CN110377044A - A kind of the finite time height and Attitude tracking control method of unmanned helicopter - Google Patents
A kind of the finite time height and Attitude tracking control method of unmanned helicopter Download PDFInfo
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Abstract
The invention discloses a kind of finite time height of unmanned helicopter and Attitude tracking control methods: firstly, considering the model of waving of main rotor and aileron, establishing height and posture collective model；Then, building finite time interference observer estimates unknown time-varying interference, obtains interference estimate；Then, based on the interference estimate observed, in conjunction with adding exponential integral method, design height and the compound anti-interference tracking control unit of posture；Finally, choosing controller gain and observer gain appropriate by design rule, the finite time tracking of height, posture is realized.The present invention improves the accuracy, rapidity, anti-interference of unmanned helicopter height and posture closed loop tracking system.
Description
Technical field
The present invention relates to a kind of finite time height of unmanned helicopter and Attitude tracking control methods, belong to nobody and go straight up to
The technical field of flight control of machine.
Background technique
In recent years, unmanned helicopter causes the extensive concern of people with its unique advantage, as VTOL, low latitude fly
Row, flight etc. in the narrow complex environment such as mountain area, building.Based on these advantages, unmanned helicopter is widely used in navigating
Bat, rescue, detection and other tasks.However, unmanned helicopter be a nonlinearity, drive lacking, close coupling system.This
Outside, its flying quality is highly susceptible to the influence of interference, such as fitful wind.Therefore, design a kind of high performance flight controller at
For a challenging research topic.
Currently, the main linear control of the control method of unmanned helicopter system and two kinds of nonlinear Control.Traditional control
Method processed is based primarily upon linear numerical modei.But the linearisation of model occurs at equalization point, when system state departure balances
When point, controller performance will be greatly reduced.In order to overcome the shortcomings of linear control method, more and more nonlinear control methods
It is used for unmanned helicopter control, such as sliding formwork control, Reverse Step Control, Model Predictive Control.However these methods can only guarantee
The Asymptotic Stability of closed-loop system.
Document (I.A.Raptis, K.P.Valavanis, W.A.Moreno, A novel nonlinear
backstepping controller design for helicopters using the rotation matrix,IEEE
Transactions on Control Systems Technology, vol.19, no.2,2011,465-473.) it proposes anti-
Introduce nested saturation feedback function in step design, posture controlled using the architectural characteristic of spin matrix, make helicopter with
The scheduled position of track and reference yaw track.Document (K.Yan, Q.Wu, M.Chen, Robust adaptive
backstepping control for unmanned autonomous helicopter with flapping
dynamics,2017 13th IEEE International Conference on Control&Automation(ICCA),
2017, pp.1027-1032.) propose it is a kind of anti-with the robust adaptive for waving dynamic (dynamical) unmanned autonomous helicopter
Controller is walked, Nonlinear Disturbance Observer is devised and estimates extraneous unknown disturbances.The controller of this article design has handled the external world not
Know the influence of interference.But all signals for only demonstrating closed-loop system are that uniform bound is stable.
Summary of the invention
In view of the nonlinearity, drive lacking, strong coupling feature of unmanned helicopter system, the present invention provide it is a kind of nobody
The finite time height and Attitude tracking control method of helicopter are a kind of by finite time interference observer technology and plus power product
The compound anti-interference height and posture finite time tracking controller design method that point method combines, have unmanned helicopter system
The tracking performance and strong anti-interference performance of finite time.
