CN108267961A - Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function - Google Patents

Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function Download PDF

Info

Publication number
CN108267961A
CN108267961A CN201810142264.9A CN201810142264A CN108267961A CN 108267961 A CN108267961 A CN 108267961A CN 201810142264 A CN201810142264 A CN 201810142264A CN 108267961 A CN108267961 A CN 108267961A
Authority
CN
China
Prior art keywords
formula
represent
max
quadrotor
derivative
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.)
Withdrawn
Application number
CN201810142264.9A
Other languages
Chinese (zh)
Inventor
陈强
胡忠君
胡轶
吴春
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.)
Zhejiang University of Technology ZJUT
Original Assignee
Zhejiang University of Technology ZJUT
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 Zhejiang University of Technology ZJUT filed Critical Zhejiang University of Technology ZJUT
Priority to CN201810142264.9A priority Critical patent/CN108267961A/en
Publication of CN108267961A publication Critical patent/CN108267961A/en
Withdrawn legal-status Critical Current

Links

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
    • G05B13/04—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, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Remote Sensing (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Computation (AREA)
  • Software Systems (AREA)
  • Health & Medical Sciences (AREA)
  • Algebra (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Feedback Control In General (AREA)

Abstract

A kind of quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function, for the dynamic system of quadrotor, select a kind of symmetrical time-varying tangential type constraint liapunov function, a kind of quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function of design.The design of symmetrical time-varying tangential type constraint liapunov function is to ensure that the state of system and output can be limited in certain range, avoid excessive overshoot, while can also reduce arrival time.So as to improve the dynamic response performance of quadrotor system.The present invention provides a kind of quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function, and system is made to have preferable dynamic response process.

