CN109521786A - Quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer - Google Patents
Quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer Download PDFInfo
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Abstract
The quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer that the invention discloses a kind of, the expression formula of quadrotor drone roll angle, pitch angle and yaw angle and is transformed into second order model comprising steps of establish that there is only the kinetic models of the quadrotor drone of disturbed condition by method；Corresponding Proportional integral observer is constructed based on second order model；Sliding Mode Attitude controller is designed according to Proportional integral observer, flight control is carried out to quadrotor drone in conjunction with the Sliding Mode Attitude controller of roll angle, pitch angle and yaw angle；The present invention combines Proportional integral observer with Sliding Mode Attitude controller, is estimated by the partial feedback function of Proportional integral observer the shape and position input nonlinearities state of quadrotor drone, improves the steady-state tracking precision of proportional integration state observer；There is stronger robustness and anti-interference by uncertain factor of the Sliding Mode Attitude controller to quadrotor drone；Present invention design and calculating are simple.
Description
Technical field
The invention belongs to UAV Attitude control technology fields, and in particular to a kind of four rotations based on Proportional integral observer
Wing unmanned plane Sliding Mode Attitude control method.
Background technique
Quadrotor drone structure is simple, relative load ability is strong, VTOL and mobility are good, dual-use
Every field is more and more widely used, such as aerial reconnaissance, communication, electronic interferences, resource detection, forest fire protection, side
The such as border patrol are significantly improved with scientific and technological rapid development, the automation of unmanned plane and intelligence degree, become global evolution
Hot spot has also obtained very big attention and development accordingly, with respect to the research of UAV Flight Control technology.UAV Attitude and speed
Degree control is the basis of UAV Flight Control, and control performance greatly affects the safe flight efficiency of unmanned plane.It is close
Many methods are applied in UAV Flight Control for example over year: PID control, feedback linearization method, ANN Control
Wherein PID linear control method can meet the basic flight operation control of quadrotor drone to equal, but deviateing equalization point or depositing
In disturbance, control performance will be unable to be protected.Gain asymmetry control can be handled unmanned plane model linearization, be simplified
The design of controller.Feedback linearization method is to make have linear relationship between the input and output of new system using overall-finished housing.
Dynamic inversion control based on neural network method can be in the case where unmanned plane be difficult to obtain accurate mathematical model, using mind
System Discrimination is carried out through network, but its computation complexity is high and convergence hardly results in guarantee.In summary, in the prior art,
The control method of quadrotor drone is needed to carry out whole feedbacks to the quantity of state of entire quadrotor drone system, and entire
The computation complexity of quadrotor drone system is higher, is unfavorable for the popularization and application of quadrotor drone.
Summary of the invention
The quantity of state feedback quantity of system is bigger in quadrotor drone control process for above-mentioned in the prior art
And the higher problem of computation complexity, the present invention is in proposing a kind of quadrotor drone sliding formwork appearance based on Proportional integral observer
State control method, this method is by combining proportional integration state controller and Sliding Mode Attitude controller can be to quadrotor drone
Good dynamic Control platform is carried out, specific technical solution is as follows:
A kind of quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer, which comprises
S1, there is only the kinetic models of the quadrotor drone of disturbed condition for foundation:
Wherein, φ is roll angle, and θ is pitch angle, and ψ is yaw angle, and l is distance of each rotor to unmanned plane mass center；di(i=1,2,3)
For unknown external disturbance, and di≤||d||；KiIt (i=1,2,3) is resistance coefficient；Ix, Iy, IzRespectively the three of aircraft body
Axis rotary inertia；u1, u2, u3The respectively control input quantity of roll angle, pitch angle and yaw angle, and respectively by the roll angle
φ, pitching angle theta and the corresponding kinetic model of yaw angle ψ are converted to second order model；
S2, corresponding Proportional integral observer is constructed based on the second order model；
S3, Sliding Mode Attitude controller is designed according to the Proportional integral observer, passes through the Sliding Mode Attitude controller meter
Calculate the control rate of the quadrotor drone.