The present invention uses following technical scheme to solve above-mentioned technical problem:
The present invention provides the finite time height and Attitude tracking control method of a kind of unmanned helicopter, including following step
It is rapid:
Step 1: model and time-varying interference are waved in consideration, establish height and posture collective model；
The height and posture collective model are as follows:
Wherein: Θ=[ηT z]T, Uz=-CθCφTm, m is the quality of unmanned helicopter, g, η=[φ θ ψ]T∈R3, z and VzIt respectively indicates
Acceleration of gravity, posture, height and height corresponding linear velocity of the unmanned helicopter under inertial coodinate system, ωb=[p q r]T
∈R3Indicate that attitude angular velocity of the unmanned helicopter under body coordinate system, p, q, r are respectively angular velocity in roll, pitch angle speed
Degree, yaw rate；For attitude vectors transformation matrix, φ, θ and ψ distinguish unmanned helicopter
Roll angle, pitch angle and yaw angle, Sφ、Cφ、Cθ、SθAnd TθRespectively indicate sin φ, cos φ, cos θ, sin θ and tan θ, J=
diag{Ixx Iyy IzzIt is inertial matrix, Ixx,Iyy,IzzRespectively unmanned helicopter is around x, y, the rotary inertia of z-axis；A and b points
Not Wei main rotor vertical and horizontal angle of flap, respectively by longitudinal input signal δlonWith lateral input signal δlatControl；AlonWith
BlatRespectively actual gain of the control input signal to main rotor longitudinal direction angle of flap and lateral angle of flap, AcAnd BdIt is revolved based on respectively
The coefficient of coup of the wing and aileron, c and d are respectively the vertical and horizontal angle of flap of aileron, ClonAnd DlatRespectively control input letter
Number arrive aileron vertical and horizontal angle of flap actual gain；τfAnd τsIt is time constant；τbThe power generated for main rotor and empennage
Square,TmAnd TtThe respectively resultant force of the resultant force of main rotor generation and empennage generation；Cma,Cmb?
For physical parameter related with main rotor rigidity；zmAnd ztThe respectively z-axis axis of main rotor and tail rotor shaft to helicopter center of gravity
To distance, xtFor the x-axis axial distance of tail rotor shaft to helicopter center of gravity；For main rotor wing rotation
The resultant couple of generation,WithIt is normal number relevant to the generation of the reaction torque of main rotor；D=[(Jdω)T mdvz]T,
dω=[dp dq dr]TTime-varying of the role of delegate in unmanned helicopter system posture channel is interfered, dvzRole of delegate is gone straight up in nobody
The time-varying of machine system vertical direction speed channels is interfered, dp、dq、drRespectively act on roll angle, pitch angle, yaw rate
The interference in channel；
Step 2: building finite time interference observer estimates unknown time-varying interference, obtains interference estimate；
Enable p=χ1, q=χ2, r=χ3,Vz=χ4,dp=d1,dq=d2,dr=d3,dvz=d4, interference d that can be micro- to n ranki
There is a known Lipschitz constant Li> 0, the finite time interference observer are as follows:
Wherein, work as i=1, when 2,3,4, λi,jThe observer gain being positive, j=0,1,2,
It is χ respectivelyi、di、Estimated value,Sgn () is sign function, y1=[Tmbzm-Ttzt+Cmbb-
qr(Izz-Iyy)]/Ixx+d1, y2=[Tmazm+Cmaa-pr(Ixx-Izz)]/Iyy+d2, y3=[Ttxt-Qm-pq(Iyy-Ixx)]/Izz+
d3,y4=(mg-CθCφTm)/m+d4；
Step 3: based on the resulting interference estimate of step 2, design height and the compound anti-interference finite time of posture with
Track controller carries out the tracking of interference compensation and height, posture；
The height and the compound anti-interference finite time tracking controller design device of posture are as follows:
Wherein, α=α1/α2∈ (1,2), α1、α2It is positive odd number, Θref=[φref θref ψref zref]T, φref、θref
And ψrefRespectively desired roll angle, pitch angle and yaw angle, zrefFor desired height；e1=Θ-Θref=[eφ eθ eψ
ez]T, eφFor rolling angle tracking error, eθFor pitching angle tracking error, eψTo yaw angle tracking error, ezFor height tracing error；
ea=a-arefAnd eb=b-brefRespectively longitudinal angle of flap waves angle error, a with lateralrefAnd brefRespectively desired main rotation
The vertical and horizontal angle of flap of the wing, k1,1,k1,2,k1,3,k1,4,k2,1,k2,2,k2,3,k2,4,k3,k4For controller gain；
Step 4: choosing observer gain and controller gain, by height and the compound anti-interference finite time of posture with
The finite time stability of track controller realization unmanned helicopter height and posture closed loop tracking system.