Description

Quadrotor based on symmetrical time-varying tangential type constraint liapunov function is complete State constraint control method
Technical field
The present invention relates to a kind of full shapes of quadrotor based on symmetrical time-varying tangential type constraint liapunov function State constrained control method makes quadrotor system have preferable dynamic response process.
Background technology
The one kind of quadrotor as rotary aircraft, with its is small, mobility is good, design is simple, system The advantages that of low cost is made, has attracted the extensive concern of domestic and international university, research institution, company.However, since quadrotor is flown Device is small and light-weight, is 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 System does not know robustness with external disturbance etc..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 causes 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.
Invention content
In order to overcome the shortcomings of that the mapping of existing quadrotor system is poor, the present invention provides one kind to be based on The quadrotor total state constrained control method of symmetrical time-varying tangential type liapunov function reduces overshoot and surpasses Between timing, making quadrotor system tool, there are one good dynamic response performances.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows：
A kind of quadrotor total state constrained control based on symmetrical time-varying tangential type constraint liapunov function Method includes the following steps：
Step 1, the dynamic model of quadrotor system, initial value, sampling time and the control of initialization system are established 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, represent 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 represent three positions of the quadrotor under inertial coodinate system, U respectivelyfRepresent that quadrotor flies The input torque of row device, m are the quality of quadrotor, and g represents acceleration of gravity,
Formula (1) is substituted into formula (2) to obtain：
Dynamic model in 1.3 quadrotor rotation processes is：
Wherein, τx,τy,τzThe moment components of each axis on body coordinate system, I are represented respectivelyxx,Iyy,IzzMachine is represented respectively The component of the rotary inertia of each axis under body coordinate system, × expression multiplication cross, ωpRepresent rolling angular speed, ωqRepresent pitch angle Speed, ωrRepresent yaw rate,Represent rolling angular acceleration,Represent pitching angular acceleration,Represent that yaw angle adds Speed；
Low-speed operations or floating state are in view of aircraft, attitude angle variation is smaller, it is believed that
Therefore formula (4) is rewritten as：
Simultaneous formula (3) and formula (5), the kinetic model for obtaining quadrotor are：
Wherein, ux=cos φ sin θ cos ψ+sin φ sin ψs, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, the desired value of θ is：
Wherein, φdFor the expected signal value of φ, θdFor θ expected signal values, arcsin is arcsin function；
Step 2, in each sampling instant, calculation 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 errors and its first derivative：
Wherein, zdRepresent the desired signal of z；
2.2 design constraint liapunov functionsAnd solve its first derivative：
Wherein, Kb1For time-varying parameter, meet Kb1>|e1|max, | e1|maxFor | e1| maximum value, α1For void Intend controlled quentity controlled variable, expression formula is：
Wherein, k11For normal number；
Formula (10) is substituted into formula (9), is obtained：
Wherein,
2.3 design liapunov function V12For：
Wherein, Ks1For time-varying parameter, meet Ks1>|s1|max, | s1|maxFor | s1| maximum value,
The first derivative of solution formula (12), can；：
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 errors are respectively e2,e3, then have：
Wherein, xd,ydX, the desired signal of y are represented respectively；
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 For：
Its, middle k21,k31For normal number；
Formula (19) is substituted into formula (18), is obtained：
Wherein,
2.7 design liapunov function V22,V32
Wherein, Ks2For s2Boundary, meet Ks2>|s2|max, | s2|maxFor | s2| maximum value；Wherein Ks3For s3Boundary, Meet Ks3>|s3|max, | s3|maxFor | s3| maximum value；
The first derivative of solution formula (21), obtains：
Wherein
By formula (23), (6) substitute into formula (22), respectively：
2.8 by formula (24), (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, x4dRepresent the desired value of φ, x5dRepresent the desired value of θ, x6d Represent the desired value of ψ, e4Represent the tracking error of φ, e5Represent the tracking error of θ, e6Represent 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 is：
Wherein, kj1For normal number；
Formula (29) is substituted into formula (28), is obtained：
Wherein,
2.11 design constraint liapunov function Vj2：
Wherein, KsjFor sjBoundary, meet Ksj>|sj|max, | sj|maxFor | sj| maximum value；
The first derivative of solution formula (31), obtains：
Wherein
Formula (33) and formula (6) are substituted into formula (32), respectively：
2.12 separately design τ by formula (34), (35), (36)x,τy,τz：
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows：
Formula (16) is substituted into formula (15) by 3.1, is obtained：
Formula (26) is substituted into formula (24), (25) by 3.2, is obtained：
Formula (37) is substituted into formula (34), (35), (36) by 3.3, is obtained
3.4 know that quadrotor system is stable by (38), (39), (40).
Quadrotor total state the present invention is based on symmetrical time-varying tangential type constraint liapunov function is limited control Method processed improves the mapping of system, reduces overshoot and arrival time.
