CN109240321A - A kind of nonsingular set time neural network control method of rigid aircraft - Google Patents

A kind of nonsingular set time neural network control method of rigid aircraft Download PDF

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CN109240321A
CN109240321A CN201811137004.9A CN201811137004A CN109240321A CN 109240321 A CN109240321 A CN 109240321A CN 201811137004 A CN201811137004 A CN 201811137004A CN 109240321 A CN109240321 A CN 109240321A
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set time
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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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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

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  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
  • Feedback Control In General (AREA)

Abstract

A kind of nonsingular set time neural network control method of rigid aircraft, probabilistic rigid aircraft Attitude Tracking problem is concentrated for having, nonsingular set time sliding-mode surface is devised, not only ensure that the set time convergence of state, but also solves singular value problem；It introduces neural network and approaches total uncertain function, devise nonsingular set time controller.The present invention realizes the Attitude Tracking error of aerocraft system and the control of angular speed error set time uniform ultimate bounded under external interference and the uncertain factor of rotary inertia.

Description

A kind of nonsingular set time neural network control method of rigid aircraft
Technical field
The present invention relates to a kind of nonsingular set time neural network control method of rigid aircraft, it is especially in the presence of outer Portion's interference and the uncertain rigid aircraft Attitude tracking control method 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 The nonsingular set time neural network control method of kind rigid aircraft, and in system, there are external disturbances and rotary inertia In uncertain situation, the controlling party of the set time uniform ultimate bounded of posture tracking error and angular speed error is realized Method.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of nonsingular set time neural network control method of rigid aircraft, 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 quaternionRespectively it is mapped in rectangular coordinate system in space x, y, the value in z-axis；It is q respectivelyvAnd q4's Derivative；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:
The 1.3 desired kinematical equations of rigid aircraft system are as follows:
Wherein qdv=[qd1,qd2,qd3]TAnd qd4The vector section and scalar component of respectively desired unit quaternion and MeetΩd∈R3For desired angular speed；Respectively qdv,qd4Derivative,For qdvTransposition；It indicates are as follows:
1.4 are moved by the rigid aircraft relative attitude of quaternion representation:
Ωe=Ω-C Ωd (11)
Wherein ev=[e1,e2,e3]TAnd e4The respectively vector section and scalar component of Attitude Tracking error；Ωe= [Ωe1,Ωe2,Ωe3]T∈R3For angular speed error；For corresponding direction cosine matrix And meet | | C | |=1 He For the derivative of C；
According to formula (1)-(11), rigid aircraft Attitude Tracking error dynamics and kinematical equation are as follows:
WhereinWithRespectively evAnd e4Derivative；For evTransposition；WithRespectively ΩdAnd ΩeDerivative； (Ωe+CΩd)×With Ω×It is of equal value；WithIt respectively indicates are as follows:
1.5 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain portion Point, then formula (14) is write as again:
Further obtain:
1.6 pairs of formulas (12) carry out differential, obtain:
Wherein For total uncertain set；For evSecond dervative；
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,λ1And λ2For normal number；m1,n1,p1,r1For positive odd number, meet m1> n1,p1 < r1< 2p1,WithIt is symbol Function；I=1,2,3；
Step 3, set time nerve network controller is designed, process is as follows:
3.1 define neural network are as follows:
WhereinFor input vector, Φi(Xi)∈R4For Base Function,ForTransposition,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；ForThe 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, Γ=diag (Γ1,Γ2,Γ3), K1=diag (k11,k12,k13),K2=diag (k21,k22,k23),K3 =diag (k31,k32,k33), WithIt is 3 × 3 symmetrical diagonal matrix；For's Derivative, S=[S1,S2,S3]T；k11,k12,k13,k21,k22,k23,k31,k32,k33For normal number； WithIt is sign function； sgn(S1),sgn(S2),sgn(S3) it is sign function；
3.3 design updates rule are as follows:
Wherein γi> 0, τi> 0,ForEstimation, 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, andFor the maximum value in the two；
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；ForTransposition；
Derivation is carried out to formula (26), is obtained:
Wherein ForTwo norms；For the minimum value in the two；
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 (28), is obtained:
Wherein It is to take its minimum value；υ2It is greater than for one Zero upper dividing value；
Based on the above analysis, the Attitude Tracking error of rigid aircraft system is consistent most in the set time with angular speed error Whole bounded.