As further technical solution of the present invention, the observer gain and controller gain chosen in step 4 are as follows:
k1,1> 0, k1,2> 0, k1,3> 0, k1,4> 0；
It enables
h1,3=(2-1/ α) 2(1-1/α)k1,3 1+α, h1,4=(2-1/ α) 2(1-1/α)k1,4 1+α,
Then k2,1, k2,2, k2,3, k2,4Meet k2,1/h1,1-ρ1,1> 0, k2,2/h1,2-ρ1,2> 0, k2,3/h1,3-ρ1,3> 0,
k2,4/h1,4-ρ1,4> 0, k3,k4Meet k3> 0, k4> 0, i=1,2,3,4, j=0,1,2, λi,j> 0.
As further technical solution of the present invention, a in step 3refAnd brefExpression formula be respectively as follows:
As further technical solution of the present invention, the corresponding observation error system of observer in step 2 are as follows:
Wherein,
Technical effect
Technical solution proposed by the present invention generates following technical effects compared to existing technology:
(1) the higher differentiation finite time interference observer designed can be used for observing constant value interference, slope interference, high-order
The interference of the diversified forms such as interference, sinusoidal interference and its all-order derivative, and make observation error in Finite-time convergence to 0, tool
There is versatility.
(2) by finite time observer technology and plus exponential integral method combine, the compound anti-interference finite time control of design
Device processed can effectively deal with interference negative effect caused by system, arrive height and Attitude Tracking error in Finite-time convergence
0。
(3) compound anti-interference finite-time control technical idea proposed by the invention is suitable for other technologies field
Design of system control has a extensive future.
Detailed description of the invention
Fig. 1 is unmanned helicopter height and posture closed-loop system control block diagram；
Fig. 2 is the step flow chart of technical solution；
Fig. 3 is the coordinate system structure chart of unmanned helicopter；
Fig. 4 is posture and height tracing error responses figure, wherein (a) is roll angle, (b) is pitch angle, is (c) yaw
Angle is (d) height；
Fig. 5 is the correlation curve of posture and height physical location and desired locations, wherein (a) is roll angle, (b) is to bow
The elevation angle (c) is yaw angle, is (d) height；
Fig. 6 is observation error response diagram, wherein (a) is the interference in angular velocity in roll channel, (b) logical for rate of pitch
The interference in road is (c) interference in yaw rate channel, (d) is the interference in height velocity channel；
Fig. 7 is the comparison diagram for interfering actual value and observation, wherein (a) is the interference in angular velocity in roll channel, (b) is
The interference in rate of pitch channel is (c) interference in yaw rate channel, (d) is the interference in height velocity channel；
Fig. 8 is control signal intensity figure, wherein (a) is Tm, (b) it is Tt, (c) it is δlon, (d) it is δlat。
Specific embodiment
Technical solution of the present invention is described in further detail with reference to the accompanying drawing:
Step 1: it successively provides the 6DOF model of unmanned helicopter, wave the calculating of model, power and torque, then integrate
Obtain considering the height and attitude mode of interference.
(a) the unmanned helicopter model of 6DOF are as follows:
Wherein, m indicates the quality of unmanned helicopter, g, P=[x y z]T∈R3, η=[φ θ ψ]T∈R3With V=[Vx
Vy Vz]T∈R3Respectively indicate its acceleration of gravity under inertial coodinate system, position, posture and linear velocity；ωb=[p q r]T
∈R3And fb=[fx fy fz]T∈R3、τb=[τx τy τz]T∈R3Respectively indicate its attitude angular velocity under body coordinate system
With suffered power, torque；P, q, r are respectively angular velocity in roll, rate of pitch, yaw rate.And by body coordinate system to
The transformation matrix of inertial coodinate system is defined asφ, θ and ψ
Roll angle, pitch angle and the yaw angle of unmanned helicopter respectively, Sφ、Cφ、Cθ、SθAnd TθRespectively indicate sin φ, cos φ, cos θ,
Sin θ and tan θ.Attitude vectors transformation matrixPitch angle is maintained at when general flightTherefore H is nonsingular.J=diag { Ix Iy IzIt is inertial matrix, Ixx,Iyy,IzzIt is unmanned helicopter around x, y, z
The rotary inertia of axis.