The present invention technical concept be：For the dynamic system of quadrotor, design is a kind of to be based on symmetrical time-varying Tangential type constrains the quadrotor total state constrained control method of liapunov function.Symmetrical time-varying tangential type constraint Lee The design of Ya Punuofu functions is to ensure that the state of system and output can be limited in certain range, avoid excessive Overshoot, while arrival time can also be reduced.So as to improve the dynamic response performance of quadrotor system.
Beneficial effects of the present invention are：Total state is limited, and reduces overshoot, reduces arrival time, improves mapping.
Description of the drawings
Fig. 1 is the position tracking effect diagram of the present invention.
Fig. 2 is the attitude angle tracking effect schematic diagram of the present invention.
Fig. 3 is the position and speed tracking effect schematic diagram of the present invention.
Fig. 4 is the attitude angular velocity tracking effect schematic diagram of the present invention.
The positioner that Fig. 5 is the present invention inputs schematic diagram.
The posture angle controller that Fig. 6 is the present invention inputs schematic diagram.
Fig. 7 is the control flow schematic diagram of the present invention.
Specific embodiment
The present invention will be further described below in conjunction with the accompanying drawings.
With reference to Fig. 1-Fig. 7, a kind of quadrotor based on symmetrical time-varying tangential type constraint liapunov function is complete State constraint control method, includes the following steps：
Step 1, the dynamic model of quadrotor system, initial value, sampling time and the control of initialization system are established 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, represent 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 represent three positions of the quadrotor under inertial coodinate system, U respectivelyfRepresent that quadrotor flies The input torque of row device, m are the quality of quadrotor, and g represents acceleration of gravity,
Formula (1) is substituted into formula (2) to obtain：
Dynamic model in 1.3 quadrotor rotation processes is：
Wherein, τx,τy,τzThe moment components of each axis on body coordinate system, I are represented respectivelyxx,Iyy,IzzMachine is represented respectively The component of the rotary inertia of each axis under body coordinate system, × expression multiplication cross, ωpRepresent rolling angular speed, ωqRepresent pitch angle Speed, ωrRepresent yaw rate,Represent rolling angular acceleration,Represent pitching angular acceleration,Represent that yaw angle adds Speed；
Low-speed operations or floating state are in view of aircraft, attitude angle variation is smaller, it is believed that
Therefore formula (4) is rewritten as：
Simultaneous formula (3) and formula (5), the kinetic model for obtaining quadrotor are：
Wherein, ux=cos φ sin θ cos ψ+sin φ sin ψs, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, the desired value of θ is：
Wherein, φdFor the expected signal value of φ, θdFor θ expected signal values, arcsin is arcsin function；
Step 2, in each sampling instant, calculation 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 errors and its first derivative：
Wherein, zdRepresent the desired signal of z；
2.2 design constraint liapunov functionsAnd solve its first derivative：
Wherein, Kb1For time-varying parameter, meet Kb1>|e1|max, | e1|maxFor | e1| maximum value, α1For void Intend controlled quentity controlled variable, expression formula is：
Wherein, k11For normal number；
Formula (10) is substituted into formula (9), is obtained：
Wherein,
2.3 design liapunov function V12For：
Wherein, Ks1For time-varying parameter, meet Ks1>|s1|max, | s1|maxFor | s1| maximum value, solve formula (12) single order Derivative 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 errors are respectively e2,e3, then have：
Wherein, xd,ydX, the desired signal of y are represented respectively；
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 For：
Wherein, k21,k31For normal number；
Formula (19) is substituted into formula (18), is obtained：
Wherein,
2.7 design liapunov function V22,V32
Wherein, Ks2For s2Boundary, meet Ks2>|s2|max, | s2|maxFor | s2| maximum value；Wherein Ks3For s3Boundary, Meet Ks3>|s3|max, | s3|maxFor | s3| maximum value；
The first derivative of solution formula (21), obtains：
Wherein
By formula (23), (6) substitute into formula (22), respectively：
2.8 separately design u by formula (24), (25)x,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, x4dRepresent the desired value of φ, x5dRepresent the desired value of θ, x6d Represent the desired value of ψ, e4Represent the tracking error of φ, e5Represent the tracking error of θ, e6Represent 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 is：
Wherein, kj1For normal number；
Formula (29) is substituted into formula (28), is obtained：
Wherein,
2.11 design constraint liapunov function Vj2：
Wherein, KsjFor sjBoundary, meet Ksj>|sj|max, | sj|maxFor | sj| maximum value；
The first derivative of solution formula (31), obtains：
Wherein
Formula (33) and formula (6) are substituted into formula (32), respectively：
2.12 separately design τ by formula (34), (35), (36)x,τy,τz：
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows：
Formula (16) is substituted into formula (15) by 3.1, is obtained：
Formula (26) is substituted into formula (24), (25) by 3.2, is obtained：
Formula (37) is substituted into formula (34), (35), (36) by 3.3, is obtained
3.4 know that quadrotor system is stable by (38), (39), (40).
