CN108594837A - Model-free quadrotor drone contrail tracker and method based on PD-SMC and RISE - Google Patents
Model-free quadrotor drone contrail tracker and method based on PD-SMC and RISE Download PDFInfo
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- 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
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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Abstract
The invention discloses model-free quadrotor drone contrail trackers and method based on PD SMC and RISE, devise the positioner based on PD SMC algorithms, the controller combines the characteristics of easily designed PD control device and SMC controller strong robustness, and without accurate outer ring model.Second, the attitude controller based on RISE algorithms is devised, the buffeting of system is substantially reduced using the continuous control signal of RISE algorithms.Advantageous effect of the present invention：Lyapunov theorem of stability demonstrates the stability of inner ring and outer rings subsystem respectively.The simulation experiment result demonstrates the validity of put forward controller herein.
Description
Technical field
The present invention relates to quadrotor drone Trajectory Tracking Control technical field, more particularly to it is a kind of based on PD-SMC and
The model-free quadrotor drone contrail tracker and method of RISE.
Background technology
Quadrotor drone is one kind of rotor wing unmanned aerial vehicle, interior in a limited space can realize VTOL, hovering etc..
Compared with traditional heligyro, quadrotor drone is with the advantages that low cost, mechanical mechanism is simple, mobility strong.Closely
Nian Lai, quadrotor drone have obtained more and more scientific research institutions and enterprise with it in dual-use huge applications potentiality
Concern.
However, the control of quadrotor drone is not a simple job.First, the movement of quadrotor drone is
It is realized by changing the rotating speed of four propellers, therefore it is required that controller has higher response speed.Second, quadrotor nobody
Machine has the characteristics that non-linear, drive lacking, quantity of state are strong coupling.Third carrys out common small-sized quadrotor drone
It says, rotary inertia, aerodynamics parameter etc. can not be measured accurately.Importantly, due to common quadrotor drone matter
Amount and size are all smaller, therefore are easy to by disturbing and model uncertainty is interfered.
In view of the above-mentioned problems, scientific research personnel has been developed that different control methods.Because quadrotor model can be into line
Property, so some linear control methods can be used for controlling quadrotor drone.Wherein, proportion differential (PD) controls
Device is easily designed with its, the advantages that not requiring model information is widely used.
In the prior art, Eduardo adds feedforward control on the basis of tandem PD control device, solves the rail of robot
Mark tracking control problem, and the addition for demonstrating feedforward control can ensure the consistent asymptotically stable in the large of error system.
In the prior art, quadrotor attitude controller is decomposed into non-linear partial and linear segment by He zefang.It is right
Nonlinear system is converted to linear system using feedback linearization, in non-linear partial after then designing PD control device to conversion
System carry out control and PD control device parameter is adjusted by Ziegler-Nichols rules.
In the prior art, it is contemplated that the optimal control problem of PD control device, Bencharef is using bat algorithm to PD control
Device is improved, and solves the stable control of quadrotor drone posture and height.In view of quadrotor drone exists
The uncertain problem of model, Wang use two with the nonlinear feedforward compensation device of PD components to eliminate known portions and obtain
To two Hurwitz linear subsystems.Hereafter L is applied1Adaptive controller comes compensation model uncertainty and disturbance.In addition,
PID controller is also widely used in quadrotor drone control aspect.The prior art has studied under PID controller, wink
When influence of the load variation to unmanned plane.Also, using fuzzy logic to PID controller parameter KP、KIAnd KDCarry out on-line tuning
To improve the robustness of PID controller.
Due to quadrotor drone there are model uncertainty, strong nonlinearity, easily by disturbance the features such as, researcher propose
A series of Nonlinear Robust Controllers.Sliding formwork control (SMC) or variable-structure controller are one kind of Nonlinear Robust Controller,
It is suitable for certain nonlinearuncertain systems.Sliding formwork control has a wide range of applications in terms of quadrotor Trajectory Tracking Control.