(b) model is waved
Main rotor waves model are as follows:
Aileron waves model are as follows:
Wherein, τf,τsIt is time constant, a, b are the vertical and horizontal angle of flap of main rotor, respectively by longitudinal input letter
Number δlonWith lateral input signal δlatControl.Alon,BlatTo control input signal having to main rotor vertical and horizontal angle of flap
Imitate gain, Ac,BdFor the coefficient of coup of main rotor and aileron, c, d are the vertical and horizontal angle of flap of aileron, Clon,DlatFor control
Actual gain of the input signal to aileron vertical and horizontal angle of flap.
(c) calculating of power and torque
Because of a, b very little meets sina ≈ a, sinb ≈, cosa ≈ 1, cosb ≈ 1, when height controls unmanned helicopter in x,
Power suffered by the direction y is much smaller than the power in the direction z, therefore fb=[0 0-Tm]T, the torque that main rotor and empennage generate isTm,TtThe respectively resultant force of the resultant force of main rotor generation and empennage generation.Cma,CmbBe with
The related physical parameter of main rotor rigidity.zm,ztThe z-axis of respectively main rotor and tail rotor shaft to helicopter center of gravity it is axial away from
From；xtFor the x-axis axial distance of tail rotor shaft to helicopter center of gravity.Qm=CMQ·Tm 3/2+DMQIt is generated for main rotor wing rotation
Resultant couple, CMQ,DMQIt is normal number relevant to the generation of the reaction torque of main rotor.
(d) highly with posture collective model
Enable Θ=[ηT z]T, Uz=-CθCφTm。
Consider main rotor and aileron waves dynamic characteristic, establishes the height and posture collective model of unmanned helicopter are as follows:
Wherein, D=[(Jdω)T mdvz]T,dω=[dp dq dr]TRole of delegate is in unmanned helicopter system posture channel
Time-varying interference, dvzRole of delegate is interfered in the time-varying of unmanned helicopter system vertical direction speed channels, dp、dq、drRespectively make
Interference for roll angle, pitch angle, yaw rate channel.
Step 2: design finite time interference observer obtains interference estimate and its derivative estimated value.
To enable p=χ convenient for indicating1, q=χ2, r=χ3,Vz=χ4,dp=d1,dq=d2,dr=d3,dvz=d4.It can to n rank
Micro- di(i=1,2,3,4) there is a known Lipschitz constant Li> 0 designs following finite time interference observer:
Illustrate: i=1, when 2,3,4,It is respectivelyEstimated value, functionAnd sgn () is the sign function of standard.y1=[Tmbzm-Ttzt+Cmbb-qr(Izz-Iyy)]/Ixx+
d1, y2=[Tmazm+Cmaa-pr(Ixx-Izz)]/Iyy+d2, y3=[Ttxt-Qm-pq(Iyy-Ixx)]/Izz+d3,y4=(mg-CθCφ
Tm)/m+d4。λi,jIt (j=0,1,2) is positive observer gain to be designed.
Corresponding observation error system are as follows:
Wherein,For observation error, suitable observer gain is chosen
λi,j(j=0,1,2), can make observation error in finite time T1Converge to zero.The finite time observer of formula (5) form is applicable in
In the interference of the forms such as constant value, slope, high-order, sine.
Step 3: interference and its derivative estimated value obtained in step 2 are used for feedforward compensation, seen in conjunction with finite time
It surveys device technology and adds exponential integral method, design compound anti-interference height and posture finite time tracking controller design device, make height and appearance
State tracking error finite time convergence control is to 0.
Control signal Tm,Tt,δlon,δlatConcrete form it is as follows:
Wherein α=α1/α2∈(1,2),α1、α2For positive odd number, Θref=[φref θref ψref zref]TFor expectation posture and
Highly, φref、θrefAnd ψrefRespectively desired roll angle, pitch angle and yaw angle, zrefFor desired height；e1=Θ-
Θref=[eφ eθ eψ ez]TFor tracking error, eφFor rolling angle tracking error, eθFor pitching angle tracking error, eψFor yaw angle
Tracking error, ezFor height tracing error；ea=a-aref,eb=b-brefRespectively longitudinal angle of flap waves angle error with lateral.
aref,brefIt separately designs are as follows:
k1,1,k1,2,k1,3,k1,4,k2,1,k2,2,k2,3,k2,4,k3,k4For gain to be designed.
