CN109212976B - Input-limited small celestial body soft landing robust trajectory tracking control method - Google Patents

Input-limited small celestial body soft landing robust trajectory tracking control method Download PDF

Info

Publication number
CN109212976B
CN109212976B CN201811380868.3A CN201811380868A CN109212976B CN 109212976 B CN109212976 B CN 109212976B CN 201811380868 A CN201811380868 A CN 201811380868A CN 109212976 B CN109212976 B CN 109212976B
Authority
CN
China
Prior art keywords
celestial body
small celestial
model
soft landing
fuzzy
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201811380868.3A
Other languages
Chinese (zh)
Other versions
CN109212976A (en
Inventor
崔平远
龙嘉腾
朱圣英
高艾
徐瑞
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN201811380868.3A priority Critical patent/CN109212976B/en
Publication of CN109212976A publication Critical patent/CN109212976A/en
Application granted granted Critical
Publication of CN109212976B publication Critical patent/CN109212976B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/0275—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using fuzzy logic only
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
    • 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
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

Landscapes

  • Engineering & Computer Science (AREA)
  • Artificial Intelligence (AREA)
  • Physics & Mathematics (AREA)
  • Software Systems (AREA)
  • Automation & Control Theory (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Fuzzy Systems (AREA)
  • Mathematical Physics (AREA)
  • Feedback Control In General (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses an input-limited small celestial body soft landing robust trajectory tracking control method, and belongs to the technical field of deep space exploration. The implementation method of the invention comprises the following steps: step 1, establishing a small celestial body landing dynamic model; step 2, establishing a small celestial body soft landing T-S fuzzy model; and 3, determining comprehensive conditions of the controller by adopting the small celestial body soft landing T-S fuzzy model in the step 2, and realizing accurate soft landing at a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster. According to the method, the comprehensive conditions of the robust controller are obtained through the T-S fuzzy model of the small celestial body soft landing, and the precise soft landing of the specific position of the surface of the small celestial body is realized under the conditions of complex disturbance and uncertainty and limited amplitude of a thruster.

