CN106774373B - A kind of quadrotor drone finite time Attitude tracking control method - Google Patents
A kind of quadrotor drone finite time Attitude tracking control method Download PDFInfo
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Abstract
A kind of quadrotor drone finite time Attitude tracking control method, the present invention relates to the modeling of quadrotor drone attitude control system and finite time Attitude tracking control methods.The disturbance torque that comprehensive analysis of the present invention quadrotor drone faces, unknown rotary inertia, the factors such as control output saturation and Actuators Failures failure devise passive fault tolerant control device based on parameter adaptive method, and make it have stability in finite time energy.Step of the present invention are as follows: step 1: the kinematics model of quadrotor drone Attitude Tracking is established；Step 2: the kinetic model of quadrotor drone Attitude Tracking is established；Step 3: the posture filtering error of quadrotor drone is defined；Step 4: design finite time Integral Sliding Mode face；Step 5: the finite time Attitude tracking control device of quadrotor drone is designed.The present invention is used for UAV Flight Control field.
Description
Technical field
The present invention relates to quadrotor drone finite time Attitude tracking control methods.
Background technique
Quadrotor drone can pinpoint the small-sized unmanned aircraft to spiral as one kind with VTOL, because of its machinery knot
The plurality of advantages such as structure is simple, highly-safe, use cost is low all have been widely used in business and civil field, such as
Federal Aviation management board approved Gas Company carries out oil field prospecting, the Bladeworx company of Israel using quadrotor
Monitoring unmanned system is researched and developed to protect Jerusalem light rail damage.In addition, quadrotor drone is taken photo by plane in video, agricultural
The application aspects such as plant protection, cargo carrying also achieve great development.
For quadrotor drone as a kind of underactuated control system, reliable gesture stability is that it completes every aerial mission
Essential condition and guarantee.And many because being known as of quadrotor drone attitude control system stability are influenced, such as system is used
Amount is uncertain, the disturbance torques such as the interference of external wind square and the gyroscopic couple as caused by rotor；The execution of quadrotor drone
Mechanism is brshless DC motor, is influenced to be likely to occur partial failure failure by manufacturing process and high-intensitive task；In addition, brushless
Direct current generator has the maximum instantaneous electric current allowed, if control signal is excessive, causes the loading current of motor excessive, it is possible to
Motor is burnt, then needs to consider the factor of control output saturation in control design case.These above-mentioned factor moment affect four
The control performance of rotor wing unmanned aerial vehicle attitude control system, it is unstable to even result in system.
Currently, being directed to the gesture stability of quadrotor drone, many control design case methods, such as PID control are had existed,
Linear quadratic planning, adaptive robust control etc., but all come with some shortcomings and defect.On the one hand, these control design case methods
Only consider above-mentioned some effects factor, such as external wind square disturbance-proof design robust controller (periodical: AIAA
Infotech@Aerospace Conference；Author: Steven L.Waslander and Carlos Wang；Publication time:
2009；Title of article: Wind Disturbance Estimation and Rejection for Quadrotor
Position Control；The page number: 2009-1983), and for actuator failures design fault-tolerant controller (periodical:
Journal of Guidance,Control,and Dynamics；Author: Alexander Lanzon, Alessandro
Freddi and Sauro Longhi；Publication time: 2014；Title of article: Flight Control of a Quadrotor
Vehicle Subsequent to a Rotor Failure；The page number: 580-591) etc., rarely research institution is to above-mentioned shadow
The factor of sound carries out comprehensive analysis and designs control program；On the other hand, equal for the research achievement of UAV Attitude control at present
Stablize for the asymptotic time, without reference to finite time stability, and finite-time control method is because of its time optimal, fast convergence
Property and high-precision control performance superiority, have better actual application prospect.
Summary of the invention
Nothing that the purpose of the present invention is to solve quadrotor drones under conditions of facing various factors affecting stabilities
Method realizes the problem of finite time Attitude Tracking, proposes a kind of quadrotor drone finite time Attitude tracking control method.