But sliding formwork control has two in application aspect, when buffeting problem, second is that when calculating SMC controller equivalent elements
It needs to know accurate model.For first problem, the prior art gives two and reduces the method buffeted：One is will control
It is decomposed into continuous control and switching control, reduces switching part amplitude；Second is to replace sign function with a saturation function
Or it is buffeted using integral sliding mode control device to reduce.For Second Problem, the solution of the prior art is：One is the introduction of
Adaptive control laws to carry out On-line Estimation to unknown model parameter；Second is that quadrotor drone, which is considered as input and state, to be had
Boundary (BIBS), unknown dynamic is estimated by the calculating to system input and output.
It by above-mentioned analysis, can obtain, solve the method for Sliding mode controller equivalent part mainly using different
Method of estimation unknown dynamic is estimated, but controller can be made to become complicated in this way.Therefore, a controller had been designed both
It is the mainspring that the present invention studies that the simple structure as PD control device has the strong robustness of similar SMC controllers again.
In addition, not only needing it is expected attitude angle in most of attitude controller design process, but also need it is expected angle speed
Degree, and it is expected that the calculating of angular speed is complicated, and it is quick-fried if directly carrying out differential to expected angle to may result in differential
Fried problem.Current most of documents do not provide corresponding solution.
Invention content
The purpose of the present invention is exactly to solve the above-mentioned problems, it is proposed that the model-free quadrotor based on PD-SMC and RISE
Unmanned plane contrail tracker and method, the controller and method consider quadrotor drone system easily by non-linear and mould
The influence of type uncertain (including parameter uncertainty, inside and outside interference etc.), it is proposed that outer shroud positioner and interior
Ring attitude controller.
To achieve the goals above, the present invention adopts the following technical scheme that：
The invention discloses a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE, packet
It includes：Outer shroud positioner and inner ring attitude controller；
The outer ring controller is based on PD-SMC algorithms, specially：
Wherein, position tracking error：Kξ=diag (Kx,Ky,Kz)；
Kp,KdIt is PD control device gain matrix, H is SMC controller gains, and μ is sliding-mode surface gradient constant matrix；
M is quadrotor quality, Kx、Ky、KzEqual air damping coefficient, G are gravitational acceleration vector, and d disturbs for outer shroud, and E is
Position tracking error,WithThe respectively single order and second dervative of position tracking error；ξdFor desired locations,Respectively
For desired speed and desired acceleration；ξ、ξ、The respectively position of quadrotor drone, speed and acceleration；
The inner ring attitude controller is based on RISE control methods, specially：
Wherein, Ks, β be positive definite parameter matrix, I3×3For three rank unit matrixs；NdFor auxiliary function；e2, r be filtering miss
Difference function,For the first derivative of filtering error, J is moment of inertia matrix.
Further, the inner ring attitude controller in the design process, expectation angular speed is carried out using differential tracker
Calculating.
The invention discloses a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE
Design method includes the following steps：
(1) dynamic model of quadrotor drone is determined；
(2) assume that the time-varying disturbance acted in quadrotor drone is bounded, provide desired trajectory ξd(t), exist
In the presence of disturbance and model it is uncertain in the case of, be based on PD-SMC control algolithms, design virtual controlling input u, ensure position with
Track error is asymptotically convergent to zero；
(3) u is inputted according to the virtual controlling of design, determines outer ring controller；
(4) RISE algorithms are based on, design continuous control inputs τi(i=1,2,3) so that attitude control system is locally to refer to
Number is stablized；
(5) τ is inputted according to the continuous control of designi(i=1,2,3) determines interior ring controller.
Further, in the step (2), design virtual controlling input u is specially：
Wherein, F=[R1,3u,R2,3u,R3,3u]T；Kp,KdIt is PD control device gain matrix, H is SMC controller gains, μ
For sliding-mode surface gradient constant matrix；E is position tracking error,For the first derivative of position tracking error, R1,3, R2,3, R3,3Point
It is not the third column element of spin matrix R.