The feasibility of extracting method in order to verify, The present invention gives emulation knot of the control method on MATLAB platforms 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=kb2=kb3= 1.5+0.1sint,kb4=kb5=kb6=2+0.1sint；Formula (12), formula (21) and formula (31) ks1=ks2=ks3=3.5+ 0.1sint,ks4=ks5=ks6=4+0.1sint.
From Fig. 1 and Fig. 2 it is found that system output has good transient response, arrival time is 5.06 seconds, and overshoot is 0.0015。
From Fig. 3 and Fig. 4 it is found that system mode has good transient response, arrival time is 5.48 seconds, overshoot 0.
In conclusion the quadrotor total state based on symmetrical time-varying tangential type constraint liapunov function is limited Control method can effectively improve the mapping of quadrotor system total state.
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 Above-described embodiment is limited to, without departing from essence spirit of the present invention and the premise without departing from 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 quadrotor total state constrained control side based on symmetrical time-varying tangential type constraint liapunov function Method, which is characterized in that the control method includes the following steps：
Step 1, the dynamic model of quadrotor system, initial value, sampling time and the control ginseng of initialization system are established 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, represent 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 represent three positions of the quadrotor under inertial coodinate system, U respectivelyfRepresent quadrotor Input torque, m be quadrotor quality, g represent acceleration of gravity,
Formula (1) is substituted into formula (2) to obtain：
Dynamic model in 1.3 quadrotor rotation processes is：
Wherein, τx,τy,τzThe moment components of each axis on body coordinate system, I are represented respectivelyxx,Iyy,IzzRepresent that body is sat respectively The component of the rotary inertia of each axis under mark system, × expression multiplication cross, ωpRepresent rolling angular speed, ωqRepresent rate of pitch, ωrRepresent yaw rate,Represent rolling angular acceleration,Represent pitching angular acceleration,Represent yaw angular acceleration；
Low-speed operations or floating state are in view of aircraft, attitude angle variation is smaller, it is believed that
Therefore formula (4) is rewritten as：
Simultaneous formula (3) and formula (5), the kinetic model for obtaining quadrotor are：
Wherein, ux=cos φ sin θ cos ψ+sin φ sin ψs, uy=cos φ sin θ sin ψ-sin φ cos ψ；
1.4, according to formula (6), define φ, the desired value of θ is：
Wherein, φdFor the expected signal value of φ, θdFor θ expected signal values, arcsin is arcsin function；
Step 2, in each sampling instant, calculation 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 errors and its first derivative：
Wherein, zdRepresent the desired signal of z；
2.2 design constraint liapunov functionsAnd solve its first derivative：
Wherein, Kb1For time-varying parameter, meet Kb1>|e1|max, | e1|maxFor | e1| maximum value, α1Virtually to control Amount processed, expression formula are：
Wherein, k11For normal number；
Formula (10) is substituted into formula (9), is obtained：
Wherein,
2.3 design liapunov function V12For：
Wherein, Ks1For time-varying parameter, meet Ks1>|s1|max, | s1|maxFor | s1| maximum value,
The first derivative of solution formula (12), can；：
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 errors are respectively e2,e3, then have：
Wherein, xd,ydX, the desired signal of y are represented respectively；
2.6 design constraint liapunov functionsIts single order is solved respectively to lead Number, 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 is：
Its, middle k21,k31For normal number；
Formula (19) is substituted into formula (18), is obtained：
Wherein,
2.7 design liapunov function V22,V32
Wherein, Ks2For s2Boundary, meet Ks2>|s2|max, | s2|maxFor | s2| maximum value；Wherein Ks3For s3Boundary, meet Ks3>|s3|max, | s3|maxFor | s3| maximum value；
The first derivative of solution formula (21), obtains：
Wherein
By formula (23), (6) substitute into formula (22), respectively：
2.8 separately design u by formula (24), (25)x,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, x4dRepresent the desired value of φ, x5dRepresent the desired value of θ, x6dRepresent ψ Desired value, e4Represent the tracking error of φ, e5Represent the tracking error of θ, e6Represent 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 is：
Wherein, kj1For normal number；
Formula (29) is substituted into formula (28), is obtained：
Wherein,
2.11 design constraint liapunov function Vj2：
Wherein, KsjFor sjBoundary, meet Ksj>|sj|max, | sj|maxFor | sj| maximum value；
The first derivative of solution formula (31), obtains：
Wherein
Formula (33) and formula (6) are substituted into formula (32), respectively：
2.12 separately design τ by formula (34), (35), (36)x,τy,τz：
Wherein, k42,k52,k62For normal number；
Step 3, the stability of quadrotor system is verified, process is as follows：
Formula (16) is substituted into formula (15) by 3.1, is obtained：
Formula (26) is substituted into formula (24), (25) by 3.2, is obtained：
Formula (37) is substituted into formula (34), (35), (36) by 3.3, is obtained
3.4 know that quadrotor system is stable by (38), (39), (40).
CN201810142264.9A 2018-02-11 2018-02-11 Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function Withdrawn CN108267961A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810142264.9A CN108267961A (en) 2018-02-11 2018-02-11 Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810142264.9A CN108267961A (en) 2018-02-11 2018-02-11 Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function