A kind of quadrotor drone finite time Attitude tracking control method the following steps are included:
Step 1: the kinematics model of quadrotor drone Attitude Tracking is established；
Step 2: the kinetic model of quadrotor drone Attitude Tracking is established；
Step 3: the posture filtering error of quadrotor drone is defined according to the kinematics model that step 1 is established；
Step 4: finite time Integral Sliding Mode face is designed according to the posture filtering error that step 3 defines；
Step 5: the finite time Integral Sliding Mode face for kinetic model and the step 4 design established according to step 2, if
Count the finite time Attitude tracking control device of quadrotor drone.
The invention has the benefit that
1. the present invention considers the disturbance torque that quadrotor drone in practical projects faces, unknown rotary inertia, control
The various factors for influencing stability such as system output saturation and Actuators Failures failure, and analyzed and modeled；
2. finite time Attitude tracking control scheme proposed by the present invention, structure is simple and easy to implement, and has Passive fault-tolerant control
Performance does not need detection, the separation even Controller Reconfiguration process of fault message；
3. finite time Attitude tracking control scheme proposed by the present invention, designed control is made using parameter adaptive method
Boundary of the device processed independent of system rotary inertia information and disturbance torque, improves the robustness of UAV system.
4. finite time Attitude tracking control scheme proposed by the present invention, can be realized in finite time quadrotor nobody
The Attitude tracking control of machine improves the transient performance and steady-state performance of UAV system.
Detailed description of the invention
Fig. 1 is quadrotor drone Attitude tracking control analysis flow chart diagram.
Fig. 2 is quadrotor drone attitude dynamics modeling analysis schematic diagram.
Fig. 3 is Attitude Tracking error convergence curve graph.
Fig. 4 is angular speed error convergence curve graph.
Fig. 5 is the change curve of estimates of parameters.
Fig. 6 is the change curve of control moment.
Specific embodiment
Specific embodiment 1: a kind of design of quadrotor drone finite time Attitude tracking control method of the present invention
It is:
First, kinematics model is established according to the relative motion of quadrotor drone Attitude Tracking；It analyzes and is modeled in reality
The disturbance torque that quadrotor faces in the engineering of border, unknown rotary inertia, control output saturation and Actuators Failures failure etc. are each
Kind influences the factor of stability, establishes the kinetic model of quadrotor drone Attitude Tracking；
Second, it is calmed the principle of attitude error based on finite time, defines posture filtering error；Based on to Parameters variation and
Insensitive sliding-mode control is disturbed, designs finite time Integral Sliding Mode face, and inhibit constant value interference by introducing integral term,
Reduce steady-state error；
Third, be based on the simple design principle of structure, design passive fault tolerant control device, do not need fault message detection,
Separation even Controller Reconfiguration process；And based on the design principle for improving UAV system robustness, utilize parameter adaptive
Method makes designed controller independent of the boundary of system rotary inertia information and disturbance torque.
According to the above design, as shown in Figure 1, being illustrated in conjunction with the embodiment of quadrotor drone Attitude tracking control
A kind of quadrotor drone finite time Attitude tracking control method the following steps are included:
Step 1: the kinematics model of quadrotor drone Attitude Tracking is established；
Detailed process are as follows:
Consider the posture by quaternion representation quadrotor drone, then the relative motion of quadrotor drone Attitude Tracking can
It indicates are as follows:
Wherein,Drone body coordinate system is respectively indicated relative to desired coordinate
The Attitude Tracking error and angular speed error of system, and haveIt respectively indicates
The ontology posture and angular speed of unmanned plane；Respectively indicate the expectation posture of unmanned plane
With desired angular speed, and ωd,Known and bounded；Indicate drone body coordinate
It is the posture spin matrix relative to desired coordinate system, and hasWith | | C | |=1；Indicate quaternary number multiplication；·TTable
Show the transposition of vector or matrix；Indicate real number field；I indicates three rank unit matrixs；| | | | 2 models of representative vector or matrix
Number；Multiplication cross matrix