Step 4: controller gain and observer gain appropriate are chosen by design rule, realizes unmanned helicopter height
With the finite time stability of posture closed loop tracking system.
The observer gain and controller gain chosen in step 4 are as follows:
k1,1> 0, k1,2> 0, k1,3> 0, k1,4> 0；
It enables
h1,3=(2-1/ α) 2(1-1/α)k1,3 1+ α, h1,4=(2-1/ α) 2(1-1/α)k1,4 1+α,
Then k2,1, k2,2, k2,3, k2,4Meet k2,1/h1,1-ρ1,1> 0, k2,2/h1,2-ρ1,2> 0, k2,3/h1,3-ρ1,3> 0,
k2,4/h1,4-ρ1,4> 0, k3,k4Meet k3> 0, k4> 0, i=1,2,3,4, j=0,1,2, λi,j> 0.
For have unknown disturbances height and attitude mode, if design controller such as formula (7) to (10), can
Realize finite time stability, i.e. height tracing error and Attitude Tracking error is in finite time T2Converge to zero.
In order to verify the validity of height and posture finite time tracking controller design method proposed by the invention, MATLAB is used
Numerical simulation is carried out.
The original state of unmanned helicopter is η0=[0.5 0.5 0.5]Trad,z0=2m, desired attitude angle and height
For ηref=[0.5sint 0.5sint 0.5sint]Trad,zref=5m, interference expression formula are set as d1=2.5sin (0.3t+
30),d2=1.2sin (0.5t+15), d3=1.8sin (0.2t+30), d4=1.8sin (0.9t+15).In Fig. 4 (a) to (d)
It shows in the presence of interference, posture and height tracing error can converge in 0, Fig. 5 (a) to (d) quickly and be
The correlation curve of posture and height physical location and desired locations, (a) to (d) shows the tracking of observation error system in Fig. 6
Performance, each disturbance-observer error, which can be converged to quickly and accurately, shows interference actual value and observation in 0, Fig. 7 (a) to (d)
The comparison of value, (a) to (d) shows the change curve of each control input signal in Fig. 8.Simulation result shows that the present invention designs
Height and the compound anti-interference finite time tracking controller design device of posture be effective.
It is above to implement only therefore limit the scope of protection of the present invention to illustrate technical idea of the invention.It is worth note
Meaning, any improvement made in technical idea of the invention to technical solution all belong to the scope of protection of the present invention.
Claims (4)
1. the finite time height and Attitude tracking control method of a kind of unmanned helicopter, which comprises the following steps:
Step 1: model and time-varying interference are waved in consideration, establish height and posture collective model；
The height and posture collective model are as follows:
Wherein: Θ=[ηT z]T, Uz=-CθCφTm, m is the quality of unmanned helicopter, g, η=[φ θ ψ]T∈R3, z and VzIt respectively indicates
Acceleration of gravity, posture, height and height corresponding linear velocity of the unmanned helicopter under inertial coodinate system, ωb=[p q r]T
∈R3Indicate that attitude angular velocity of the unmanned helicopter under body coordinate system, p, q, r are respectively angular velocity in roll, pitch angle speed
Degree, yaw rate；For attitude vectors transformation matrix, φ, θ and ψ distinguish unmanned helicopter
Roll angle, pitch angle and yaw angle, Sφ、Cφ、Cθ、SθAnd TθRespectively indicate sin φ, cos φ, cos θ, sin θ and tan θ, J=
diag{Ixx Iyy IzzIt is inertial matrix, Ixx,Iyy,IzzRespectively unmanned helicopter is around x, y, the rotary inertia of z-axis；A and b points
Not Wei main rotor vertical and horizontal angle of flap, respectively by longitudinal input signal δlonWith lateral input signal δlatControl；AlonWith
BlatRespectively actual gain of the control input signal to main rotor longitudinal direction angle of flap and lateral angle of flap, AcAnd BdIt is revolved based on respectively
The coefficient of coup of the wing and aileron, c and d are respectively the vertical and horizontal angle of flap of aileron, ClonAnd DlatRespectively control input letter
Number arrive aileron vertical and horizontal angle of flap actual gain；τfAnd τsIt is time constant；τbThe power generated for main rotor and empennage
Square,TmAnd TtThe respectively resultant force of the resultant force of main rotor generation and empennage generation；Cma,Cmb?