Description

Input-limited small celestial body soft landing robust trajectory tracking control method
Technical Field
The invention relates to an input-limited small celestial body soft landing robust trajectory tracking control method, and belongs to the technical field of deep space exploration.
Background
In future, the small celestial body landing detection task expects to implement various scientific detection activities such as accurate soft landing on unknown celestial bodies, in-situ detection on target celestial bodies and target areas, sampling return and the like.
Implementing a precise soft landing at a particular location of a target celestial body presents the following challenges: 1. the small celestial body gravitational field is complex and difficult to accurately model; 2. in the landing process, complex disturbance and an uncertain dynamic environment exist; 3. the actuator thruster has thrust amplitude constraint, and actuator output saturation can occur when the actuator thruster is used for dealing with large disturbance and uncertain conditions. This puts higher demands on the design of land guidance and control systems.
Aiming at the possible problems of the precise soft landing of the small celestial body, a robust track tracking control method is needed to be designed under the conditions of complex disturbance and uncertainty in the precise landing process and limited amplitude of a thruster, so that the precise soft landing of a specific position on the surface of the small celestial body is realized.
Disclosure of Invention
The invention discloses a robust trajectory tracking control method for input-limited small celestial body soft landing, which aims to solve the technical problems that: and aiming at the conditions of complex disturbance and uncertainty in the soft landing process of the small celestial body and limited amplitude of a thruster, the precise soft landing of a specific position on the surface of the small celestial body is realized based on robust track tracking control.
The invention is realized by the following technical scheme.
The invention discloses an input-limited small celestial body soft landing robust trajectory tracking control method, which comprises the steps of firstly establishing a small celestial body landing dynamic model; on the basis, a small celestial body soft landing T-S fuzzy model is established; and determining the comprehensive conditions of the controller by adopting a small celestial body soft landing T-S fuzzy model, thereby completing the design of a small celestial body soft landing robust trajectory tracking controller, and realizing accurate soft landing at a specific position of the surface of a small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of a thruster.
The invention discloses an input-limited small celestial body soft landing robust trajectory tracking control method, which comprises the following steps of:
step 1, establishing a small celestial body landing dynamic model.
Under the inertial coordinate system of the small celestial body, the dynamic model of the lander is
Figure BDA0001871843520000021
Wherein r ═ x, y, z]TAnd v ═ vx,vy,vz]TPosition and velocity vectors, respectively; ω ═ 0,0, ω]TThe rotation angular velocity of the small celestial body is obtained; a ═ Tx,Ty,Tz]TRespectively controlling three-axis components of the force acceleration of the detector under an inertial system;
Figure BDA0001871843520000022
vector expression of acceleration of small celestial body gravity, U being a gravitational potential function, acT/m is the control acceleration vector, m is the detector mass,
Figure BDA0001871843520000023
is a thrust vector, T | | | is the magnitude of the thrust,
Figure BDA0001871843520000024
acceleration of unmodeled disturbance force, IspSpecific impulse of thruster, g0The gravity acceleration is the earth sea level. The acceleration of gravity of the small celestial body is expressed as
Figure BDA0001871843520000025
Wherein, mu is GM as gravitational constant, G is universal gravitational constant, M is the mass of the celestial body, ap＝[apx,apy,apz]T＝-[υxx,υyy,υzz]T/r5Is a gravitational perturbation acceleration vector upsilonx，υyAnd upsilonzIs given by formula (3)
Figure BDA0001871843520000026
The probe kinetic equation (1) is simplified and expressed as a form in the equation (4) according to the equations (1) to (3).
Figure BDA0001871843520000031
Wherein x is [ r ]T,vT]T，
Figure BDA0001871843520000032
B＝[03×3,I3×3]TIs fp＝ad+apPerturbing the acceleration. In engineering practice, the thruster amplitude is required to satisfy about in the formulaAnd (4) bundling.
||T||≤Tmax(5)
And 2, establishing a T-S fuzzy model for the soft landing of the small celestial body.
And constructing a small celestial body soft landing model by adopting a T-S fuzzy control model. Definition of
Figure BDA00018718435200000312