The relative motion of UAV Attitude tracking based on the description of (1) formula, establishes the fortune of quadrotor drone Attitude Tracking
It is dynamic to learn model are as follows:
Wherein, E (ev)=(e0I+e×), and have | | E (ev) | |=1；e×Indicate the multiplication cross matrix of e；A circle at the top of character
Point indicates the first derivative to the time；
Step 2: the kinetic model of quadrotor drone Attitude Tracking is established；
Detailed process are as follows:
The executing agency of quadrotor drone is brshless DC motor, has the maximum instantaneous electric current allowed, in order to keep away
Exempt from motor to burn, it is necessary to consider the constraint of control output saturation in control design case；And executing agency in the progress of work by
In manufacturing process and high-intensitive task influence it is possible that partial failure failure；In addition, quadrotor drone always by
The influence of the disturbance torques such as the interference of external wind square and gyroscopic couple.Above-mentioned factor is modeled in quadrotor drone attitude dynamics
It is required to consider in analysis, specific modeling analysis is as shown in Figure 2；
In conclusion consider the disturbance torque that faces of quadrotor drone, unknown rotary inertia, control output saturation and
Actuators Failures failure establishes the kinetic model of quadrotor drone Attitude Tracking are as follows:
Wherein, symmetric positive definite matrixIndicate the unknown rotary inertia of unmanned plane；δ=diag (δ1,δ2,δ3) indicate to execute
The failure matrix of device, 0 < δi≤ 1, i=1,2,3；Indicate control instruction produed by the controller；Sat (u)=
[sat(u1),sat(u2),sat(u3)]TIndicate that controller exports saturated characteristic, sat (ui)=sgn (ui)·min{|ui|,uimax,
uimaxIndicate the output maximum value of i-th of control component, sgn () indicates sign function；Defining θ is controller output beyond saturation
The part of amplitude, then sat (u)=θ+u, then have θ=[θ1,θ2,θ3]T, whereinI=
1,2,3；(ωe+Cωd)×=ω×Indicate the multiplication cross matrix of ω；Indicate ωeMultiplication cross matrix；diag(δ1,δ2,δ3) indicate
The elements in a main diagonal is respectively δ1,δ2,δ3Diagonal matrix；
Expression disturbance torque, including external wind square and the gyroscopic couple as caused by rotor, disturbance torque are unknown
But bounded, i.e., | | Γ | |≤dΓ(1+ | | ω | |), dΓ> 0 is constant；
The purpose of quadrotor drone gesture stability be by design finite time Attitude tracking control device so that nobody
Machine can realize Attitude Tracking in finite time, that is, attitude error e and angular speed that UAV Attitude is tracked are missed
Poor ωeLevel off to origin in finite time；
Step 3: the posture filtering error of quadrotor drone is defined according to the kinematics model that step 1 is established；
Detailed process are as follows:
Define the posture filtering error of quadrotor drone are as follows:
Wherein,For Virtual Controller,-1Representing matrix it is inverse；0 < r1< 1；K1=
diag(k11,k12,k13) it is diagonal matrix, k1i> 0, i=1,2,3；Power function
Wherein
It can be proved that the attitude error e that can calm is in finite time T by the posture filtering error z that calmseInside converge to
Origin.From z=0According to step 1 establish quadrotor drone Attitude Tracking kinematics model (2), in
It is to haveIt is V to this error dynamics system design liapunov functione=eTE, derivation can obtain
According to the theory of finite-time control it is found that attitude error e will be in finite timeInterior receipts
Origin is held back, wherein e (0) indicates the initial value of attitude error；According to (4) formula ωeIt also will be in finite time TeInterior receipts
It holds back.
Therefore, following step need to only consider to design the calm posture filtering error z of finite time Attitude tracking control device
Attitude error e and angular speed error ω are realized simultaneouslyeFinite time it is calm；
Step 4: finite time Integral Sliding Mode face is designed according to the posture filtering error that step 3 defines；
Detailed process are as follows:
It is missed according to Parameters variation and the insensitive sliding-mode control of disturbance, and based on the calm posture filtering of finite time
The thought of difference considers design finite time Integral Sliding Mode face, and inhibits constant value interference by introducing integral term, reduces stable state and misses
Difference.Therefore the posture filtering error design finite time Integral Sliding Mode face defined according to (4) formula is as described below:
Wherein, power function sigp(z)=[sigp(z1),sigp(z2),sigp(z3)]T, wherein sigp(zi)=| zi|psgn(zi), i=1,2,3；τ indicates integration variable；C=diag (c1,c2,c3), c1> 0, c2> 0, c3> 0；0 < p < 1.