The present invention is under external interference and the uncertain factor of rotary inertia, with a kind of the nonsingular solid of rigid aircraft It fixes time neural network control method, realizes system tenacious tracking, guarantee that the Attitude Tracking error of system and angular speed error are solid It fixes time uniform ultimate bounded.Technical concept of the invention are as follows: fly for containing external disturbance and the uncertain rigidity of rotary inertia Row device system devises nonsingular set time controller in conjunction with neural network using sliding-mode control.It is nonsingular solid Designing for sliding-mode surface of fixing time not only guarantees that the set time of system mode restrains, but also solves singular value problem.The present invention In system there are under external interference and the uncertain situation of rotary inertia, posture tracking error and angular speed error are realized The control method of set time uniform ultimate bounded.
The invention has the benefit that designed set time sliding-mode surface effective solution singular value problem；It is being System realizes the fixation of posture tracking error and angular speed error there are under external interference and the uncertain situation of rotary inertia Time consistency ultimate boundness, and convergence time is unrelated with the original state of system.
Detailed description of the invention
Fig. 1 is rigid aircraft Attitude Tracking error schematic diagram of the invention；
Fig. 2 is rigid aircraft angular speed error 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 nonsingular set time neural network control method of rigid aircraft, the controlling party 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:
1.5 the kinematical equation of rigid aircraft system 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；Ω∈R3It is the angular speed of rigid aircraft；I3It is R3×3Unit matrix；It indicates are as follows:
The kinetics equation of 1.6 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:
The 1.7 desired kinematical equations of rigid aircraft system are as follows:
Wherein qdv=[qd1,qd2,qd3]TAnd qd4The vector section and scalar component of respectively desired unit quaternion and MeetΩd∈R3For desired angular speed；Respectively qdv,qd4Derivative,For qdvTransposition；It indicates are as follows:
1.8 are moved by the rigid aircraft relative attitude of quaternion representation:
Ωe=Ω-C Ωd(11)
Wherein ev=[e1,e2,e3]TAnd e4The respectively vector section and scalar component of Attitude Tracking error；Ωe= [Ωe1,Ωe2,Ωe3]T∈R3For angular speed error；For corresponding direction cosine matrix And meet | | C | |=1 He For the derivative of C；
According to formula (1)-(11), rigid aircraft Attitude Tracking error dynamics and kinematical equation are as follows:
WhereinWithRespectively evAnd e4Derivative；For evTransposition；WithRespectively ΩdAnd ΩeDerivative； (Ωe+CΩd)×With Ω×It is of equal value；WithIt respectively indicates are as follows:
1.5 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain portion Point, then formula (14) is write as again:
Further obtain:
1.6 pairs of formulas (12) carry out differential, obtain:
Wherein For total uncertain set；For evSecond dervative；
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,λ1And λ2For normal number；m1,n1,p1,r1For positive odd number, meet m1> n1,p1 < r1< 2p1,sgn(ei) andIt is symbol Function；I=1,2,3；
Step 3, set time nerve network controller is designed, process is as follows:
3.1 define neural network are as follows:
WhereinFor input vector, Φi(Xi)∈R4For Base Function,ForTransposition,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；ForThe 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, Γ=diag (Γ1,Γ2,Γ3), K1=diag (k11,k12,k13),K2=diag (k21,k22,k23),K3 =diag (k31,k32,k33), WithIt is 3 × 3 symmetrical diagonal matrix；For's Derivative, S=[S1,S2,S3]T；k11,k12,k13,k21,k22,k23,k31,k32,k33For normal number；WithIt is sign function； sgn(S1),sgn(S2),sgn(S3) it is sign function；
3.3 design updates rule are as follows:
Wherein γi> 0, τi> 0,ForEstimation, 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, andFor the maximum value in the two；
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；ForTransposition；
Derivation is carried out to formula (26), is obtained:
Wherein ForTwo norms；For the minimum value in the two；
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 (28), is obtained:
Wherein It is to take its minimum value；υ2It is greater than for one Zero upper dividing value；
Based on the above analysis, the Attitude Tracking error of rigid aircraft system is consistent most in the set time with angular speed error Whole 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 qd (0)=[0,0,0,1]T；It is expected that angular speedRadian per second；Rotator inertia square The nominal section J of battle array0=[40,1.2,0.9；1.2,17,1.4；0.9,1.4,15] kilogram * square metres, inertial matrix not really Determine portion Δ J=diag [sin (0.1t), 2sin (0.2t), 3sin (0.3t)]；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, m1=9, n1=5, p1= 3,r1=5；The parameter of controller is as follows:K1=K2=K3=I3；More new law parameter is as follows: The parameter selection of sigmoid function is as follows: l1=2, l2=8, l3=10, l4=-0.5.
The Attitude Tracking error of rigid aircraft and the response schematic diagram difference of angular speed error are as depicted in figs. 1 and 2, can To find out that Attitude Tracking error and angular speed error can converge in zero domain of equalization point at 3.5 seconds or so；Rigidity flies The sliding-mode surface response schematic diagram of row device is as shown in Figure 3, it can be seen that sliding-mode surface can converge to one zero of equalization point at 2 seconds or so In domain；Control moment and parameter Estimation the response schematic diagram difference of rigid aircraft 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, realize that the Attitude Tracking error of system is consistent in the set time with angular speed error Ultimate boundness, 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)