All integers between integers a, b are meant and all integers include a, b. Under the condition of saturation with an actuator, the ith fuzzy rule of the T-S fuzzy model is
Figure BDA0001871843520000033
Wherein the content of the first and second substances,
Figure BDA0001871843520000034
is the variable of the front-piece,
Figure BDA0001871843520000035
fuzzy rules, which are quantified by membership functions; r iszAnd mzThe numbers of the front piece variables and the fuzzy rules are respectively expressed as positive integers. In addition, variables
Figure BDA0001871843520000036
And
Figure BDA0001871843520000037
respectively state variable, control input and measurement output. Variables of
Figure BDA0001871843520000038
For external inputs, including disturbances, measuring noise or reference inputs, variables
Figure BDA0001871843520000039
For control output, the control performance is evaluated. For all
Figure BDA00018718435200000310
(Ai,B2,i) Is stable, (C)2,i,Ai) Is detectable. sat (-) is a saturation function. Considering energy bounded perturbations
Figure BDA00018718435200000311
For the design of a tracking controller, a T-S fuzzy model is converted into a linear fractional transform LFT model
Figure BDA0001871843520000041
p＝Θq (9)
Wherein
Figure BDA0001871843520000042
Respectively, a dummy input and a dummy output of the controlled object. Writing a controlled object model based on T-S fuzzy logic into a formula (10), wherein the controlled object model is a model shown in a formula (1) or a formula (4)
Figure BDA0001871843520000043
And is
Figure BDA0001871843520000044
Figure BDA0001871843520000045
Wherein the content of the first and second substances,
Figure BDA0001871843520000046
is zjCorresponding to fuzzy sets
Figure BDA0001871843520000047
Membership function of (c). Since the degree of membership is normalized to the interval 0,1]In the interior, the following properties are obtained
Figure BDA0001871843520000048
Introduction of
Figure BDA0001871843520000049
ψ＝[x d sat(u)]T，
Figure BDA00018718435200000410
Then formula (11) is converted into
Figure BDA0001871843520000051
Therefore, by introducing dead zone non-linearity dz (u) u-sat (u), the T-S model of the controlled object with actuator saturation constraint is converted into the following form
Figure BDA0001871843520000052
ps＝dz(u) (16)
pf＝Θfqf(17)
Wherein
Figure BDA0001871843520000053
In the case of a pseudo-input,
Figure BDA0001871843520000054
is a dummy output. Note thetaf,i＝gi(z)，nq＝n+np+ny，
Figure BDA0001871843520000055
And theta is not less than 0f≤I。
Figure BDA0001871843520000056
Figure BDA0001871843520000057
Figure BDA0001871843520000058
Figure BDA0001871843520000059
Introducing linear fractional transform gain scheduling controller
Figure BDA0001871843520000061
pk,f＝Θfqk,f(23)
Wherein x isk，pk,f，qk,fRespectively with x, pf，qfThe dimensions are the same. The dead zone nonlinearity dz (u) is used as an input to handle saturation nonlinearity and is obtained online. Matrix array
Figure BDA0001871843520000062
The respective partition matrix in (1) is the controller gain.
And 3, determining comprehensive conditions of the controller by adopting the small celestial body soft landing T-S fuzzy model in the step 2, and realizing accurate soft landing at a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster.
For a given scalar, when there is a positive definite matrix
Figure BDA0001871843520000063
Time, symmetric matrix
Figure BDA0001871843520000064
Figure BDA0001871843520000065
Satisfaction formula (24) - (26)
Figure BDA0001871843520000066
Figure BDA0001871843520000067
Figure BDA0001871843520000071
Wherein, the matrix
Figure BDA0001871843520000072
And HΓAre respectively in each column of
Figure BDA0001871843520000073
And Ker [ C ]y,0EyDyd,0]Has an n-order gain scheduling output as in (22), the feedback controller will asymptotically stabilize and d ∈ Ws for any bounded disturbancesThe performance index of the closed loop system will be less than γ.
And (3) realizing accurate soft landing of a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster through the comprehensive conditions of the controllers shown in the formulas (24) to (26).
Has the advantages that:
the invention discloses an input-limited small celestial body soft landing robust trajectory tracking control method, which obtains the comprehensive conditions of a robust controller through a small celestial body soft landing T-S fuzzy model, and realizes the accurate soft landing of a specific position of the surface of a small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of a thruster.
Drawings
FIG. 1 is a flow chart of input limited small celestial body soft landing robust trajectory tracking control instruction generation;
FIG. 2 is a comparison curve of three-axis position deviation using the robust trajectory tracking control method and the non-robust method of the present invention;
FIG. 3 is a comparison curve of the triaxial thrust control output using the robust trajectory tracking control method and the non-robust method of the present invention.
