CN109917649A - A kind of aircraft arc tangent output constraint control method - Google Patents
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Abstract
A kind of aircraft arc tangent output constraint control method, for the dynamic system of quadrotor, constant cut type anyway constrains liapunov function when selecting a kind of symmetrical, design it is a kind of based on it is symmetrical when the constant constraint of cut type anyway liapunov function quadrotor export constrained control method.The design of the constant constraint of cut type anyway liapunov function 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 symmetrical.So as to improve the dynamic response performance of quadrotor system.The present invention provides a kind of aircraft arc tangent output constraint control method, and system is made to have preferable dynamic response process.
Description
Technical field
The present invention relates to a kind of aircraft arc tangent output constraint control methods, there is quadrotor system preferably
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 Reverse Step Control based on constraint liapunov function
Method is suggested, and 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, the present invention provides a kind of aircraft arc tangent output constraints
Control method reduces overshoot and overshoot time, and quadrotor system is made to have a good dynamic response performance.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows:
A kind of aircraft arc tangent output constraint control method, 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, the desired value of θ are 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:
e1=z-zd,
Wherein, zdIndicate the desired signal of z；
2.2 design constraint liapunov functionsAnd it solves its single order and leads
Number:
Wherein, Kb1For e1Boundary, meet Kb1>|e1|max, | e1|maxFor | e1| maximum value,α1For void
Quasi- control amount, expression formula are as follows:
Wherein, k11For normal number；
Formula (10) are substituted into formula (9), are obtained:
Wherein,
2.3 design liapunov function V12Are as follows:
The first derivative of solution formula (12), obtains:
Wherein
Formula (14) and formula (6) are substituted into formula (13), obtained:
2.4 design Uf:
Wherein, k12For normal number；
2.5 define x, and y tracking error is respectively e2,e3, then have:
e2=x-xd,e3=y-yd,
Wherein, xd,ydRespectively indicate x, the desired signal of y；
2.6 design constraint liapunov functions Its first derivative is solved respectively, is obtained:
Wherein, Kb2For e2Boundary, meet Kb2>|e2|max, | e2|maxFor | e2| maximum value；Kb3For e3Boundary, meet
Kb3>|e3|max, | e3|maxFor | e3| maximum value；α2,α3For virtual controlling amount, expression
Formula are as follows:
Wherein, k21,k31For normal number；
Formula (19) are substituted into formula (18), are obtained:
Wherein,
2.7 design liapunov function V22,V32
The first derivative of solution formula (21), obtains:
Wherein
By formula (23), (6) substitute into formula (22), respectively:
2.8 by formula (24), and (25) separately design ux,uy:
Wherein, k22,k32For normal number；
2.9 define posture angle tracking error and its first derivative:
ej=xj-xjd,
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；
2.10 design constraint liapunov functionAnd it solves its single order and leads
Number:
Wherein, kjFor normal number, KbjFor ejBoundary, meet Kbj>|ej|max, | ej|maxFor | ej| maximum value；αjFor the virtual controlling amount of attitude angle, expression formula are as follows:
Wherein, kj1For normal number；
Formula (29) are substituted into formula (28), are obtained:
Wherein
2.11 design constraint liapunov functions:
The first derivative of solution formula (31), obtains:
WhereinFormula (33) and formula (6) are substituted into formula (32),
Respectively:
2.12 by formula (34), and (35), (36) separately design τx,τy,τz:
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows:
Formula (16) are substituted into formula (15) by 3.1, are obtained:
Formula (26) are substituted into formula (24), (25) by 3.2, are obtained:
3.3 wushu (37) substitute into formula (34), (35), (36), obtain
3.4 by (38), and (39), (40) know that quadrotor system is stable.
The present invention provides a kind of aircraft arc tangent output constraint control method, improves the mapping of system, reduces
Overshoot and arrival time.
Technical concept of the invention are as follows: for the dynamic system of quadrotor, design a kind of aircraft arc tangent
Output constraint control method.The design of the constant constraint of cut type anyway liapunov function is to guarantee the defeated of system when symmetrical
It can limit out and avoid excessive overshoot in a certain range, while arrival time can also be reduced.Fly so as to improve quadrotor
The dynamic response performance of row device system.
