CN109932902A - A kind of quadrotor output constrained control method - Google Patents

A kind of quadrotor output constrained control method Download PDF

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CN109932902A
CN109932902A CN201910099075.2A CN201910099075A CN109932902A CN 109932902 A CN109932902 A CN 109932902A CN 201910099075 A CN201910099075 A CN 201910099075A CN 109932902 A CN109932902 A CN 109932902A
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陈强
胡忠君
胡轶
吴春
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Zhejiang University of Technology ZJUT
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    • 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
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Abstract

A kind of quadrotor output constrained control method, for the dynamic system of quadrotor, constant tangential type constrains liapunov function when selecting a kind of symmetrical, design it is a kind of based on it is symmetrical when constant tangential type constraint liapunov function quadrotor export constrained control method.The design of constant tangential type constraint 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 provide it is a kind of based on it is symmetrical when constant tangential type constraint liapunov function quadrotor export constrained control method, make system that there is preferable dynamic response process.

Description

A kind of quadrotor output constrained control method
Technical field
The present invention relates to a kind of quadrotors to export constrained control method, 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 flies Row device is small in size and light-weight, in-flight vulnerable to external disturbance, how to realize the high-performance movement control to quadrotor System has become a hot issue.For the control problem of quadrotor, there are many control methods, such as PID to control System, Active Disturbance Rejection Control, sliding formwork control, Reverse Step Control etc..
Wherein Reverse Step Control has been widely used for nonlinear system, advantage include fast response time, it is easy to implement, And robustness of external disturbance uncertain to system etc..Traditional Reverse Step Control only considers the stable state of quadrotor Performance, there is no pay close attention to its transient response performance too much.Therefore, traditional backstepping control method makes quadrotor The application of system in a practical situation has very big obstruction.To solve this problem, the contragradience based on constraint liapunov function Control method is suggested, and this method can effectively improve the mapping of quadrotor system in a practical situation.
Summary of the invention
Mapping in order to overcome the shortcomings of existing quadrotor system is poor, and the present invention provides a kind of bases The quadrotor of constant tangential type constraint liapunov function exports constrained control method when symmetrical, reduces super Tune amount and overshoot time make quadrotor system 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 quadrotor output constrained 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 of the inertial coordinate based on the earth Matrix 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 quadrotor The input torque of aircraft, 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 yaw angle Acceleration；
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:
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,α1For void Quasi- control amount, expression formula are as follows:
Wherein, k11For normal number；
Formula (10) are substituted into formula (9), are obtained:
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,ydX is respectively indicated, The desired signal of y；
2.6 design constraint liapunov functionsIt asks respectively Its first derivative is solved, is obtained:
Wherein, Kb2For e2Boundary, meet Kb2>|e2|max, | e2|maxFor | e2| maximum value；Kb3For e3Boundary, it is full Sufficient Kb3>|e3|max, | e3|maxFor | e3| maximum value；α2,α3For virtual controlling amount, table Up to formula are as follows:
Wherein, k21,k31For normal number；
Formula (19) are substituted into formula (18), are obtained:
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 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 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:
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.
The present invention is based on it is symmetrical when constant tangential type constraint liapunov function the limited control of quadrotor output Method processed 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 when one kind is based on symmetrical not The quadrotor for becoming tangential type constraint liapunov function exports constrained control method.Constant tangential type is about when symmetrical The design of beam liapunov function is avoided excessive to guarantee that the output of system can limit in a certain range Overshoot, while arrival time can also be reduced.So as to improve the dynamic response performance of quadrotor 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 quadrotor output constrained 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 of the inertial coordinate based on the earth Matrix 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 quadrotor The input torque of aircraft, 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 yaw angle Acceleration；
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:
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,α1For void Quasi- control amount, expression formula are as follows:
Wherein, k11For normal number；
Formula (10) are substituted into formula (9), are obtained:
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 functionsIt asks respectively Its first derivative is solved, is obtained:
Wherein, Kb2For e2Boundary, meet Kb2>|e2|max, | e2|maxFor | e2| maximum value；Kb3For e3Boundary, it is full Sufficient Kb3>|e3|max, | e3|maxFor | e3| maximum value；α2,α3For virtual controlling amount, table Up to formula are as follows:
Wherein, k21,k31For normal number；
Formula (19) are substituted into formula (18), are obtained:
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, 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 solve its first derivative:
Its, middle 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:
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 present invention gives emulation of the control method on MATLAB platform As a result:
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 4.23 seconds, and overshoot is 0.0245。
In conclusion based on it is symmetrical when constant tangential type constraint liapunov function quadrotor output by Limit control method can effectively improve the mapping of quadrotor 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 It is only limited to above-described embodiment, without departing from essence spirit of the present invention and without departing from range involved by substantive content of the present invention Under the premise of it can be made it is various deformation be implemented.

Claims (1)

1. a kind of quadrotor exports constrained 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 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, 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；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:
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 functionsOne is solved respectively Order derivative obtains:
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:
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:
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.
CN201910099075.2A 2018-02-11 2019-01-31 A kind of quadrotor output constrained control method Withdrawn CN109932902A (en)

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Application publication date: 20190625