FIG. 4 is a combined thrust control output comparison curve of the robust trajectory tracking control method and the non-robust method.
Detailed Description
For a better understanding of the objects and advantages of the invention, reference is made to the following description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention. This example takes the landing of a small celestial body Eros 433.
As shown in fig. 1, the input-limited robust trajectory tracking control method for soft landing of small celestial bodies disclosed in this embodiment includes the following specific implementation steps:
step 1, establishing a small celestial body landing dynamic model.
Under the inertial coordinate system of the small celestial body, the dynamic model of the lander is
Figure BDA0001871843520000081
Wherein r ═ x, y, z]TAnd v ═ vx,vy,vz]TPosition and velocity vectors, respectively; ω ═ 0,0, ω]TIs the small celestial body rotation angular velocity, omega is 3.31 × 10-4rad/s；a＝[Tx,Ty,Tz]TRespectively controlling three-axis components of the force acceleration of the detector under an inertial system;
Figure BDA0001871843520000082
vector expression of acceleration of small celestial body gravity, U being a gravitational potential function, acT/m is the control acceleration vector, m is the detector mass, its initial mass m0＝300kg，
Figure BDA0001871843520000083
Is a thrust vector, T | | | is the magnitude of the thrust,
Figure BDA0001871843520000084
acceleration of unmodeled disturbance force, Isp150s is thrust device specific impulse g0＝9.81m/s2The gravity acceleration is the earth sea level. In particular, the gravitational potential function is described in simplified form by equation (2)
Figure BDA0001871843520000085
Wherein, mu is GM as an attraction constant, G is a universal attraction constant, and M is 6.69 × 1015kg is the mass of the small celestial body. I isU＝(AUx2+BUy2+CUz2)/r2Wherein A isU＝18.25M kg·km2，BU＝62.9M kg·km2，CU＝64.25M kg·km2，(AU<BU<CU) The inertia moments of the small celestial body about the x axis, the y axis and the z axis are respectively.
Figure BDA0001871843520000091
Is the detector position vector length. According to the formula (3), the acceleration of gravity of the small celestial body is expressed as
Figure BDA0001871843520000092
Wherein, ap＝[apx,apy,apz]T＝-[υxx,υyy,υzz]T/r5Is a gravitational perturbation acceleration vector upsilonx，υyAnd upsilonzIs given by formula (3)
Figure BDA0001871843520000093
According to equations (1) to (4), the probe kinetics equation (1) is expressed in a simplified form in equation (5).
Figure BDA0001871843520000094
Wherein x is [ r ]T,vT]T，
Figure BDA0001871843520000095
B＝[03×3,I3×3]TIs fp＝ad+apPerturbationAcceleration. In engineering practice, the thruster amplitude is required to satisfy the constraint in the equation.
||T||≤Tmax(6)
Wherein, TmaxThe maximum amplitude of the thrust output by the thruster is 20N.
And 2, establishing a small celestial body landing tracking control method.
The landing tracking control of the small celestial body is constructed by adopting a T-S fuzzy control method. Definition of
Figure BDA0001871843520000096
All integers between integers a, b are meant and all integers include a, b. Under the condition of saturation with an actuator, the ith fuzzy rule of the T-S fuzzy model is
Figure BDA0001871843520000101
Wherein the content of the first and second substances,
Figure BDA0001871843520000102
is the variable of the front-piece,
Figure BDA0001871843520000103
fuzzy rules, which are quantified by membership functions; r iszAnd mzThe numbers of the front piece variables and the fuzzy rules are respectively expressed as positive integers. In addition, variables
Figure BDA0001871843520000104
And
Figure BDA0001871843520000105
respectively state variable, control input and measurement output. Variables of
Figure BDA0001871843520000106
For external inputs, including disturbances, measuring noise or reference inputs, variables
Figure BDA0001871843520000107
To controlAnd an output for evaluating control performance. For all
Figure BDA0001871843520000108
Suppose (A)i,B2,i) Is stable, (C)2,i,Ai) Is detectable. sat (-) is a saturation function. Considering energy bounded perturbations
Figure BDA0001871843520000109
For the design of a tracking controller, a T-S fuzzy model is converted into a linear fractional transform LFT model
Figure BDA00018718435200001010
p＝Θq (10)
Wherein
Figure BDA00018718435200001011
Respectively, a dummy input and a dummy output of the controlled object. Controlled object model writing based on T-S fuzzy logic
Figure BDA00018718435200001012
And is
Figure BDA0001871843520000111
Figure BDA0001871843520000112
Wherein the content of the first and second substances,
Figure BDA0001871843520000113
is zjCorresponding to fuzzy sets
Figure BDA0001871843520000114
Membership function of (c). Since the degree of membership is normalized toInterval [0,1]In the interior, the following properties are obtained