For (5) formula design sliding-mode surface it can be proved that system the sliding mode stage have finite time convergence control characteristic,
That is: when S=0, posture filtering error z will be in Finite-time convergence to origin；
It proves: can be obtained by S=0Designing liapunov function isDerivation can obtain
Wherein
According to the theory of finite-time control it is found that posture filtering error z will be in finite timeIt is interior
Origin is converged to, wherein z (0) indicates the initial value of posture filtering error.Result further combined with step 3 is it is found that quadrotor
The attitude error e and angular speed error ω of UAV Attitude trackingeIn finite time Tz+TeInside converge to origin；
Step 5: the finite time Integral Sliding Mode face for kinetic model and the step 4 design established according to step 2, if
Count the finite time Attitude tracking control device of quadrotor drone；
Detailed process are as follows:
The finite time Integral Sliding Mode face (5) for considering the kinetic model (2) established in step 2 and being designed in step 4,
System sliding formwork dynamic can be obtained:
Wherein,Due to unmanned plane rotary inertia and
The boundary of disturbance torque is unknown, and relevant parameter is required to parameter adaptive estimation, accordingly, it is considered to which form every in Θ, can do
Reasonable assumption is as follows out: | | Θ | |≤b Φ, Φ=(1+ | | ω | |+| | ω | |2), parameter b > 0 is unknown, needs adaptively to estimate
Meter；
In order to improve the transient performance and steady-state performance of system, the kinetic model (3) and step established according to step 2
The finite time Integral Sliding Mode face (5) of four designs, designs the Attitude tracking control device of quadrotor drone are as follows:
Wherein, gain matrix K is controlled2=diag (k21,k22,k23), K3=diag (k31,k32,k33), and k2i> 0, k3i> 0, i
=1,2,3；0 < r2< 1；Power functionWherein
I=1,2,3；For the estimated value of parameter b, provided by parameters described below adaptive updates rule (8)；
Design parameter adaptive updates rule are as follows:
Wherein, λ > 0, η > 0 is constant, and meets λ η > 1.
Think highly of as can be seen that the design of the fault-tolerant controller does not need the detection of any fault message, separation even control
Structure process, and design process considers the saturation amplitude requirement of actuator；And made using parameter adaptive method designed
Finite time Attitude tracking control device (7) be not rely on the boundary of system rotary inertia information and disturbance torque, can guarantee
Designed controller has certain robustness for interference and systematic uncertainty.
It can be proved that formula (7) design finite time Attitude tracking control device and formula (8) design parameter adaptive more
Under the action of new law, quadrotor drone can realize Attitude Tracking in finite time.
It proves: for the kinetic model (3) of quadrotor drone, considering finite time Integral Sliding Mode face (5) and system
Sliding formwork dynamic (6) designs liapunov function are as follows:
Wherein, δminFor the minimal eigenvalue for the matrix delta that fails.
V derivation can be obtained along system path:
Wherein, | | | |1Indicate 1 norm of vector.For any vector, set up | | | |1>=| | | |, therefore have
In view of for any φ > 0, total establishmentWherein 0 < ζ < 1, therefore scaleIt can obtain
Substitute the above to (9) Shi Ke get
Wherein,JmaxIndicate the maximum of rotary inertia J
Characteristic value；
According to the theory of finite-time control it is found that quadrotor drone Attitude tracking control system can be in finite timeInterior completion sliding formwork approaches dynamic, wherein V0For the initial value of liapunov function V, 0 < θ < 1.Further
In conjunction with the result of step 3 and step 4 it is found that quadrotor drone can be in finite time Tf+Tz+TeInterior realization attitude error e and
Angular speed error ωeWhile it is calm, realize finite time Attitude tracking control.