The invention has the benefit that reducing overshoot, arrival time is reduced, improves 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, a kind of aircraft arc tangent output constraint control method, 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, attitude angle variation is smaller, it is believed thatTherefore 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, the desired value of θ are 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:
e1=z-zd,
Wherein, zdIndicate the desired signal of z；
2.2 design constraint liapunov functionsAnd it solves its single order and leads
Number:
Wherein, Kb1For e1Boundary, meet Kb1>|e1|max, | e1|maxFor | e1| maximum value,α1For void
Quasi- control amount, expression formula are as follows:
Wherein, k11For normal number；
Formula (10) are substituted into formula (9), are obtained:
Wherein,
2.3 design liapunov function V12Are as follows:
The first derivative of solution formula (12), obtains:
Wherein
Formula (14) and formula (6) are substituted into formula (13), obtained:
2.4 design Uf:
Wherein, k12For normal number；
2.5 define x, and y tracking error is respectively e2,e3, then have:
e2=x-xd,e3=y-yd,
Wherein, xd,ydRespectively indicate x, the desired signal of y；
2.6 design constraint liapunov functions Its first derivative is solved respectively, is obtained:
Wherein, Kb2For e2Boundary, meet Kb2>|e2|max, | e2|maxFor | e2| maximum value；Kb3For e3Boundary, meet
Kb3>|e3|max, | e3|maxFor | e3| maximum value；α2,α3For virtual controlling amount, expression
Formula are as follows:
Wherein, k21,k31For normal number；
Formula (19) are substituted into formula (18), are obtained:
Wherein,
2.7 design liapunov function V22,V32
The first derivative of solution formula (21), obtains:
Wherein
By formula (23), (6) substitute into formula (22), respectively:
2.8 by formula (24), and (25) separately design ux,uy:
Wherein, k22,k32For normal number；
2.9 define posture angle tracking error and its first derivative:
ej=xj-xjd,
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；
2.10 design constraint liapunov functionAnd it solves its single order and leads
Number:
Wherein, kjFor normal number, KbjFor ejBoundary, meet Kbj>|ej|max, | ej|maxFor | ej| maximum value；αjFor the virtual controlling amount of attitude angle, expression formula are as follows:
Wherein, kj1For normal number；
Formula (29) are substituted into formula (28), are obtained:
Wherein
2.11 design constraint liapunov functions:
The first derivative of solution formula (31), obtains:
Wherein
Formula (33) and formula (6) are substituted into formula (32), respectively:
2.12 by formula (34), and (35), (36) separately design τx,τy,τz:
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows:
Formula (16) are substituted into formula (15) by 3.1, are obtained:
Formula (26) are substituted into formula (24), (25) by 3.2, are obtained:
3.3 wushu (37) substitute into formula (34), (35), (36), obtain
3.4 by (38), and (39), (40) know that quadrotor system 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 (17) and formula (27)d=1, xd=1, yd=1, ψd=0.5；Formula
(10), k in formula (19) and formula (29)11=2, k21=2, k31=2, k41=2, k51=2, k61=2；Formula (16), formula (26) and formula
(37) k in12=2, k22=2, k32=2, k42=2, k52=2, k62=2；Formula (9), formula (18) and formula (28) kb1=1.5, kb2=
1.5,kb3=1.5, kb4=2, kb5=2, kb6=2.
From Fig. 1 and Fig. 2 it is found that system has good transient response, arrival time is 6.24 seconds, overshoot 0.
In conclusion aircraft arc tangent output constraint control method can effectively improve the wink of quadrotor system
State property energy.