Figure BDA0001871843520000115
Introduction of
Figure BDA0001871843520000116
ψ＝[x d sat(u)]T，
Figure BDA0001871843520000117
Then formula (11) is converted into
Figure BDA0001871843520000118
Therefore, by introducing dead zone non-linearity dz (u) u-sat (u), the T-S model of the controlled object with actuator saturation constraint is converted into the following form
Figure BDA0001871843520000119
ps＝dz(u) (17)
pf＝Θfqf(18)
Wherein
Figure BDA00018718435200001110
In the case of a pseudo-input,
Figure BDA00018718435200001111
is a dummy output. Note thetaf,i＝gi(z)，nq＝n+np+ny，
Figure BDA0001871843520000121
And theta is not less than 0f≤I。
Figure BDA0001871843520000122
Figure BDA0001871843520000123
Figure BDA0001871843520000124
Figure BDA0001871843520000125
Introducing linear fractional transform gain scheduling controller
Figure BDA0001871843520000126
pk,f＝Θfqk,f(24)
Wherein x isk，pk,f，qk,fRespectively with x, pf，qfThe dimensions are the same. The dead zone nonlinearity dz (u) is used as an input to handle saturation nonlinearity and can be obtained online. Matrix array
Figure BDA0001871843520000127
The respective partition matrix in (1) is the controller gain.
And 3, determining comprehensive conditions of the controller by adopting the small celestial body soft landing T-S fuzzy model in the step 2, and realizing accurate soft landing at a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster.
For a given scalar quantity, if there is a positive definite matrix
Figure BDA0001871843520000131
Symmetric matrix
Figure BDA0001871843520000132
Figure BDA0001871843520000133
Satisfaction formula (25) - (27)
Figure BDA0001871843520000134
Figure BDA0001871843520000135
Figure BDA0001871843520000136
Wherein, the matrix
Figure BDA0001871843520000137
And HΓAre respectively in each column of
Figure BDA0001871843520000138
And Ker [ C ]y,0EyDyd,0]Has an n-order gain scheduling output as in (22), the feedback controller will asymptotically stabilize and d ∈ W for any bounded disturbancesThe performance index of the closed loop system will be less than γ.
And (3) realizing accurate soft landing of a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster through the comprehensive conditions of the controllers shown in the formulas (25) to (27).
The simulation initial conditions are
Figure BDA0001871843520000139
End conditions at landing are
Figure BDA0001871843520000141
Fig. 2, fig. 3 and fig. 4 respectively show the comparison curves of the three-axis position deviation, the three-axis thrust control output and the resultant thrust control output of the robust trajectory tracking control method and the non-robust method. Compared with a robust method, the robust trajectory tracking control method provided by the invention can ensure landing precision on the premise of meeting the constraint of thrust amplitude in a complex disturbance and uncertain dynamic environment.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. The input-limited small celestial body soft landing robust trajectory tracking control method is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step 1, establishing a small celestial body landing dynamic model;
step 2, establishing a small celestial body soft landing T-S fuzzy model;
and 3, determining comprehensive conditions of the controller by adopting the small celestial body soft landing T-S fuzzy model in the step 2, and realizing accurate soft landing at a specific position of the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster.
The specific implementation method of the step 1 is that,
under the inertial coordinate system of the small celestial body, the dynamic model of the lander is
Figure FDA0002412599320000011
Wherein r ═ x, y, z]TAnd
Figure FDA0002412599320000012
position and velocity vectors, respectively; ω ═ 0,0, ω]TThe rotation angular velocity of the small celestial body is obtained;
Figure FDA0002412599320000013
respectively controlling three-axis components of the force acceleration of the detector under an inertial system;
Figure FDA0002412599320000014
vector expression of acceleration of small celestial body gravity, U being a gravitational potential function, acT/m is the control acceleration vector, m is the detector mass, T ∈ R3Is a thrust vector, T | | | is the magnitude of the thrust, ad∈R3Acceleration of unmodeled disturbance force, IspSpecific impulse of thruster, g0The gravity acceleration of the earth sea level is obtained; the acceleration of gravity of the small celestial body is expressed as
Figure FDA0002412599320000015
Wherein, mu is GM as an attraction constant, G is a universal attraction constant, M is the mass of the small celestial body,
Figure FDA0002412599320000016
is a gravitational perturbation acceleration vector upsilonx，υyAnd upsilonzIs given by formula (3)
Figure FDA0002412599320000017
According to the formula (1) - (3), the detector kinetic equation (1) is simplified and expressed into a form in the formula (4);