A kind of quadrotor drone finite time Attitude tracking control method of the invention gives numerical simulation verifying, says
The bright control method when quadrotor drone faces various factors affecting stabilities, proposed can be realized finite time posture
Tracking, and there is preferable control performance, it is specific as follows:
The model parameter of quadrotor drone is chosen are as follows:
Disturbance torque
Rotary inertia is uncertain
Angular speed initial value ω (0)=[0.10-0.1]Trad/s；Initial attitude qv(0)=[0.3-0.2 0.3 0.8832]T；
Control output saturation amplitude uimax=0.001Nm；；
It is expected that the track of tracking are as follows:
It is expected that posture initial value qdv(0)=[0.7 0.5 0.4123 0.3]T,
It is expected that angular velocity omegad=0.05 × [sin (0.1t) 2sin (0.2t) 3sin (0.3t)]Trad/s；
Actuators Failures failure are as follows:
The estimation initial value of parameter adaptive more new law is all 0；
Controller design and parameter adaptive more new law are wanted in formula (4), (5), (7), (8) in conjunction with the present invention
It asks, takes parameter as follows respectively: ci=0.15, p=0.7；k1i=0.2, r1=0.6；k2i=0.4, k3i=0.1, r2=0.75；λ
=5, η=1；In order to avoid the buffeting of sign function, taken in simulating, verifyingInstead of sign function, wherein ρ is taken as
0.01。
Attitude error convergence curve figure and angular speed when Fig. 3, Fig. 4 are respectively quadrotor drone progress Attitude Tracking miss
Poor convergence curve figure, can therefrom find out, unmanned plane completed Attitude Tracking within 20 seconds time, and steady-state error is controllable
10-6With 10-5Magnitude, therefore tracking accuracy with higher；Fig. 5 is the change curve of estimates of parameters, shows parameter
Estimated value finally converges to 0；Fig. 6 is the change curve of control moment, can therefrom be found out, since control exports saturation amplitude
Limitation, control moment is constrained in the range of 0.001Nm, and at 10 seconds, the curve bur phenomenon that 15 seconds and 20 seconds whens occur
The generation of failure of removal is corresponded to, but designed controller can overcome, illustrates that there is good failure tolerant ability.
Other steps and parameter are same as the specific embodiment one.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications all should belong to
The protection scope of the appended claims of the present invention.
Claims (1)
1. a kind of quadrotor drone finite time Attitude tracking control method, it is characterised in that: the quadrotor drone has
Attitude tracking control method between in limited time the following steps are included:
Step 1: the kinematics model of quadrotor drone Attitude Tracking is established；
Detailed process are as follows:
By the posture of quaternion representation quadrotor drone, the relative motion of quadrotor drone Attitude Tracking is indicated are as follows:
Wherein, ev, ωeRespectively indicate Attitude Tracking error and angular speed of the drone body coordinate system relative to desired coordinate system
Error, e0, attitude error e be e respectivelyvScalar sum vector；qv, ω respectively indicates the ontology posture and angular speed of unmanned plane,
q0, q be q respectivelyvScalar sum vector；qdv, ωdRespectively indicate unmanned plane expectation posture and desired angular speed, qd0、qdRespectively
It is qdvScalar sum vector；C indicates posture spin matrix of the drone body coordinate system relative to desired coordinate system,It indicates
Quaternary number multiplication；q×For the multiplication cross matrix of q；
The relative motion of UAV Attitude tracking based on the description of (1) formula, establishes the kinematics of quadrotor drone Attitude Tracking
Model are as follows:
Wherein, E (ev)=(e0I+e×), and | | E (ev) | |=1, e×Indicate the multiplication cross matrix of e；I indicates three rank unit matrixs；
Step 2: the kinetic model of quadrotor drone Attitude Tracking is established；
Detailed process are as follows:
Establish the kinetic model of quadrotor drone Attitude Tracking are as follows:
Wherein, J indicates the unknown rotary inertia of unmanned plane；δ=diag (δ1,δ2,δ3) indicate actuator failure matrix, 0 < δi
≤ 1, i=1,2,3；U=[u1,u2,u3]TIndicate control instruction produed by the controller；Sat (u)=[sat (u1),sat(u2),
sat(u3)]TIndicate that controller exports saturated characteristic, sat (ui)=sgn (ui)·min{|ui|,uimax, uimaxIt indicates i-th
The output maximum value of component is controlled, sgn () indicates sign function；Defining θ is part of the controller output beyond saturation amplitude,