Publications (1)

Publication Number Publication Date
CN108267961A true CN108267961A (en) 2018-07-10

Family

ID=62773973

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810142264.9A Withdrawn CN108267961A (en) 2018-02-11 2018-02-11 Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function

Country Status (1)

Country Link
CN (1) CN108267961A (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109557933A (en) * 2018-11-27 2019-04-02 浙江工业大学 A kind of rigid aircraft state constraint control method based on imperial Burger observer
CN110687787A (en) * 2019-10-11 2020-01-14 浙江工业大学 Mechanical arm system self-adaptive control method based on time-varying asymmetric obstacle Lyapunov function
CN110750050A (en) * 2019-10-11 2020-02-04 浙江工业大学 Neural network-based mechanical arm system preset performance control method
WO2021237500A1 (en) * 2020-05-27 2021-12-02 深圳市大疆创新科技有限公司 Flight control method and device

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109557933A (en) * 2018-11-27 2019-04-02 浙江工业大学 A kind of rigid aircraft state constraint control method based on imperial Burger observer
CN109557933B (en) * 2018-11-27 2021-08-03 浙江工业大学 Rigid aircraft state constraint control method based on Longberger observer
CN110687787A (en) * 2019-10-11 2020-01-14 浙江工业大学 Mechanical arm system self-adaptive control method based on time-varying asymmetric obstacle Lyapunov function
CN110750050A (en) * 2019-10-11 2020-02-04 浙江工业大学 Neural network-based mechanical arm system preset performance control method
WO2021237500A1 (en) * 2020-05-27 2021-12-02 深圳市大疆创新科技有限公司 Flight control method and device

Similar Documents

Publication Publication Date Title
CN108037662B (en) A kind of limited backstepping control method of quadrotor output based on Integral Sliding Mode obstacle liapunov function
CN107831670B (en) It is a kind of based on it is asymmetric when constant obstacle liapunov function quadrotor export limited backstepping control method
CN108267961A (en) Quadrotor total state constrained control method based on symmetrical time-varying tangential type constraint liapunov function
CN108388119A (en) Based on it is symmetrical when constant tangential type constrain the quadrotor total state constrained control method of liapunov function
CN109917650A (en) A kind of Spacecraft Attitude Control of asymmetric varying constraint
CN108388118A (en) The quadrotor total state constrained control method of liapunov function is constrained based on asymmetric time-varying tangential type
CN108427278A (en) Based on it is symmetrical when the compound constraint liapunov function of varying index tangent quadrotor total state constrained control method
CN108536162A (en) Based on it is symmetrical when the not compound constraint liapunov function of varying index tangent quadrotor total state constrained control method
CN108388117A (en) Based on it is symmetrical when constant tangential type constrain the quadrotor of liapunov function and export constrained control method
CN108052115B (en) It is a kind of based on it is asymmetric when constant obstacle liapunov function quadrotor total state be limited backstepping control method
CN109917651A (en) A kind of Spacecraft Attitude Control that symmetrical time-varying output is limited
CN108303892A (en) The quadrotor that liapunov function is constrained based on asymmetric time-varying tangential type exports constrained control method
CN108333950A (en) Quadrotor based on the compound constraint liapunov function of symmetrical time-varying tangent cosine exports constrained control method
CN108427279A (en) Based on it is symmetrical when the compound constraint liapunov function of varying index tangent quadrotor export constrained control method
CN108549216A (en) Based on it is asymmetric when the constant compound constraint liapunov function of logarithm secant quadrotor export constrained control method
CN108549218A (en) Based on it is symmetrical when the constant compound constraint liapunov function of tangent cosine quadrotor export constrained control method
CN108594647A (en) Quadrotor total state constrained control method based on the compound constraint liapunov function of symmetrical time-varying logarithm tangent
CN108563115A (en) Based on it is symmetrical when the constant compound constraint liapunov function of logarithm tangent quadrotor total state constrained control method
CN108388116A (en) The quadrotor that liapunov function is constrained based on symmetrical time-varying tangential type exports constrained control method
CN108388128A (en) Based on it is symmetrical when constant cut type anyway constrain the quadrotor of liapunov function and export constrained control method
CN108563117A (en) Based on symmetrical time-varying anyway cut type constrain liapunov function quadrotor export constrained control method
CN108427274A (en) Quadrotor based on the compound constraint liapunov function of symmetrical time-varying logarithm secant exports constrained control method
CN108490768A (en) Based on it is asymmetric when constant tangential type constrain the quadrotor of liapunov function and export constrained control method
CN108388129A (en) Quadrotor total state constrained control method based on the compound constraint liapunov function of asymmetric time-varying logarithm tangent
CN108563116A (en) Based on it is asymmetric when constant cut type anyway constrain the quadrotor of liapunov function and export constrained control method

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
WW01 Invention patent application withdrawn after publication
WW01 Invention patent application withdrawn after publication

Application publication date: 20180710