Figure FDA0002412599320000021
wherein x is [ r ]T，vT]T，
Figure FDA0002412599320000022
B＝[03×3，I3×3]TIs fp＝ad+apIs perturbation acceleration; in engineering practice, the amplitude of the thruster is required to satisfy the constraint in the formula;
||T||≤Tmax(5)
the specific implementation method of the step 2 is that,
constructing a small celestial body soft landing model by adopting a T-S fuzzy control model; definitions | [ a, b ] denotes all integers between integers a, b, including a, b; under the condition of saturation with an actuator, the ith fuzzy rule of the T-S fuzzy model is
Figure FDA0002412599320000023
Wherein z isi，j∈|[1，rz]Is the variable of the front-piece,
Figure FDA0002412599320000024
fuzzy rules, which are quantified by membership functions; r iszAnd mzThe numbers of the front piece variables and the fuzzy rules are respectively expressed as positive integers; in addition, variables
Figure FDA0002412599320000025
And
Figure FDA0002412599320000026
respectively, a state variable, a control input and a measurement output; variables of
Figure FDA0002412599320000027
For external inputs, including disturbances, measuring noise or reference inputs, variables
Figure FDA0002412599320000028
For control output, to evaluate control performance, for all i ∈ | [1, m | ]z]，(Ai，B2，i) Is stable, (C)2，i，Ai) Is detectable; sat (-) is a saturation function; considering energy bounded perturbations
Figure FDA0002412599320000029
For the design of a tracking controller, a T-S fuzzy model is converted into a linear fractional transform LFT model
Figure FDA00024125993200000210
p＝Θq (9)
Wherein
Figure FDA0002412599320000031
Respectively a pseudo input and a pseudo output of the controlled object; writing a controlled object model based on T-S fuzzy logic into a formula (10), wherein the controlled object model is a model shown in a formula (1) or a formula (4)
Figure FDA0002412599320000032
And is
Figure FDA0002412599320000033
Figure FDA0002412599320000034
Wherein the content of the first and second substances,
Figure FDA0002412599320000035
is zjCorresponding to fuzzy sets
Figure FDA0002412599320000036
A membership function of; since the degree of membership is normalized to the interval 0,1]In the interior, the following properties are obtained
Figure FDA0002412599320000037
Introduction of
Figure FDA0002412599320000038
ψ＝[x d sat(u)]T，
Figure FDA0002412599320000039
Then formula is converted into
Figure FDA00024125993200000310
Therefore, by introducing dead zone non-linearity dz (u) u-sat (u), the T-S model of the controlled object with actuator saturation constraint is converted into the following form
Figure FDA0002412599320000041
ps＝dz(u) (16)
pf＝Θfqf(17)
Wherein
Figure FDA0002412599320000042
In the case of a pseudo-input,
Figure FDA0002412599320000043
is a false output; note thetaf，i＝gi(z)，nq＝n+np+ny，
Figure FDA0002412599320000044
And theta is not less than 0f≤I；
Figure FDA0002412599320000045
Figure FDA0002412599320000046
Figure FDA0002412599320000047
Figure FDA0002412599320000048
Introducing linear fractional transform gain scheduling controller
Figure FDA0002412599320000049
pk，f＝Θfqk，f(23)
Wherein x isk，pk，f，qk，fRespectively with x, pf，qfThe dimensions are the same; dead zone non-linearity dz (u) as input to handle saturation non-linearity and obtain matrix on-line
Figure FDA0002412599320000051
The respective partition matrix in (1) is the controller gain.
The specific implementation method of the step 3 is that,
for a given scalar, when there is a positive definite matrix
Figure FDA0002412599320000052
Time, symmetric matrix
Figure FDA0002412599320000053
Figure FDA0002412599320000054
Satisfaction formula (24) - (26)
Figure FDA0002412599320000055
Figure FDA0002412599320000056
Figure FDA0002412599320000057
Wherein, the matrix
Figure FDA0002412599320000058
And HΓAre respectively in each column of
Figure FDA0002412599320000059
And Ker [ C ]y，0EyDyd，0]Has an n-order gain scheduling output as in (22), the feedback controller will asymptotically stabilize and d ∈ W for any bounded disturbancesThe performance index of the closed loop system will be less than gamma;
and realizing accurate soft landing at a specific position on the surface of the small celestial body under the conditions of complex disturbance and uncertainty and limited amplitude of the thruster through the comprehensive conditions of a controller shown in a formula.
CN201811380868.3A 2018-11-20 2018-11-20 Input-limited small celestial body soft landing robust trajectory tracking control method Active CN109212976B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201811380868.3A CN109212976B (en) 2018-11-20 2018-11-20 Input-limited small celestial body soft landing robust trajectory tracking control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201811380868.3A CN109212976B (en) 2018-11-20 2018-11-20 Input-limited small celestial body soft landing robust trajectory tracking control method