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 aircraft arc tangent output constraint control method, which comprises the 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 of the inertial coordinate based on the earth
T:
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, the desired value of θ are 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 design constraint liapunov functionsAnd solve its first derivative:
Wherein, Kb1For e1Boundary, meet Kb1> | e1|max, | e1|maxFor | e1| maximum value,α1Virtually to control
Amount processed, expression formula are as follows:
Wherein, k11For normal number；
Formula (10) are substituted into formula (9), are obtained:
Wherein,
2.3 design liapunov function V12Are as follows:
The first derivative of solution formula (12), obtains:
Wherein
Formula (14) and formula (6) are substituted into formula (13), obtained:
2.4 design Uf:
Wherein, k12For normal number；
2.5 define x, and y tracking error is respectively e2, e3, then have:
Wherein, xd, ydRespectively indicate x, the desired signal of y；
2.6 design constraint liapunov functions Its first derivative is solved respectively, is obtained:
Wherein, Kb2For e2Boundary, meet Kb2> | e2|max, | e2|maxFor | e2| maximum value；Kb3For e3Boundary, meet Kb3
> | e3|max, | e3|maxFor | e3| maximum value；
α2, α3For virtual controlling amount, expression formula are as follows:
Wherein, k21, k31For normal number；
Formula (19) are substituted into formula (18), are obtained:
Wherein,
2.7 design liapunov function V22, V32
The first derivative of solution formula (21), obtains:
Wherein
By formula (23), (6) substitute into formula (22), respectively:
2.8 by formula (24), and (25) separately design ux, uy:
Wherein, k22, k32For normal number；
2.9 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, x6dIndicate ψ
Desired value, e4Indicate the tracking error of φ, e5Indicate the tracking error of θ, e6Indicate the tracking error of ψ；
2.10 design constraint liapunov functionAnd solve its first derivative:
Wherein, kjFor normal number, KbjFor ejBoundary, meet Kbj> | ej|max, | ej|maxFor | ej| maximum value；αjFor the virtual controlling amount of attitude angle, expression formula are as follows:
Wherein, kj1For normal number；
Formula (29) are substituted into formula (28), are obtained:
Wherein
2.11 design constraint liapunov functions:
The first derivative of solution formula (31), obtains:
Wherein
Formula (33) and formula (6) are substituted into formula (32), respectively:
2.12 by formula (34), and (35), (36) separately design τx, τy, τz:
Wherein, k42, k52, k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows:
Formula (16) are substituted into formula (15) by 3.1, are obtained:
Formula (26) are substituted into formula (24), (25) by 3.2, are obtained:
3.3 wushu (37) substitute into formula (34), (35), (36), obtain
3.4 by (38), and (39), (40) know that quadrotor system is stable.
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| CN201810212241.0A CN108388128A (en) | 2018-03-15 | 2018-03-15 | Based on it is symmetrical when constant cut type anyway constrain the quadrotor of liapunov function and export constrained control method |
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| CN201910191619.8A Withdrawn CN109917649A (en) | 2018-03-15 | 2019-03-14 | A kind of aircraft arc tangent output constraint control method |
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| CN106094855A (en) * | 2016-07-27 | 2016-11-09 | 浙江工业大学 | A kind of terminal cooperative control method of four rotor wing unmanned aerial vehicles |
| CN106444799A (en) * | 2016-07-15 | 2017-02-22 | 浙江工业大学 | Quadrotor unmanned plane control method based on fuzzy expansion state observer and adaptive sliding formwork |
| CN106873624A (en) * | 2017-03-26 | 2017-06-20 | 天津大学 | Flight control method is hung based on the rotor wing unmanned aerial vehicle of Partial feedback linearization four |
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| CN107561931A (en) * | 2017-07-11 | 2018-01-09 | 浙江工业大学 | A kind of quadrotor nonlinear sliding mode posture control method based on monoexponential function |
| CN108549218A (en) * | 2018-03-15 | 2018-09-18 | 浙江工业大学 | Based on it is symmetrical when the constant compound constraint liapunov function of tangent cosine quadrotor export constrained control method |
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2018
- 2018-03-15 CN CN201810212241.0A patent/CN108388128A/en not_active Withdrawn
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2019
- 2019-03-14 CN CN201910191619.8A patent/CN109917649A/en not_active Withdrawn
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| CN106444799A (en) * | 2016-07-15 | 2017-02-22 | 浙江工业大学 | Quadrotor unmanned plane control method based on fuzzy expansion state observer and adaptive sliding formwork |
| CN106094855A (en) * | 2016-07-27 | 2016-11-09 | 浙江工业大学 | A kind of terminal cooperative control method of four rotor wing unmanned aerial vehicles |
| CN106873624A (en) * | 2017-03-26 | 2017-06-20 | 天津大学 | Flight control method is hung based on the rotor wing unmanned aerial vehicle of Partial feedback linearization four |
| CN107479371A (en) * | 2017-07-03 | 2017-12-15 | 浙江工业大学 | A kind of four rotor wing unmanned aerial vehicle finite time self-adaptation control methods based on quick non-singular terminal sliding formwork |
| CN107561931A (en) * | 2017-07-11 | 2018-01-09 | 浙江工业大学 | A kind of quadrotor nonlinear sliding mode posture control method based on monoexponential function |
| CN108549218A (en) * | 2018-03-15 | 2018-09-18 | 浙江工业大学 | Based on it is symmetrical when the constant compound constraint liapunov function of tangent cosine quadrotor export constrained control method |
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Application publication date: 20190621 |