1. a kind of nonsingular set time neural network control method of rigid aircraft, it is characterised in that: the method includes 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 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；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:
The 1.3 desired kinematical equations of rigid aircraft system are as follows:
Wherein qdv=[qd1,qd2,qd3]TAnd qd4The vector section and scalar component and satisfaction of respectively desired unit quaternionΩd∈R3For desired angular speed；Respectively qdv,qd4Derivative,For qdvTransposition；Table It is shown as:
1.4 are moved by the rigid aircraft relative attitude of quaternion representation:
Ωe=Ω-C Ωd (11)
Wherein ev=[e1,e2,e3]TAnd e4The respectively vector section and scalar component of Attitude Tracking error；Ωe=[Ωe1, Ωe2,Ωe3]T∈R3For angular speed error；For corresponding direction cosine matrix and Meet | | C | |=1 He For the derivative of C；
According to formula (1)-(11), rigid aircraft Attitude Tracking error dynamics and kinematical equation are as follows:
WhereinWithRespectively evAnd e4Derivative；For evTransposition；WithRespectively ΩdAnd ΩeDerivative；(Ωe+ CΩd)×With Ω×It is of equal value；WithIt respectively indicates are as follows:
1.5 rotator inertia matrix Js meet J=J0+ Δ J, wherein J0With Δ J respectively indicate J nominal section and uncertain part, Then formula (14) is write as again:
Further obtain:
1.6 pairs of formulas (12) carry out differential, obtain:
Wherein For total uncertain set；For evSecond dervative；
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,λ1And λ2For normal number；m1,n1,p1,r1For positive odd number, meet m1> n1,p1< r1 < 2p1,WithIt is sign function； I=1,2,3；
Step 3, set time nerve network controller is designed, process is as follows:
3.1 define neural network are as follows:
Gi(Xi)=Wi *TΦ(Xi)+εi (21)
WhereinFor input vector, Φi(Xi)∈R4For Base Function, Wi *TFor Wi *'s Transposition, 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；For 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, 0 < r3< 1, r4> 1, i=1,2, 3；Γ=diag (Γ1,Γ2,Γ3), K1=diag (k11,k12,k13),K2=diag (k21,k22,k23),K3=diag (k31, k32,k33), WithIt is 3 × 3 symmetrical diagonal matrix；ForDerivative, S= [S1,S2,S3]T；k11,k12,k13,k21,k22,k23,k31,k32,k33For normal number； WithIt is sign function； sgn(S1),sgn(S2),sgn(S3) it is sign function；
3.3 design updates rule are as follows:
Wherein γi> 0, τi> 0,ForEstimation, 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, andFor the maximum value in the two；
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:
WhereinI=1,2,3；STIt is the transposition of S；ForTransposition；
Derivation is carried out to formula (26), is obtained:
Wherein||Wi *| | it is Wi *Two norms；For the minimum value in the two；
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 (28), is obtained:
Wherein It is to take its minimum value；υ2It is greater than for one Zero upper dividing value；
Based on the above analysis, the Attitude Tracking error of rigid aircraft system and angular speed error consistent finally have in the set time Boundary.
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CN112987567A (en) * 2021-02-09 2021-06-18 河北科技大学 Fixed time self-adaptive neural network sliding mode control method of nonlinear system
CN112987567B (en) * 2021-02-09 2022-07-22 河北科技大学 Fixed time self-adaptive neural network sliding mode control method of nonlinear system
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