CN109164820A - A kind of calm method of nonsingular set time posture of rigid aircraft based on neural network estimation - Google Patents

A kind of calm method of nonsingular set time posture of rigid aircraft based on neural network estimation Download PDF

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CN109164820A
CN109164820A CN201811114118.1A CN201811114118A CN109164820A CN 109164820 A CN109164820 A CN 109164820A CN 201811114118 A CN201811114118 A CN 201811114118A CN 109164820 A CN109164820 A CN 109164820A
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set time
follows
rigid aircraft
neural network
nonsingular
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陈强
谢树宗
孙明轩
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Zhejiang University of Technology ZJUT
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Zhejiang University of Technology ZJUT
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Priority to CN201910874872.3A priority patent/CN110471439B/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft

Abstract

A kind of calm method of nonsingular set time posture of rigid aircraft based on neural network estimation, probabilistic rigid aircraft posture Stabilization is concentrated for having, devise nonsingular set time sliding-mode surface, it not only ensure that the set time convergence of state, but also solve singular value problem；It introduces neural network and approaches total uncertain function, devise nonsingular 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

A kind of rigid aircraft nonsingular set time posture town based on neural network estimation Determine method
Technical field
The present invention relates to it is a kind of based on neural network estimation the nonsingular set time posture of rigid aircraft calm method, It is especially in the presence of external disturbance 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 There is external do based on the calm method of the nonsingular set time posture of rigid aircraft that neural network is estimated, and in system in kind It disturbs in the uncertain situation of rotary inertia, realizes the control method of the set time uniform ultimate bounded of system mode.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of calm method of nonsingular set time posture of rigid aircraft based on neural network estimation, including following step It is rapid:
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'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 ∈ R3 It 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 nonsingular set time sliding-mode surface are as follows:
Wherein, With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qiDerivative, 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:
WhereinFor input vector, Φi(Xi)∈R4For Base Function,For 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 { } isThe 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)∈R3×3For 3 × 3 symmetrical diagonal matrix；K2=diag (k21,k22,k23)∈R3×3For 3 × 3 symmetrical diagonal matrix；K3=diag (k31,k32,k33)∈R3×3For 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:
WhereinI=1,2,3；STIt 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.
The present invention is flown under external interference and the uncertain factor of rotary inertia with the rigidity estimated based on neural network The nonsingular set time posture of row device is calmed method, realizes system stability contorting, guarantees that system mode realizes that the set time is consistent Ultimate boundness.Technical concept of the invention are as follows: for containing external disturbance and the uncertain rigid aircraft system of rotary inertia, benefit Nonsingular neural network set time controller is devised in conjunction with neural network with sliding-mode control.When nonsingular fixed Between the design of sliding-mode surface not only guarantee the set time convergence of system mode, but also solve singular value problem.The present invention is being System realizes the control of the set time uniform ultimate bounded of system mode there are under external interference and the uncertain situation of rotary inertia Method processed.
The invention has the benefit that designed set time sliding-mode surface effective solution singular value problem；It is being System there are under external interference and the uncertain situation of rotary inertia, realizing the set time uniform ultimate bounded of system mode, and 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 side of nonsingular set time posture of rigid aircraft based on neural network estimation Method, the 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'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 ∈ R3 It 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 nonsingular set time sliding-mode surface are as follows:
Wherein,
With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qiDerivative, 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:
WhereinFor input vector, Φi(Xi)∈R4For Base Function,For 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 { } isThe 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)∈R3×3For 3 × 3 symmetrical diagonal matrix；K2=diag (k21,k22,k23)∈R3×3For 3 × 3 symmetrical diagonal matrix；K3=diag (k31,k32,k33)∈R3×3For 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:
WhereinI=1,2,3；STIt 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.
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 designs set time sliding-mode surface effective solution singular value problem；Exist in system extraneous Under interference and the uncertain situation of rotary inertia, the set time uniform ultimate bounded of system mode, and convergence time are realized It 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)

  1. A kind of method 1. nonsingular set time posture of rigid aircraft based on neural network estimation is calmed, it is characterised in that: It the described method comprises the following steps:
    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 quaternionRespectively 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 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 It is as follows:
    Select nonsingular 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, nonsingular 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 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, 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)∈R3×3For 3 × 3 symmetrical diagonal matrix；K3=diag (k31,k32,k33)∈R3×3For 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 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； | | | | 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 υ2 It 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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US8436283B1 (en) * 2008-07-11 2013-05-07 Davidson Technologies Inc. System and method for guiding and controlling a missile using high order sliding mode control
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Application publication date: 20190108