control method the following steps are included:
Step 1, the kinematics and dynamics modeling of rigid aircraft is established, system mode and control parameter are initialized,
Process is as follows:
The kinematical equation of 1.1 rigid aircraft systems are as follows:
Wherein qv=[q1,q2,q3]TAnd q4The respectively vector section and scalar component and satisfaction of unit quaternionq1,q2,q3Respectively it is mapped in rectangular coordinate system in space x, y, the value in z-axis;It is q respectivelyvAnd q4
Derivative;For qvTransposition;Ω∈R3It is the angular speed of rigid aircraft;I3It is R3×3Unit matrix;It indicates are as follows:
The kinetics equation of 1.2 rigid aircraft systems are as follows:
Wherein J ∈ R3×3It is the rotator inertia matrix of aircraft;It is the angular acceleration of aircraft;u∈R3With d ∈
R3It is control moment and external disturbance;Ω×It indicates are as follows:
1.3 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain portion
Point, then formula (4) is write as again:
Further obtain:
1.4 pairs of formulas (1) carry out differential, obtain:
WhereinFor total uncertain set;ΩT
For the transposition of Ω;For qvSecond dervative;For J0It is inverse;It indicates are as follows:
Respectively q1,q2,q3Derivative;
Step 2, for external disturbance and the uncertain rigid aircraft system of rotary inertia, the sliding-mode surface of design,
Process is as follows:
Select set time sliding-mode surface are as follows:
Wherein,sgn
(qi),With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qi
Derivative, i=1,2,3;
Define S=[S1,S2,S3]T, to S derivation, obtain:
Formula (8) are substituted into (11), are obtained:
Step 3, neural network set time controller is designed, process is as follows:
3.1 define neural network are as follows:
Gi(Xi)=Wi *TΦ(Xi)+εi (13)
WhereinFor input vector, Φi(Xi)∈R4For Base Function, Wi *∈
R4For ideal weighted vector, is defined as:
Wherein Wi∈R4For weighted vector, εiFor approximate error, meet | εi|≤εN, i=1,2,3, εNFor the normal of very little
Number;Arg min { } is Wi *The set for taking its minimum value all;
3.2 consideration set time controllers are designed to:
WhereinFor 3 × 3 symmetrical diagonal matrix,For WiEstimated value Φ (X)=
[Φ(X1),Φ(X2),Φ(X3)]T,L=[L1,L2,L3]T,
Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix,0 < r1<
1, r2> 1, K1=diag (k11,k12,k13)∈R3×3For 3 × 3 symmetrical diagonal matrix;K2=diag (k21,k22,k23)∈R3×3
For 3 × 3 symmetrical diagonal matrix;K3=diag (k31,k32,k33)∈R3×3For 3 × 3 symmetrical diagonal matrix;For WiEstimate
Meter;
3.2 design updates rule are as follows:
Wherein γi> 0, pi> 0,ForDerivative, i=1,2,3;Φ(Xi) it is selected as sigmoid function below:
Wherein l1,l2,l3And l4For approximation parameters, Φ (Xi) meet 0 < Φ (Xi) < Φ0, and
Step 4, set time stability proves that process is as follows:
4.1 prove that all signals of rigid aircraft system are all uniform ultimate boundeds, and design liapunov function is such as
Lower form:
WhereinSTIt is the transposition of S;It isTransposition;
Derivation is carried out to formula (18), is obtained:
Wherein min { } indicates minimum value; | | | | two norms of expression value;
Then determine that all signals of rigid aircraft system are all uniform ultimate boundeds;
4.2 prove set time convergence, and design liapunov function is following form:
Derivation is carried out to formula (20), is obtained:
Wherein
υ2It is greater than zero upper dividing value for one;
Based on the above analysis, rigid aircraft system mode is in set time uniform ultimate bounded.
For the validity for verifying proposed method, this method carries out simulating, verifying for aerocraft system.System initialization ginseng
Number is provided that
The initial value of system: q (0)=[0.3, -0.2, -0.3,0.8832]T, Ω (0)=[1,0, -1]TRadian per second;Turn
The nominal section J of dynamic inertial matrix0=[40,1.2,0.9;1.2,17,1.4;0.9,1.4,15] kilogram * square metres, the moment of inertia
Uncertain portion's Δ J=diag [sin (0.1t), 2sin (0.2t), 3sin (0.3t)] of battle array;External disturbance d (t)=[0.2sin
(0.1t),0.3sin(0.2t),0.5sin(0.2t)]T* meters of ox;The parameter of sliding-mode surface is as follows: λ1=1, λ2=1, a1=1.5, a2
=1.5;The parameter of controller is as follows:K1=K2=K3=I3;More new law parameter is as follows: ηi=1, εi=0.1, i
=1,2,3,The parameter selection of sigmoid function is as follows: l1=2, l2=8, l3
=4, l4=-0.5.
