CN110471292A - A kind of calm method of the adaptive set time posture of rigid aircraft - Google Patents

A kind of calm method of the adaptive set time posture of rigid aircraft Download PDF

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CN110471292A
CN110471292A CN201910875121.3A CN201910875121A CN110471292A CN 110471292 A CN110471292 A CN 110471292A CN 201910875121 A CN201910875121 A CN 201910875121A CN 110471292 A CN110471292 A CN 110471292A
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set time
follows
rigid aircraft
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rigid
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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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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

A kind of calm method of the adaptive set time posture of rigid aircraft, concentrates probabilistic rigid aircraft attitude stabilization problem for having, devises set time adaptive controller in conjunction with adaptive technique using sliding-mode control；The design of set time sliding-mode surface guarantees the set time convergence of system mode；It is not always known in addition, adaptive updates rule is used to estimating system, including external interference and the uncertain upper bound of rotary inertia, therefore always uncertain upper bound information is not necessarily to be known in advance.The present invention realizes the control of the set time uniform ultimate bounded of system mode under external interference and the uncertain factor of rotary inertia.

Description

A kind of calm method of the adaptive set time posture of rigid aircraft
Technical field
The present invention relates to a kind of calm methods of the adaptive set time posture of rigid aircraft, are especially in the presence of external dry It disturbs 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.
Self adaptive control refers to the dynamic that controller can correct itself control parameter to adapt to system itself with external disturbance Characteristic makes system be optimal control to obtain satisfied dynamic property.This method is not only suitable for linear system, is also applied for Nonlinear system is controlled mainly for the uncertainty of system.The research object of self adaptive control is that have to a certain degree The uncertain and easy system by external environmental interference.For these reasons, many self-adaptation control methods are used to control Spacecraft system.
Therefore, set time sliding formwork control technology and self-adaptation control method are effectively combined, reduce external disturbance and The set time control of rigid aircraft posture is realized in influence of the system parameter uncertainty to system control performance.
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 calm method of the adaptive set time posture of kind rigid aircraft, in system, there are external disturbance and rotary inertia are uncertain In the case of, realize the control of the set time uniform ultimate bounded of system mode.
In order to solve the above-mentioned technical problem technical solution proposed by the present invention is as follows:
A kind of calm method of the adaptive set time posture of rigid aircraft, comprising the following steps:
Step 1, the kinematics and dynamics modeling of rigid aircraft system is established, system mode and control ginseng are initialized Number, process are 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 rigid aircraft；It is the angular acceleration of rigid 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, meetAnd c1,c2,c3For normal number；ΩTFor the transposition of Ω；For qvSecond dervative；For J0's It 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, With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qiLead Number, i=1,2,3；
Step 3, adaptive set time controller is designed, process is as follows:
3.1 design set time controllers are as follows:
Wherein S=[S1,S2,S3]T, Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix；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, k11,k12,k13,k21,k22,k23,k31,k32,k33It is positive Constant,Respectively c1,c2,c3Estimation；0 < r1< 1, r2> 1；
The more new law of 3.2 design auto-adaptive parameters:
Wherein η1,η2,η3,ε1,ε2,ε3For normal number；RespectivelyDerivative；ForTwo norms,ForTwo norms, | | Ω | | be Ω two norms；
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；
Derivation is carried out to formula (16), is obtained:
WhereinFor the derivative of S, k3min=min { k31,k32,k33, min { } indicates minimum value；δ1,δ2,δ3It is normal Number；
Therefore, 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 (18), is obtained:
Wherein γ2It 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 under external interference and the uncertain factor of rotary inertia, with rigid aircraft it is adaptive fixed when Between posture calm method, realize system stability contorting, guarantee system mode realize set time uniform ultimate bounded.Of the invention Technical concept are as follows: for external disturbance and the uncertain rigid aircraft system of rotary inertia is contained, using sliding-mode control, then Combining adaptive control, devises adaptive set time controller.The design of set time sliding-mode surface guarantees system mode Set time convergence.In addition, being restrained based on designed adaptive updates, it is not necessary that total uncertain upper bound information is known in advance.This Invention, there are under external interference and the uncertain situation of rotary inertia, realizes that the set time of system mode is unanimously final in system The control method of bounded.
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 adaptive set time posture of rigid aircraft are calmed method, the method includes with Lower step:
Step 1, the kinematics and dynamics modeling of rigid aircraft system is established, system mode and control ginseng are initialized Number, process are 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 rigid aircraft；It is the angular acceleration of rigid 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, meetAnd c1,c2,c3For normal number；ΩTFor the transposition of Ω；For qvSecond dervative；For J0's It 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, With sgn (qi) it is sign function, λ1> 0, λ2> 0, a2> 1, For qiLead Number, i=1,2,3；
Step 3, adaptive set time controller is designed, process is as follows:
3.1 design set time controllers are as follows:
Wherein S=[S1,S2,S3]T, Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix；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, k11,k12,k13,k21,k22,k23,k31,k32,k33It is positive Constant,Respectively c1,c2,c3Estimation；0 < r1< 1, r2> 1；
The more new law of 3.2 design auto-adaptive parameters:
Wherein η1,η2,η3,ε1,ε2,ε3For normal number；RespectivelyDerivative；ForTwo norms,ForTwo norms, | | Ω | | be Ω two norms；
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；
Derivation is carried out to formula (16), is obtained:
WhereinFor the derivative of S, k3min=min { k31,k32,k33, min { } indicates minimum value；δ1,δ2,δ3It is normal Number；
Therefore, 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 (18), is obtained:
Wherein γ2It 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 rigid aircraft system.
System initialization parameter setting is as follows:
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 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)

  1. The method 1. a kind of adaptive set time posture of rigid aircraft is calmed, it is characterised in that: the method includes following Step:
    Step 1, the kinematics and dynamics modeling of rigid aircraft system 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 rigid aircraft；It is the angular acceleration of rigid aircraft；u∈R3And 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 part, Then formula (4) is write as again:
    Further obtain:
    1.4 pairs of formulas (1) carry out differential, obtain:
    WhereinFor total uncertain set, meet And c1,c2,c3For normal number；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 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 qiLead Number, i=1,2,3；
    Step 3, adaptive set time controller is designed, process is as follows:
    3.1 design set time controllers are as follows:
    Wherein S=[S1,S2,S3]T, L=[L1,L2,L3]T,Γ=diag (Γ1,Γ2,Γ3)∈R3×3For 3 × 3 symmetrical diagonal matrix；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, k11,k12,k13,k21,k22,k23,k31,k32,k33It is positive Constant,Respectively c1,c2,c3Estimation；0 < r1< 1, r2> 1；
    The more new law of 3.2 design auto-adaptive parameters:
    Wherein η1,η2,η3,ε1,ε2,ε3For normal number；RespectivelyDerivative；ForTwo norms, ForTwo norms, | | Ω | | be Ω two norms；
    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；
    Derivation is carried out to formula (16), is obtained:
    WhereinFor the derivative of S, k3min=min { k31,k32,k33, min { } indicates minimum value；δ1,δ2,δ3It is normal Number；
    Therefore, 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 (18), is obtained:
    Wherein γ2It 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.
CN201910875121.3A 2018-09-25 2019-09-17 A kind of calm method of the adaptive set time posture of rigid aircraft Pending CN110471292A (en)

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Application publication date: 20191119