Then sat (u)=θ+u, then have θ=[θ1,θ2,θ3]T, wherein(ωe+C
ωd)×=ω×Indicate the multiplication cross matrix of ω；For ωeMultiplication cross matrix；
Γ indicates disturbance torque, including external wind square and the gyroscopic couple as caused by rotor, | | Γ | |≤dΓ(1+||ω|
|), dΓ> 0 is constant；
Step 3: the posture filtering error of quadrotor drone is defined according to the kinematics model that step 1 is established；
Detailed process are as follows:
Define the posture filtering error of quadrotor drone are as follows:
Wherein,For Virtual Controller；·-1Representing matrix it is inverse；0 < r1< 1；K1=diag
(k11,k12,k13) it is diagonal matrix, k1i> 0, i=1,2,3；Power functionWherein
By the posture filtering error z that calms, the attitude error e that calms is in finite time TeInside converge to origin；It is obtained by z=0According to the kinematics model (2) for the quadrotor drone Attitude Tracking that step 1 is established, then
It is V to this error dynamics system design liapunov functione=eTE, derivation can obtain:
Attitude error e will be in finite timeOrigin is inside converged to, wherein e (0) indicates the first of attitude error
Initial value；According to (4) formula ωeIt will be in finite time TeInterior convergence；
Step 4: finite time Integral Sliding Mode face is designed according to the posture filtering error that step 3 defines；
Detailed process are as follows:
The posture filtering error design finite time Integral Sliding Mode face defined according to (4) formula is as described below:
Wherein, power function sigp(z)=[sigp(z1),sigp(z2),sigp(z3)]T, wherein sigp(zi)=| zi|p sgn
(zi), i=1,2,3；τ indicates integration variable；C=diag (c1,c2,c3), c1> 0, c2> 0, c3> 0；0 < p < 1；
System has finite time convergence control characteristic in the sliding mode stage, it may be assumed that when S=0, posture filtering error z is in finite time Tz
Inside converge to origin；
It can be obtained by S=0Designing liapunov function isDerivation can obtain:
Wherein
Posture filtering error z is in finite timeOrigin is inside converged to, wherein z (0) indicates that posture filtering misses
The initial value of difference；In conjunction with step 3 result it is found that quadrotor drone Attitude Tracking attitude error e and angular speed error
ωeIn Tz+TeOrigin is converged in time；
Step 5: the finite time Integral Sliding Mode face for kinetic model and the step 4 design established according to step 2, design four
The finite time Attitude tracking control device of rotor wing unmanned aerial vehicle；
Detailed process are as follows:
System sliding formwork dynamic:
Wherein,Assuming that as follows:
| | Θ | |≤b Φ, Φ=(1+ | | ω | |+| | ω | |2), b > 0；
The finite time Integral Sliding Mode face (5) for kinetic model (3) and the step 4 design established according to step 2, four rotation of design
The Attitude tracking control device of wing unmanned plane are as follows:
Wherein, gain matrix K is controlled2=diag (k21,k22,k23), K3=diag (k31,k32,k33), and k2i> 0, k3i> 0, i=
1,2,3；0 < r2< 1；Power functionWherein For the estimated value of b, provided by formula (8)；
Design parameter adaptive updates rule are as follows:
Wherein, λ > 0, η > 0 is constant, and meets λ η > 1；
Under the action of the finite time Attitude tracking control device of formula (7) design and the parameter adaptive more new law of formula (8) design,
Quadrotor drone realizes Attitude Tracking in finite time；
For the kinetic model (3) of quadrotor drone, finite time Integral Sliding Mode face (5) and system sliding formwork dynamic are considered
(6), liapunov function is designed are as follows:
Wherein, δminFor the minimal eigenvalue for the matrix delta that fails；
V derivation can be obtained along system path:
Wherein, | | | |1Indicate 1 norm of vector；For any vector, | | | |1>=| | | | it sets up, then has:
For any φ > 0,It sets up, wherein 0 < ζ < 1, therefore scaleIt can obtain:
Substitute the above to (9) Shi Ke get:
Wherein,JmaxIndicate the maximum feature of rotary inertia J
Value；
Quadrotor drone Attitude tracking control system is in finite timeInterior completion sliding formwork approach dynamic, wherein
V0For the initial value of liapunov function V, 0 < θ < 1；In conjunction with step 3 and step 4 as a result, quadrotor drone in Tf+
Tz+TeAttitude error e and angular speed error ω is realized in timeeWhile it is calm, realize Attitude tracking control.
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| CN103365296B (en) * | 2013-06-29 | 2015-12-09 | 天津大学 | A kind of four rotor unmanned aircraft nonlinear object feedback flight control methods |
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