For physical parameter related with main rotor rigidity；zmAnd ztThe respectively z-axis axis of main rotor and tail rotor shaft to helicopter center of gravity
To distance, xtFor the x-axis axial distance of tail rotor shaft to helicopter center of gravity；Qm=CMQTm 3/2+DMQFor the generation of main rotor wing rotation
Resultant couple, CMQAnd DMQIt is normal number relevant to the generation of the reaction torque of main rotor；D=[(Jdω)T mdvz]T,dω=[dp
dq dr]TTime-varying of the role of delegate in unmanned helicopter system posture channel is interfered, dp、dq、drIt respectively acts on roll angle, bow
The interference at the elevation angle, yaw rate channel, dvzRole of delegate in unmanned helicopter system vertical direction speed channels when dry out
It disturbs；
Step 2: building finite time interference observer estimates unknown time-varying interference, obtains interference estimate；
Enable p=χ1, q=χ2, r=χ3,Vz=χ4,dp=d1,dq=d2,dr=d3,dvz=d4, interference d that can be micro- to n rankiHave one
A known Lipschitz constant Li> 0, the finite time interference observer are as follows:
Wherein, work as i=1, when 2,3,4, λi,jThe observer gain being positive, j=0,1,2,
It is χ respectivelyi、di、Estimated value,Sgn () is sign function, y1=[Tmbzm-Ttzt+Cmbb-
qr(Izz-Iyy)]/Ixx+d1, y2=[Tmazm+Cmaa-pr(Ixx-Izz)]/Iyy+d2, y3=[Ttxt-Qm-pq(Iyy-Ixx)]/Izz+
d3,y4=(mg-CθCφTm)/m+d4；
Step 3: the resulting interference estimate of step 2, design height and the compound anti-interference finite time tracking control of posture are based on
Device processed carries out the tracking of interference compensation and height, posture；
The height and the compound anti-interference finite time tracking controller design device of posture are as follows:
Wherein, α=α1/α2∈ (1,2), α1、α2It is positive odd number, Θref=[φref θref ψref zref]T, φref、θrefWith
ψrefRespectively desired roll angle, pitch angle and yaw angle, zrefFor desired height；e1=Θ-Θref=[eφ eθ eψ
ez]T, eφFor rolling angle tracking error, eθFor pitching angle tracking error, eψTo yaw angle tracking error, ezFor height tracing error；
ea=a-arefAnd eb=b-brefRespectively longitudinal angle of flap waves angle error, a with lateralrefAnd brefRespectively desired main rotation
The vertical and horizontal angle of flap of the wing, k1,1,k1,2,k1,3,k1,4,k2,1,k2,2,k2,3,k2,4,k3,k4For controller gain；
Step 4: choosing observer gain and controller gain, passes through the compound anti-interference finite time tracking control of height and posture
Device processed realizes the finite time stability of unmanned helicopter height and posture closed loop tracking system.
2. a kind of the finite time height and Attitude tracking control method of unmanned helicopter as described in claim 1, feature
It is, the observer gain and controller gain chosen in step 4 are as follows:
k1,1> 0, k1,2> 0, k1,3> 0, k1,4> 0；
It enables
h1,3=(2-1/ α) 2(1-1/α)k1,3 1+α, h1,4=(2-1/ α) 2(1-1/α)k1,4 1+α,
Then k2,1, k2,2, k2,3, k2,4Meet k2,1/h1,1-ρ1,1> 0, k2,2/h1,2-ρ1,2> 0, k2,3/h1,3-ρ1,3> 0, k2,4/
h1,4-ρ1,4> 0, k3,k4Meet k3> 0, k4> 0, i=1,2,3,4, j=0,1,2, λi,j> 0.
3. a kind of the finite time height and Attitude tracking control method of unmanned helicopter as described in claim 1, feature
It is, a in step 3refAnd brefExpression formula be respectively as follows:
4. a kind of the finite time height and Attitude tracking control method of unmanned helicopter as described in claim 1, feature
It is, the corresponding observation error system of observer in step 2 are as follows:
Wherein, ei,0=χ1-ξi,0,ei,1=di-ξi,1,
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