The attitude quaternion of rigid aircraft and the response schematic diagram difference of angular speed are as depicted in figs. 1 and 2, it can be seen that
Attitude quaternion and angular speed can converge in zero domain of equalization point at 5 seconds or so;The sliding-mode surface of rigid aircraft is rung
Answer schematic diagram as shown in Figure 3, it can be seen that sliding-mode surface can converge in zero domain of equalization point at 3 seconds or so;Rigidity flight
Control moment and parameter Estimation the response schematic diagram difference of device are as shown in Figure 4 and Figure 5.
Therefore, the present invention realizes system mode in system there are under external interference and the uncertain situation of rotary inertia
Set time uniform ultimate bounded, and convergence time is unrelated with the original state of system.
Described above is the excellent effect of optimization that one embodiment that the present invention provides is shown, it is clear that the present invention is not only
It is limited to above-described embodiment, without departing from essence spirit of the present invention and without departing from the premise of range involved by substantive content of the present invention
Under it can be made it is various deformation be implemented.
Claims (1)
- A kind of method 1. rigid aircraft set time posture based on neural network estimation is calmed, it is characterised in that: the side Method the following steps are included:Step 1, the kinematics and dynamics modeling of rigid aircraft is established, system mode and control parameter, process are initialized It is as follows:The kinematical equation of 1.1 rigid aircraft systems are as follows:Wherein qv=[q1,q2,q3]TAnd q4The respectively vector section and scalar component and satisfaction of unit quaternionq1,q2,q3Respectively it is mapped in rectangular coordinate system in space x, y, the value in z-axis;It is q respectivelyvAnd q4's Derivative;For qvTransposition;Ω∈R3It is the angular speed of rigid aircraft;I3It is R3×3Unit matrix;It indicates are as follows:The kinetics equation of 1.2 rigid aircraft systems are as follows:Wherein J ∈ R3×3It is the rotator inertia matrix of aircraft;It is the angular acceleration of aircraft;u∈R3With d ∈ R3It is control Torque processed and external disturbance;Ω×It indicates are as follows:1.3 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain part, Then formula (4) is write as again:Further obtain:1.4 pairs of formulas (1) carry out differential, obtain:WhereinFor total uncertain set;ΩTFor Ω Transposition;For qvSecond dervative;For J0It is inverse;It indicates are as follows:Respectively q1,q2,q3's Derivative;Step 2, for external disturbance and the uncertain rigid aircraft system of rotary inertia, the sliding-mode surface of design, process It is as follows:Select set time sliding-mode surface are as follows:Wherein, With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qiLead Number, i=1,2,3;Define S=[S1,S2,S3]T, to S derivation, obtain:Formula (8) are substituted into (11), are obtained:Step 3, neural network set time controller is designed, process is as follows:3.1 define neural network are as follows:Gi(Xi)=Wi *TΦ(Xi)+εi (13)WhereinFor input vector, Φi(Xi)∈R4For Base Function, Wi *∈R4For reason The weighted vector thought, is defined as:Wherein Wi∈R4For weighted vector, εiFor approximate error, meet | εi|≤εN, i=1,2,3, εNFor the normal number of very little; Arg min { } is Wi *The set for taking its minimum value all;3.2 consideration set time controllers are designed to:WhereinFor 3 × 3 symmetrical diagonal matrix,For WiEstimated value Φ (X)=[Φ (X1),Φ(X2),Φ(X3)]T,L=[L1,L2,L3]T,I=1,2,3;Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix,0 < r1< 1, r2> 1, K1=diag (k11,k12,k13)∈R3×3It is symmetrical diagonal for 3 × 3 Matrix;K2=diag (k21,k22,k23)∈R3×3For 3 × 3 symmetrical diagonal matrix;K3=diag (k31,k32,k33)∈R3×3It is 3 × 3 symmetrical diagonal matrix;For WiEstimation;3.2 design updates rule are as follows:Wherein γi> 0, pi> 0,ForDerivative, i=1,2,3;Φ(Xi) it is selected as sigmoid belowFunction:Wherein l1,l2,l3And l4For approximation parameters, Φ (Xi) meet 0 < Φ (Xi) < Φ0, andStep 4, set time stability proves that process is as follows:4.1 prove that all signals of rigid aircraft system are all uniform ultimate boundeds, and design liapunov function is following shape Formula:WhereinSTIt is the transposition of S;It isTransposition;Derivation is carried out to formula (18), is obtained:Wherein min { } indicates minimum value;I= 1,2,3;| | | | two norms of expression value;Then determine that all signals of rigid aircraft system are all uniform ultimate boundeds;4.2 prove set time convergence, and design liapunov function is following form:Derivation is carried out to formula (20), is obtained:WhereinI=1,2,3; υ2It is greater than zero upper dividing value for one;Based on the above analysis, rigid aircraft system mode is in set time uniform ultimate bounded.
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