Further, in the step (3), outer ring controller is specially：
Wherein, position tracking error：Kξ=diag (Kx,Ky,Kz)；
Kp,KdIt is PD control device gain matrix, H is SMC controller gains, and μ is sliding-mode surface gradient constant matrix；
M is quadrotor quality, Kx、Ky、KzEqual air damping coefficient, G are gravitational acceleration vector, and d disturbs for outer shroud, and E is
Position tracking error,WithThe respectively single order and second dervative of position tracking error；ξdFor desired locations,Respectively
Desired speed and desired acceleration；ξ、The respectively position of quadrotor drone, speed and acceleration.
Further, in the step (4), the first derivative of the continuous control input τ of designSpecially：
Wherein, Ks, β is positive definite parameter matrix, I3×3For three rank unit matrixs, e2, r be filtering error function.
Further, in the step (5), interior ring controller is specially：
Wherein, Ks, β be positive definite parameter matrix, I3×3For three rank unit matrixs；NdFor auxiliary function；e2, r be filtering miss
Difference function,For the first derivative of filtering error, J is moment of inertia matrix.
Further, u is inputted according to virtual controlling, calculates expected angle φd(t), θd(t) as follows：
Wherein, φd、θdRespectively it is expected corner and desired pitch angle, R1,3, R2,3, R3,3It is the third of spin matrix R respectively
Column element.
Further, the inner ring attitude controller in the design process, expectation angular speed is carried out using differential tracker
Calculating.
Further, the differential tracker design is as follows：
Wherein, ω (t) is the signal for needing to carry out differential；x1, x2Tracking ω (t) and its first derivative respectivelyConstant
R determines tracking velocity.
The beneficial effects of the invention are as follows：
The present invention devises the outer shroud positioner based on PD-SMC algorithms, which combines PD control device and be easy to
The characteristics of design and SMC controller strong robustness, and without accurate outer ring model.
The present invention devises the inner ring attitude controller based on RISE algorithms, and the continuous control signal using RISE algorithms is big
The big buffeting for reducing system.
Differential estimator is solved the Solve problems of desired angular speed by the present invention.
Demonstrate the stability of inner ring and outer rings subsystem respectively using Lyapunov theorem of stability.Emulation experiment knot
Fruit proves that the carried controller of the present invention has validity and stability well.
Description of the drawings
Fig. 1 is quadrotor drone structural schematic diagram；
Fig. 2 is controller architecture schematic diagram of the present invention；
Fig. 3 is the track following result of difference controller of the embodiment of the present invention；
Fig. 4 (a)-Fig. 4 (c) is respectively the X-axis of difference controller of the embodiment of the present invention, Y-axis, Z axis tracking error；
Fig. 5 (a)-Fig. 5 (c) is respectively that the roll angle, pitch angle, course angle tracking of difference controller of the embodiment of the present invention miss
Difference；
Fig. 6 is that the outer shroud inner ring of controller of the present invention inputs；
Fig. 7 is that the outer shroud of controller of the present invention disturbs numerical value；
Fig. 8 is the track following result of different controllers of the embodiment of the present invention under gust influence；
Fig. 9 (a)-Fig. 9 (c) is respectively the X-axis of different controllers of the embodiment of the present invention under gust influence, Y-axis, Z axis
Tracking error.
Specific implementation mode：
The present invention will be further described with example below in conjunction with the accompanying drawings：
1, quadrotor drone model
Quadrotor drone is typical Nonlinear Underactuated System.It includes three-dimensional that quadrotor drone, which has 6 degree of freedom,
Position and rotation around three body reference axis, however, quadrotor drone only has 4 independent inputs, i.e. four propellers
Pulling force.Quadrotor drone structural schematic diagram is as shown in Figure 1.Quadrotor drone dynamic model is in terrestrial coordinate system (O-
xeyeze) and body coordinate system (O-xbybzb) under establish.Symbol and symbol definition are as shown in table 1 used in the present invention.
1. quadrotor parameter of table and its definition
The Eulerian angles of position and description UAV Attitude of the quadrotor drone barycenter under terrestrial coordinate system use ξ respectively
=[x y z]TWith η=[φ θ ψ]TTo indicate.The pulling force that four propellers generate is fi, i=1,2,3,4.ωi(i=1,2,3,
4) it is the rotating speed of propeller.The pulling force and its relationship of rotating speed that so propeller generates be：
Wherein, tension coefficient kTCharacteristic depending on propeller blade.
Quadrotor drone is reduced to rigid model by the present invention.Reference newton appraises movement through discussion and Euler's rotary motion is public
Formula, quadrotor drone dynamic model can be described as：
Wherein orthogonal matrix R indicates the spin matrix from body coordinate system to terrestrial coordinate system, is specifically defined such as formula (3).
Control input u, τiWith pulling force fiRelationship be：
Note 1：In order to avoid Euler's angle model singularity problem, the present invention sets roll angle φ and pitching angle theta ranging fromCourse angle ψ ranging from (- π, π).
Note 2：Quadrotor drone parameter such as quality, rotary inertia, air damping coefficient etc. are positive constant.
Assuming that the 1. time-varying disturbances acted in quadrotor drone are bounded.
Quadrotor drone Trajectory Tracking Control can be described as：Provide desired trajectory ξd(t), there is disturbance and model not
In the case of determination, design control input u and τiTo ensure as t → ∞, | | ξd- ξ | | → 0,It needs to refer to
Go out, the characteristics of due to quadrotor drone drive lacking, it is relatively difficult to independently control all outputs, then in the present invention
In, ξd(t) and ψd(t) it is by manually providing, it is expected that corner and desired pitch angle φd(t) and θd(t) it is then by calculating Ri,3u
(i=1,2,3) it obtains.The total pulling force u and expected angle φ that propeller generatesd(t), θd(t) it can be obtained by following formula：
Note 3：In order to avoid state mutation, the present invention designs desired trajectory ξd(t) and desired course angle ψd(t) it is i order derivatives
Continuously (i=1,2,3).
2, controller design
In order to reach in the case that there are the dynamic robust position control targe of Unknown Model, controls and calculate using PD-SMC
Method carries out outer ring controller design.PD control device is used for replacing the equivalent part in SMC controllers, SMC switching parts to provide Shandong
Stick.In order to be compensated to inner ring disturbance and obtain no chatter control effect, RISE control methods are applied to inner ring posture
In controller design.Controller schematic diagram designed by the present invention is as shown in Figure 2.
The 2.1 outer ring controller designs based on PD-SMC
R is inputted by designing virtual controlling appropriatei,3U is to ensure that position tracking error is asymptotically convergent to zero.In addition,
By calculating Ri,3U solves desired roll angle φdWith desired pitching angle thetad.According to formula (2) it will be seen that outer shroud subsystem
System can be described as：
It is defined as follows position tracking error：
Formula (7) is substituted into (6), outer loop subsystems dynamic model can be described as
Wherein, G=[0 0 g]TFor gravitational acceleration vector, d=[dx dy dz]TIt is disturbed for outer shroud, E misses for position tracking
Difference,WithThe respectively single order and second dervative of position tracking error.ξd=[xd yd zd]TFor desired locations, Respectively desired speed and desired acceleration.ξ=[x y z]T,The respectively position of quadrotor drone, speed and acceleration.
According to 1 and note 3 is assumed, can obtain：
Wherein D is disturbance dξThe upper bound.From formula (8) if can be seen that F=P, system (8) is stable, and
Tracking error can also converge on zero.In order to avoid the requirement for accurate system's model during controller design, control input F
It is designed as：
Wherein, Kp=diag (Kpx, Kpy, Kpz), Kd=diag (Kdx, Kdy, Kdz) it is PD control device gain matrix, H=diag
(H1,H2,H3) it is SMC controller gains, μ=diag (μ1,μ2,μ3) it is sliding-mode surface gradient constant matrix.
Formula (10) is substituted into (8), can be obtained：
Theorem 1. considers formula (6) quadrotor drone dynamic model, it is assumed that controller parameter is selected to meet formula (12), in formula
(10) control input can ensure the Asymptotic Stability of error system, and the tracking error that formula (7) defines converges on zero.
Wherein λm() and λM() indicates the minimum and maximum characteristic value of positive definite matrix in bracket respectively.
It proves：Define a positive definite matrix：
Parameter appropriate is chosen to makeFrom formula (12) it is found that
Because of KpIt is positive definite matrix with μ, according to positive definite matrix property in appendix A：
So mended about the Schur of matrix L just like drawing a conclusion：
It can be seen that the Schur of matrix L, which is mended, is more than zero, this shows that matrix L is positive definite.
It is as follows to choose liapunov function：
Due to L, μ, KtAnd KdAll it is positive definite parameter matrix, therefore liapunov functionIt is positive.It goesFirst derivative and by formula (10), (11) substitute into and can obtain：
If can be seen that us marks Selecting All Parameters according to formula (12), first two of formula (18) are negative.For third
, then have：
Then formula (18) is also negative, i.e.,
In conclusion liapunov functionFor just,It is negative, then the PD- designed by the present invention
Under SMC controllers, quadrotor position control subsystem is asymptotically stable and tracking error and its first derivative converge on
Zero.
The 2.2 inner ring controller designs based on RISE
It is aforementioned it is found that sliding formwork control (SMC) is compensating disturbance and unknown dynamic feasible method, the present invention proposes similar
It is used for the gesture stability of quadrotor drone in the RISE continuous controllers of SMC controls.
Design corresponding continuous control input τi(i=1,2,3) so that attitude control system is local exponential stability.Four
Rotor wing unmanned aerial vehicle posture subsystem can be described as：
It is as follows to choose auxiliary error function：
e1=ηd-η (22)
Filtering error function：
Wherein λ=diag (λ1,λ2,λ3), α=diag (α1,α2,α3) it is positive definite parameter matrix, andFormula (22)-(24) are substituted into (21), then quadrotor drone posture subsystem model can
It is expressed as：
For the first derivative of filtering error, J is moment of inertia matrix.
It is as follows to define three auxiliary functions：
It can be obtained according to note 3, N and Nd are continuous, andIt is bounded：
Wherein | | | | indicate euclideam norm.Vectorial Ω is defined as Ω=[e1,e2,r]T, ρ is positive constant.So
Setting control, which inputs, is：
Wherein, Ks=diag (Ks1,Ks2,Ks3), β=diag (β1,β2,β3) it is positive definite parameter matrix, I3×3For three rank units
Matrix.Formula (26)-(28) and formula (30), which are substituted into (25), to be obtained：
1. defined function of lemma is as follows：
L (t)=rT(Nd-βsgn(e2)) (32)
β=diag (β1,β2,β3) parameter matrix and meet following condition in order to control：
Wherein | | | |∞Indicate Infinite Norm, then：
ζ is defined as follows：
Theorem 2. defines shown in attitude error subsystem such as formula (31), as controller parameter βiWhen meeting formula (33) and requiring,
Control output can ensure the local exponential stability of system (as shown in formula (30)).
It proves：It is as follows to choose liapunov function：
Wherein σ is positive function, is defined as
The first derivative of function V (Ω, t) is：
Formula (22)-(24) and (31) are substituted into above formula, can be obtained：
It can be seen that can ensure above formula using formula (32), last is zero.According to inequalityWe can obtain inequality：
Wherein, δ andFor positive constant, it is defined as
This shows for working asWhen
Wherein l is positive constant.By Lyapunov theorem of stability it is found that system is local exponential stability.
It should be pointed out that most of attitude controller design needs to be not only expected angle, and need it is expected angle
Speed.However, it may be desirable to the calculating of angular speed is extremely complex, also, may if directly carrying out differential to expected angle
There is the problems such as " differential explosion ".Rare document proposes the solution for this problem.Present invention application differential tracker is (such as
Shown in formula (40)) solve the computational problem of desired angular speed.
Wherein, ω (t) is the signal for needing to carry out differential.x1, x2Tracking ω (t) respectively,Constant r determines tracking
Speed.
ω (t) is enabled to be respectively equal to φd, θd, then x2It is just correspondingly equal to it is expected angular speedI.e.：
3, simulation result
In order to verify the validity of the put forward controller of the present invention, the present invention exists using 8-shaped track as desired trajectory
It is unknown it is dynamic in the case of carried out emulation experiment.
Note 4. is pointed out that in common SMC controllers that there are switching function sign (), the switching function to cause
Buffeting problem.It is buffeted to weaken, sign () is replaced with tanh () function, then the control input of formula (9) just becomes：
It is carried out on the tangible MatlabR2016a of emulation experiment (9.0.0.341360) 64-bit version platforms of the present invention.Installation
The computer of Matlab softwares is equipped with Intel (R) Core I7-4790CPU, 8G memories and 1000G hard disks.
Quadrotor drone model parameter is as shown in table 2.Initial position and initial attitude angle are respectively [x0 y0 z0]
=[0 0 0], [φ0 θ0 ψ0]=[0 0 0].
2. quadrotor model parameters of Table
(1) quadrotor track following under Gauss disturbance
In this Seam-Tracking Simulation, 8-shaped track is as target trajectory：
(including inside and outside disturbance, model is not true as collection overall error for the white Gaussian noise for being 0.01 using variance
It is qualitative etc.).Controller gain is respectively：Kp=diag (50,50,50), Kd=(10,10,50), H=diag (10,20,40),
μ=diag (10,10,50), α=diag (50,50,10), λ=diag (50,50,10), Ks=(10,5,5), β
=(1,5,5).
In addition, in order to preferably verify the validity of the put forward algorithm of the present invention, by the carried controller (PD-SMC+ of the present invention
RISE) control effect and PD, PID and model-free TSM control device (MFTSMC) compare.
Fig. 3 and Fig. 4 is respectively the position tracking result and tracking error of four kinds of controllers.Fig. 5 is Attitude Tracking error.
Fig. 6 is the control input of present invention design controller.From Fig. 3 and Fig. 4 as it can be seen that the controller designed by the present invention has fabulous rail
Mark tracking effect, tracking accuracy original are higher than other three controllers.Specifically, controller proposed by the invention can be by position
Control errors are set in the range of much smaller than 1%, while attitude error control is within the scope of ± 0.01rad.It is worth noting that,
In t=15s, there is larger error in four kinds of controllers, this is because in t=15s, while it is desirable to positions not
Acute variation occurs, but it is desirable to speed is mutated.Although there are larger error, the controller of the present invention can
It is rapidly corresponding to error, and quadrotor drone is controlled to target location.
(2) Trajectory Tracking Control under fitful wind
Quadrotor drone is easy to be influenced by disturbing and may be influenced by fitful wind in flight course.At this
In l-G simulation test, fitful wind is simulated with square-wave signal.It is as shown in Figure 7 that outer shroud disturbs numerical value.In the control gain of controller and (1)
It is consistent.
Fig. 8 and Fig. 9 (a)-Fig. 9 (c) is track tracking result and error under gust influence respectively.As can be seen that
Under the influence of fitful wind, controller proposed by the invention still has satisfactory tracking effect.In addition, from Fig. 9 (a)-Fig. 9
(c) it can also be seen that when desired trajectory is time-varying, Shandong of the model-free TSM control device (MFTSMC) for gust disturbances
There is no other controllers are strong for stick.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention
The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not
Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.
Claims (10)
1. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE, which is characterized in that including：
Outer shroud positioner and inner ring attitude controller；
The outer ring controller is based on PD-SMC algorithms, specially：
Wherein, position tracking error：Kξ=diag (Kx,Ky,Kz)；Kp,Kd
It is PD control device gain matrix, H is SMC controller gains, and μ is sliding-mode surface gradient constant matrix；
M is quadrotor quality, Kx、Ky、KzEqual air damping coefficient, G are gravitational acceleration vector, and d disturbs for outer shroud, and E is position
Tracking error,WithThe respectively single order and second dervative of position tracking error；ξdFor desired locations,It schedules to last respectively
Hope speed and desired acceleration；ξ、The respectively position of quadrotor drone, speed and acceleration；
The inner ring attitude controller is based on RISE control methods, specially：
Wherein, Ks, β be positive definite parameter matrix, I3×3For three rank unit matrixs；NdFor auxiliary function；e2, r be filtering error letter
Number,For the first derivative of filtering error, J is moment of inertia matrix.
2. a kind of model-free quadrotor drone Trajectory Tracking Control based on PD-SMC and RISE as described in claim 1
Device, which is characterized in that the inner ring attitude controller in the design process, using differential tracker it is expected the meter of angular speed
It calculates.
3. a kind of design method of the model-free quadrotor drone contrail tracker based on PD-SMC and RISE, feature
It is, includes the following steps：
(1) dynamic model of quadrotor drone is determined；
(2) assume that the time-varying disturbance acted in quadrotor drone is bounded, provide desired trajectory ξd(t), it is disturbed in presence
In the case of dynamic and model is uncertain, PD-SMC control algolithms are based on, design virtual controlling inputs u, ensures position tracking error
It is asymptotically convergent to zero；
(3) u is inputted according to the virtual controlling of design, determines outer ring controller；
(4) RISE algorithms are based on, design continuous control inputs τi(i=1,2,3) so that attitude control system is that part index number is steady
It is fixed；
(5) τ is inputted according to the continuous control of designi(i=1,2,3) determines interior ring controller.
4. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that in the step (2), design virtual controlling input u be specially：
Wherein, F=[R1,3u,R2,3u,R3,3u]T；Kp,KdIt is PD control device gain matrix, H is SMC controller gains, and μ is to slide
Die face gradient constant matrix；E is position tracking error,For the first derivative of position tracking error, R1,3, R2,3, R3,3It is respectively
The third column element of spin matrix R.
5. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that in the step (3), outer ring controller is specially：
Wherein, position tracking error：Kξ=diag (Kx,Ky,Kz)；Kp,Kd
It is PD control device gain matrix, H is SMC controller gains, and μ is sliding-mode surface gradient constant matrix；
M is quadrotor quality, Kx、Ky、KzEqual air damping coefficient, G are gravitational acceleration vector, and d disturbs for outer shroud, and E is position
Tracking error,WithThe respectively single order and second dervative of position tracking error；ξdFor desired locations,It schedules to last respectively
Hope speed and desired acceleration；ξ、The respectively position of quadrotor drone, speed and acceleration.
6. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that in the step (4), the first derivative of the continuous control of design input τSpecially：
Wherein, Ks, β is positive definite parameter matrix, I3×3For three rank unit matrixs, e2, r be filtering error function.
7. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that in the step (5), interior ring controller is specially：
Wherein, Ks, β be positive definite parameter matrix, I3×3For three rank unit matrixs；NdFor auxiliary function；e2, r be filtering error letter
Number,For the first derivative of filtering error, J is moment of inertia matrix.
8. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that u is inputted according to virtual controlling, calculates expected angle φd(t), θd(t) as follows：
Wherein, φd、θdRespectively it is expected corner and desired pitch angle, R1,3, R2,3, R3,3It is the third row member of spin matrix R respectively
Element.
9. a kind of model-free quadrotor drone contrail tracker based on PD-SMC and RISE as claimed in claim 3
Design method, which is characterized in that the inner ring attitude controller carries out expectation angle in the design process, using differential tracker
The calculating of speed.
10. a kind of model-free quadrotor drone Trajectory Tracking Control based on PD-SMC and RISE as claimed in claim 9
The design method of device, which is characterized in that the differential tracker design is as follows：
Wherein, ω (t) is the signal for needing to carry out differential；x1, x2Tracking ω (t) and its first derivative respectivelyConstant r determines
Tracking velocity is determined.
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