Publications (2)

Publication Number Publication Date
CN109212976A CN109212976A (en) 2019-01-15
CN109212976B true CN109212976B (en) 2020-07-07

Family

ID=64993261

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201811380868.3A Active CN109212976B (en) 2018-11-20 2018-11-20 Input-limited small celestial body soft landing robust trajectory tracking control method

Country Status (1)

Country Link
CN (1) CN109212976B (en)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110532724B (en) * 2019-09-06 2021-03-26 北京理工大学 Rapid online planning method for optimal path of burning consumption of small celestial body soft landing
CN112631285B (en) * 2020-12-08 2021-11-23 北京理工大学 Method for quickly generating small celestial body attachment autonomous obstacle avoidance track
CN112629339B (en) * 2020-12-15 2021-08-03 北京航天自动控制研究所 Rocket soft landing trajectory planning method based on direct method
CN112817233B (en) * 2021-01-06 2022-04-01 青岛科技大学 Small celestial body detector flying-around segment orbit tracking control method based on iterative learning control
CN113821057B (en) * 2021-10-14 2023-05-30 哈尔滨工业大学 Planetary soft landing control method and system based on reinforcement learning and storage medium

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104590589A (en) * 2014-12-22 2015-05-06 哈尔滨工业大学 Mars probe landing guidance method based on fuel minimization
CN107132542A (en) * 2017-05-02 2017-09-05 北京理工大学 A kind of small feature loss soft landing autonomic air navigation aid based on optics and Doppler radar

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070012820A1 (en) * 2004-08-11 2007-01-18 David Buehler Reusable upper stage

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104590589A (en) * 2014-12-22 2015-05-06 哈尔滨工业大学 Mars probe landing guidance method based on fuel minimization
CN107132542A (en) * 2017-05-02 2017-09-05 北京理工大学 A kind of small feature loss soft landing autonomic air navigation aid based on optics and Doppler radar

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
嫦娥三号自主避障软着陆控制技术;张洪华 等;《中国科学：技术科学》;20141231;第44卷(第6期);C031-51 *
月球探测器自主导航与控制方法研究;孙军伟;《中国博士学位论文全文数据库（电子期刊） 工程科技II辑》;20061115(第11期);第559-568页 *

Also Published As

Publication number Publication date
CN109212976A (en) 2019-01-15

Similar Documents

Publication Publication Date Title
CN109212976B (en) Input-limited small celestial body soft landing robust trajectory tracking control method
Jatsun et al. Study of controlled motion of exoskeleton moving from sitting to standing position
Zou et al. A compound control method based on the adaptive neural network and sliding mode control for inertial stable platform
Zhang et al. Robust backstepping control for agile satellite using double-gimbal variable-speed control moment gyroscope
Liu et al. Dynamics and control of capture of a floating rigid body by a spacecraft robotic arm
Khanpoor et al. Modeling and control of an underactuated tractor–trailer wheeled mobile robot
Moreno–Valenzuela et al. Robust trajectory tracking control of an underactuated control moment gyroscope via neural network–based feedback linearization
Wu et al. Sliding-mode control for staring-mode spacecraft using a disturbance observer
Wronka et al. Derivation and analysis of a dynamic model of a robotic manipulator on a moving base
Zhang et al. Piece-wise affine MPC-based attitude control for a CubeSat during orbital manoeuvres
Liu et al. Mass and mass center identification of target satellite after rendezvous and docking
Guo et al. Integrated vibration isolation and attitude control for spacecraft with uncertain or unknown payload inertia parameters
Yao et al. Understanding the true dynamics of space manipulators from air-bearing based ground testing
Dongare et al. Attitude pointing control using artificial potentials with control input constraints
Su et al. Reduced order model and robust control architecture for mechanical systems with nonholonomic Pfaffian constraints
Xie et al. On-orbit frequency identification of spacecraft based on attitude maneuver data
Hogan et al. Trajectory tracking, estimation, and control of a pendulum-driven spherical robot
Tang et al. Estimation of imu orientation using nesterov’s accelerated gradient improved by fuzzy control rule
Kalikhman et al. Development of digital regulators for control systems of gyroscopic devices and associated metrological installations using modern methods of synthesis to improve accuracy and dynamic characteristics
Wang et al. Force-based delay compensation for hardware-in-the-loop simulation divergence of 6-DOF space contact
Singh Control and stabilization of nonlinear uncertain elastic robotic arm
Ma et al. A novel guidance law with line-of-sight acceleration feedback for missiles against maneuvering targets
Feng et al. Reorientation control for a microsatellite with pointing and angular velocity constraints
Wibben et al. Integrated guidance and attitude control for asteroid proximity operations using higher order sliding modes
Espinosa et al. Sliding mode line-of-sight stabilization of a two-axes gimbal system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant