CN109870912A - It is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control - Google Patents
It is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control Download PDFInfo
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- G—PHYSICS
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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
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Abstract
It is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control, for the dynamic system of quadrotor, constant logarithm secant compound constraint liapunov function when selecting a kind of asymmetric, design it is a kind of based on it is asymmetric when the constant compound constraint liapunov function of logarithm secant quadrotor export constrained control method.The design of the constant compound constraint liapunov function of logarithm secant is while can also to reduce arrival time to guarantee that the output of system can limit and avoid excessive overshoot in a certain range when asymmetric.So as to improve the dynamic response performance of quadrotor system.The present invention provide it is a kind of based on it is asymmetric when the constant compound constraint liapunov function of logarithm secant quadrotor export constrained control method, make system that there is preferable dynamic response process.
Description
Technical field
The present invention relates to it is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control, make quadrotor fly
Row device system has preferable dynamic response process.
Background technique
The one kind of quadrotor as rotary aircraft, it is small in size with its, mobility is good, design is simple, system
The advantages that low in cost is made, the extensive concern of domestic and international university, research institution, company has been attracted.However, since quadrotor is flown
Device is small in size and light-weight, in-flight vulnerable to external disturbance, how to realize the High Performance Motion Control to quadrotor
Have become a hot issue.For the control problem of quadrotor, there are many control methods, such as PID control,
Active Disturbance Rejection Control, sliding formwork control, Reverse Step Control etc..
Wherein Reverse Step Control has been widely used for nonlinear system, and advantage includes fast response time, easy to implement, right
The uncertain robustness etc. with external disturbance of system.Traditional Reverse Step Control only considers the stability of quadrotor
Can, there is no pay close attention to its transient response performance too much.Therefore, traditional backstepping control method makes quadrotor system
Application in a practical situation has very big obstruction.To solve this problem, the control method based on constraint liapunov function
It is suggested, this method can effectively improve the mapping of quadrotor system in a practical situation.
Summary of the invention
In order to improve quadrotor system transients performance, constraint independent of time when asymmetric the present invention provides a kind of use
The Spacecraft Attitude Control of function reduces overshoot and overshoot time, keeps quadrotor system good with one
Good dynamic response performance.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
... it is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control, comprising the following steps:
Step 1, the dynamic model for establishing quadrotor system sets initial value, sampling time and the control of system
Parameter processed, process are as follows:
1.1 determine from the body coordinate system based on quadrotor system to the transfer square of the inertial coordinate based on the earth
Battle array T:
Wherein, φ, θ, ψ are roll angle, pitch angle, the yaw angle of quadrotor respectively, indicate aircraft successively around
The angle of each reference axis rotation of inertial coodinate system；
Dynamic model during the translation of 1.2 quadrotors is as follows:
Wherein, x, y, z respectively indicate three positions of the quadrotor under inertial coodinate system, UfIndicate that quadrotor flies
The input torque of row device, m are the quality of quadrotor, and g indicates acceleration of gravity；
Formula (1) is substituted into formula (2) to obtain:
Dynamic model in 1.3 quadrotor rotation processes are as follows:
Wherein, τx, τy, τzRespectively represent the moment components of each axis on body coordinate system, Ixx, Iyy, IzzRespectively indicate machine
The component of the rotary inertia of each axis under body coordinate system, × indicate multiplication cross, ωpIndicate rolling angular speed, ωqIndicate pitch angle
Speed, ωrIndicate yaw rate,Indicate rolling angular acceleration,Indicate pitching angular acceleration,Indicate that yaw angle adds
Speed；
In view of aircraft is in low-speed operations or floating state, it is believed that Therefore formula (4) is rewritten are as follows:
Joint type (3) and formula (5), obtain the kinetic model of quadrotor are as follows:
Wherein, ux=cos φ sin θ cos ψ+sin φ sin ψ, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, and the desired value of θ is respectively as follows:
Wherein, φdFor the expected signal value of φ, θdFor θ expected signal value, arcsin is arcsin function；
Step 2, in each sampling instant, calculating position tracking error and its first derivative；Posture angle tracking is calculated to miss
Difference and its first derivative；Design position and posture angle controller, process are as follows:
2.1 define z tracking error and its first derivative:
Wherein, zdIndicate the desired signal of z；
2.2 define q1:
2.3 design constraint liapunov functions
Wherein, Ka1, Kb1For normal number:
Wherein, | e1|maxFor | e1| maximum value；
2.4 solve formula (10) first derivative, obtain:
Wherein, α1For virtual controlling amount,
Its expression formula are as follows:
Wherein, k11For normal number；
Formula (13) are substituted into formula (12), are obtained:
2.5 design liapunov function V12Are as follows:
Solution formula (15) first derivative, obtains:
Wherein
Formula (17) and formula (6) are substituted into formula (16), obtained:
2.6 design Uf:
Wherein, k12For normal number；
2.7 define x, and y tracking error is respectively e2, e3, then have:
Wherein, xd, ydRespectively indicate x, the desired signal of y
2.8 define q2, q3:
2.9 design constraint liapunov functions:
Wherein, Ka2, Kb2, Ka3, Kb3For normal number:
Wherein, | e2|maxFor | e2| maximum value, | e3|maxFor | e3| maximum value；
2.10 solve formula (23) first derivative, obtain:
Wherein, α2, α3For virtual controlling amount, expression formula are as follows:
Wherein, k21, k31For normal number；
Formula (26) are substituted into formula (25), are obtained:
2.11 design liapunov function V22, V32Are as follows:
The first derivative of solution formula (28), obtains:
Wherein
Formula (30) and formula (6) are substituted into formula (29), obtained:
2.12 designing ux, uy:
Wherein, k22, k32For normal number；
2.13 define posture angle tracking error and its first derivative:
Wherein, j=4,5,6, x4=φ, x5=θ, x6=ψ, x4dIndicate the desired value of φ, x5dIndicate the desired value of θ, x6d
Indicate the desired value of ψ, e4Indicate the tracking error of φ, e5Indicate the tracking error of θ, e6Indicate the tracking error of ψ；
2.14 defining qj:
2.15 design constraint liapunov functions:
Wherein, Kaj, KbjFor normal number:
Wherein, | ej|maxFor | ej| maximum value；
2.16 solve formula (35) first derivative, obtain:
Wherein, αjFor virtually control amount, table
Up to formula are as follows:
Wherein, kj1For normal number；
Formula (38) are substituted into formula (37), are obtained:
2.17 design liapunov function Vj2Are as follows:
The first derivative of solution formula (40), obtains:
Wherein
Formula (42) and formula (6) are substituted into formula (41), obtained:
2.18 design τ by formula (43)x, τy, τz:
Wherein, k42, k52, k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows:
Formula (19) are substituted into formula (18) by 3.1, are obtained:
Formula (32) are substituted into formula (31) by 3.2, are obtained:
Formula (44) are substituted into formula (43) by 3.3, are obtained
3.4 by (45), and (46), (47) know that quadrotor system is stable.
The Spacecraft Attitude Control of constraint independent of time function, improves the transient state of system when the present invention uses asymmetric
Can, reduce overshoot and arrival time.
Technical concept of the invention are as follows: for the dynamic system of quadrotor, design it is a kind of using it is asymmetric when
The Spacecraft Attitude Control of constraint independent of time function.Constant logarithm secant compound constraint liapunov function when asymmetric
Design be that while also can be reduced to guarantee that the output of system can limit and avoid excessive overshoot in a certain range
Arrival time.So as to improve the dynamic response performance of quadrotor system.
Advantage of the present invention are as follows: reduce overshoot, reduce arrival time, improve mapping.
Detailed description of the invention
Fig. 1 is position tracking effect diagram of the invention.
Fig. 2 is attitude angle tracking effect schematic diagram of the invention.
Fig. 3 is that positioner of the invention inputs schematic diagram.
Fig. 4 is that posture angle controller of the invention inputs schematic diagram.
Fig. 5 is control flow schematic diagram of the invention.
Specific embodiment
The present invention will be further described with reference to the accompanying drawing.
- Fig. 5 referring to Fig.1, it is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control, including it is following
Step:
Step 1, the dynamic model for establishing quadrotor system sets initial value, sampling time and the phase of system
Control parameter is closed, process is as follows:
1.1 determine from the body coordinate system based on quadrotor system to the transfer square of the inertial coordinate based on the earth
Battle array T:
Wherein φ, θ, ψ are roll angle, pitch angle, the yaw angle of quadrotor respectively, indicate aircraft successively around used
Property coordinate system each reference axis rotation angle；
Dynamic model during the translation of 1.2 quadrotors is as follows:
Wherein x, y, z respectively indicate three positions of the quadrotor under inertial coodinate system, UfIndicate that quadrotor flies
The input torque of row device, m are the quality of quadrotor, and g indicates acceleration of gravity, and formula (1) substitution formula (2) can be obtained:
Dynamic model in 1.3 quadrotor rotation processes are as follows:
Wherein τx, τy, τzRespectively represent the moment components of each axis on body coordinate system, Ixx, Iyy, IzzRespectively indicate body
The component of the rotary inertia of each axis under coordinate system, × indicate multiplication cross, ωpIndicate rolling angular speed, ωqIndicate pitch angle speed
Degree, ωrIndicate yaw rate,Indicate rolling angular acceleration,Indicate pitching angular acceleration,Indicate that yaw angle accelerates
Degree；
In view of aircraft is typically in low-speed operations or floating state, attitude angle variation is smaller, it is believed thatTherefore formula (4) can be rewritten as:
Joint type (3) and formula (5), obtain the kinetic model of quadrotor are as follows:
Wherein ux=cos φ sin θ cos ψ+sin φ sin ψ, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, and the desired value of θ is respectively as follows:
Wherein φdFor the expected signal value of φ, θdFor θ expected signal value, arcsin is arcsin function；
Step 2, in each sampling instant, calculating position tracking error and its first derivative；Posture angle tracking is calculated to miss
Difference and its first derivative；Design position and posture angle controller, process are as follows:
2.1 define z tracking error and its first derivative:
Wherein zdIndicate the desired signal of z；
2.2 define q1:
2.3 design constraint liapunov functions
Wherein Ka1, Kb1For normal number:
Wherein | e1|maxFor | e1| maximum value；
2.4 solve formula (10) first derivative, can obtain:
Wherein α1For virtual controlling amount,
Expression formula are as follows:
Wherein k11For normal number；
Formula (13) are substituted into formula (12), can be obtained:
2.5 design liapunov function V12Are as follows:
Solution formula (15) first derivative, can obtain:
Wherein
Formula (17) and formula (6) are substituted into formula (16), can be obtained:
2.6 design Uf:
Wherein k12For normal number；
2.7 define x, and y tracking error is respectively e2, e3, then have:
Wherein xd, ydRespectively indicate x, the desired signal of y；
2.8 define q2, q3:
2.9 design constraint liapunov functions:
Wherein Ka2, Kb2, Ka3, Kb3For normal number:
Wherein | e2|maxFor | e2| maximum value, | e3|maxFor | e3| maximum value；
2.10 solve formula (23) first derivative, can obtain:
Wherein α2, α3For virtual controlling amount, expression formula are as follows:
Wherein k21, k31For normal number；
Formula (26) are substituted into formula (25), can be obtained:
2.11 design liapunov function V22, V32Are as follows:
The first derivative of solution formula (28), can obtain:
Wherein
Formula (30) and formula (6) are substituted into formula (29), can be obtained:
2.12 designing ux, uy:
Wherein k22, k32For normal number；
2.13 define posture angle tracking error and its first derivative:
Wherein j=4,5,6, x4=φ, x5=θ, x6=ψ, x4dIndicate the desired value of φ, x5dIndicate the desired value of θ, x6dTable
Show the desired value of ψ, e4Indicate the tracking error of φ, e5Indicate the tracking error of θ, e6Indicate the tracking error of ψ；
2.14 defining qj:
2.15 design constraint liapunov functions:
Wherein Kaj, KbjFor normal number:
Wherein | ej|maxFor | ej| maximum value；
2.16 solve formula (35) first derivative, can obtain:
Wherein αjFor virtually control amount, expression
Formula are as follows:
Wherein kj1For normal number；
Formula (38) are substituted into formula (37), can be obtained:
2.17 design liapunov function Vj2Are as follows:
The first derivative of solution formula (40), can obtain:
Wherein
Formula (42) and formula (6) are substituted into formula (41), can be obtained:
2.18 design τ by formula (43)x, τy, τz:
Wherein k42, k52, k62For normal number；
Step 3, the stability of quadrotor system is verified；
Formula (19) are substituted into formula (18) by 3.1, can be obtained:
Formula (32) are substituted into formula (31) by 3.2, can be obtained:
Formula (44) are substituted into formula (43) by 3.3, can be obtained
3.4 by (45), and (46), quadrotor system known to (47) is stable.
In order to verify the feasibility of proposed method, the emulation knot that The present invention gives the control methods on MATLAB platform
Fruit:
Parameter is given below: m=1.1kg, g=9.81N/kg in formula (2)；In formula (4), Ixx=1.22kgm2, Iyy=
1.22kg·m2, Izz=2.2kgm2；Z in formula (8), formula (20) and formula (33)d=1, xd=1, yd=1, ψd=0.5；Formula
(13), k in formula (26) and formula (38)11=2, k21=2, k31=2, k41=2, k51=2, k61=2；Formula (19), formula (32) and formula
(44) k in12=2, k22=2, k32=2, k42=2, k52=2, k62=2；Formula (10), formula (23) and formula (35) kb1=2.5, ka1
=3.5；kb2=2.5, ka2=3.5；kb3=2.5, ka3=3.5；kb4=3, ka4=3；kb5=3, ka5=2；kb6=3, ka6=2.
From Fig. 1 and 2 it is found that system has good transient response, arrival time is 6.41 seconds, overshoot 0.
In conclusion using it is asymmetric when constraint independent of time function Spacecraft Attitude Control can effectively improve four rotations
The mapping of rotor aircraft 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. it is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control, which is characterized in that the method packet
Include following steps:
Step 1, the dynamic model for establishing quadrotor system sets initial value, sampling time and the control ginseng of system
Number, process are as follows:
1.1 determine from the body coordinate system based on quadrotor system to the transfer matrix T of the inertial coordinate based on the earth:
Wherein, φ, θ, ψ are roll angle, pitch angle, the yaw angle of quadrotor respectively, indicate aircraft successively around inertia
The angle of each reference axis rotation of coordinate system；
Dynamic model during the translation of 1.2 quadrotors is as follows:
Wherein, x, y, z respectively indicate three positions of the quadrotor under inertial coodinate system, UfIndicate quadrotor
Input torque, m be quadrotor quality, g indicate acceleration of gravity；
Formula (1) is substituted into formula (2) to obtain:
Dynamic model in 1.3 quadrotor rotation processes are as follows:
Wherein, τx,τy,τzRespectively represent the moment components of each axis on body coordinate system, Ixx,Iyy,IzzRespectively indicate body seat
The component of the rotary inertia of each axis under mark system, × indicate multiplication cross, ωpIndicate rolling angular speed, ωqIndicate rate of pitch,
ωrIndicate yaw rate,Indicate rolling angular acceleration,Indicate pitching angular acceleration,Indicate yaw angular acceleration；
In view of aircraft is in low-speed operations or floating state, it is believed that Therefore formula (4) is rewritten are as follows:
Joint type (3) and formula (5), obtain the kinetic model of quadrotor are as follows:
Wherein, ux=cos φ sin θ cos ψ+sin φ sin ψ, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, and the desired value of θ is respectively as follows:
Wherein, φdFor the expected signal value of φ, θdFor θ expected signal value, arcsin is arcsin function；
Step 2, in each sampling instant, calculating position tracking error and its first derivative；Calculate posture angle tracking error and
Its first derivative；Design position and posture angle controller, process are as follows:
2.1 define z tracking error and its first derivative:
Wherein, zdIndicate the desired signal of z；
2.2 define q1:
2.3 design constraint liapunov functions
Wherein, Ka1,Kb1For normal number:
Wherein, | e1|maxFor | e1| maximum value；
2.4 solve formula (10) first derivative, obtain:
Wherein,α1For virtual controlling amount, expression
Formula are as follows:
Wherein, k11For normal number；
Formula (13) are substituted into formula (12), are obtained:
2.5 design liapunov function V12Are as follows:
Solution formula (15) first derivative, obtains:
Wherein
Formula (17) and formula (6) are substituted into formula (16), obtained:
2.6 design Uf:
Wherein, k12For normal number；
2.7 define x, and y tracking error is respectively e2,e3, then have:
Wherein, xd,ydRespectively indicate x, the desired signal of y；
2.8 define q2,q3:
2.9 design constraint liapunov functions:
Wherein, Ka2,Kb2,Ka3,Kb3For normal number:
Wherein, | e2|maxFor | e2| maximum value, | e3|maxFor | e3| maximum value；
2.10 solve formula (23) first derivative, obtain:
Wherein, α2,α3For virtual controlling amount, expression formula are as follows:
Wherein, k21,k31For normal number；
Formula (26) are substituted into formula (25), are obtained:
2.11 design liapunov function V22,V32Are as follows:
The first derivative of solution formula (28), obtains:
Wherein
Formula (30) and formula (6) are substituted into formula (29), obtained:
2.12 designing ux,uy:
Wherein, k22,k32For normal number；
2.13 defining posture angle tracking error and its first derivative:
Wherein, j=4,5,6, x4=φ, x5=θ, x6=ψ, x4dIndicate the desired value of φ, x5dIndicate the desired value of θ, x6dIndicate ψ
Desired value, e4Indicate the tracking error of φ, e5Indicate the tracking error of θ, e6Indicate the tracking error of ψ；
2.14 defining qj:
2.15 design constraint liapunov functions:
Wherein, Kaj,KbjFor normal number:
Wherein, | ej|maxFor | ej| maximum value；
2.16 solve formula (35) first derivative, obtain:
Wherein,αjFor virtually control amount, expression formula are as follows:
Wherein, kj1For normal number；
Formula (38) are substituted into formula (37), are obtained:
2.17 design liapunov function Vj2Are as follows:
The first derivative of solution formula (40), obtains:
Wherein
Formula (42) and formula (6) are substituted into formula (41), obtained:
2.18 design τ by formula (43)x,τy,τz:
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows:
Formula (19) are substituted into formula (18) by 3.1, are obtained:
Formula (32) are substituted into formula (31) by 3.2, are obtained:
Formula (44) are substituted into formula (43) by 3.3, are obtained
3.4 by (45), and (46), (47) know that quadrotor system is stable.
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| CN201810212162.XA CN108549216A (en) | 2018-03-15 | 2018-03-15 | Based on it is asymmetric when the constant compound constraint liapunov function of logarithm secant quadrotor export constrained control method |
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| CN201910188254.3A Withdrawn CN109870912A (en) | 2018-03-15 | 2019-03-13 | It is a kind of using it is asymmetric when constraint independent of time function Spacecraft Attitude Control |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115390447A (en) * | 2022-08-16 | 2022-11-25 | 哈尔滨逐宇航天科技有限责任公司 | Aircraft preset performance control method suitable for large-amplitude attitude maneuver |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN115390447B (en) * | 2022-08-16 | 2024-05-14 | 哈尔滨逐宇航天科技有限责任公司 | Aircraft preset performance control method adapting to great maneuvering of gestures |
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