It is further, described that the kinetic model is converted to second order model in step S1, comprising:
S11, the state variable for defining quadrotor drone state space
S12, the control variable U=[u for defining quadrotor drone1 u2 u3]T, it is based on the kinetic model
And state variableObtain the state-space model of quadrotor drone
Are as follows:
Wherein,
S13, the part roll angle φ, pitching angle theta part and yaw angle ψ portion in the state-space model are chosen respectively
Point, and it is transformed to the second order model:
Further, it is based respectively on the state variable model building of the roll angle φ, pitching angle theta part and yaw angle ψ
Proportional integral observer:Wherein,Indicate the observation to system mode x,
Indicate the observation to system output yKp, kIRespectively represent the proportional gain matrix and integral of Proportional integral observer
Coefficient.
Further, in step S3, comprising:
S31, the roll angle φ, pitching angle theta part and yaw angle ψ are based respectively on and in conjunction with the corresponding ratio of each angle
Example integral observerAnd the corresponding state variable model and equationConstruct Sliding Mode Attitude controller corresponding with roll angle φ, pitching angle theta part and yaw angle ψ respectively.
It further, further include proving institute using Lyapunov Theory of Stability building Lyapunov function in step S2
State the stability of Proportional integral observer:
S21, the state estimation error for defining the Proportional integral observer areIt willConversion are as follows:Wherein,
And it willIt is converted intoWherein,
S22, Li Yapu love theory is based on for Li Yapu love function V (ef), existIt is negative definite, then
Illustrate that the Proportional integral observer is asymptotically stability.
It further, further include proving institute using Lyapunov Theory of Stability building Lyapunov function in step S3
State the stability that Proportional integral observer combines the rear quadrotor drone with the sliding mode controller.
Quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer of the invention, by the way that ratio is long-pending
Observer is divided to combine with Sliding Mode Attitude controller, by introducing integral term in proportional integration state observer, so as to pass through
Partial feedback estimates the state of quadrotor drone, and also can be simultaneously to quadrotor drone unknown input disturbances
Estimated, to improve the steady-state tracking precision of proportional integration state observer；Meanwhile in conjunction with Sliding Mode Attitude controller, no
Only there is stronger robustness and anti-interference to the uncertain factor of quadrotor drone, and sliding mode control can be passed through
The design of device processed is so that quadrotor drone obtains satisfied dynamic quality, and Proportional integral observer observer is for compensating
Unknown disturbances can eliminate chattering phenomenon existing for traditional sliding formwork control, achieve the effect that eliminate disturbing influence；With prior art phase
Than the entire quadrotor drone design of the present invention and calculating are simple, and manufacturing cost is lower, is also easy to realize in engineering, is easy to push away
Wide application.
Detailed description of the invention
Fig. 1 is the quadrotor drone Sliding Mode Attitude controlling party described in the embodiment of the present invention based on Proportional integral observer
The flow chart of method is illustrated；
Fig. 2 is the structural design drawing signal of Proportional integral observer described in the embodiment of the present invention；
Fig. 3 is the output analogous diagram of the roll angle, pitch angle of quadrotor drone system in the embodiment of the present invention, yaw angle
Signal；
Fig. 4 is the comparison of angular velocity in roll described in the embodiment of the present invention true value and observation in cases of a disturbance
Analogous diagram signal；
Fig. 5 is the comparison of rate of pitch described in the embodiment of the present invention true value and observation in cases of a disturbance
Analogous diagram signal；
Fig. 6 is the comparison of yaw rate described in the embodiment of the present invention true value and observation in cases of a disturbance
Analogous diagram signal；
Fig. 7 is that the true value of interference value and the contrast simulation of estimated value illustrate in roll angle described in the embodiment of the present invention
Meaning；
Fig. 8 is that the true value of interference value and the contrast simulation of estimated value illustrate in pitch angle described in the embodiment of the present invention
Meaning；
Fig. 9 is that the true value of interference value and the contrast simulation of estimated value illustrate in yaw angle described in the embodiment of the present invention
Meaning.
Specific embodiment
In order to enable those skilled in the art to better understand the solution of the present invention, below in conjunction in the embodiment of the present invention
Attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.
Embodiment one
In embodiments of the present invention, a kind of quadrotor drone Sliding Mode Attitude control based on Proportional integral observer is provided
Method processed, the attitude angle suitable for quadrotor drone are less than or equal to 90 °, describe four by using the mode of Eulerian angles
The space body posture of rotor wing unmanned aerial vehicle, and it is modeled；Refering to fig. 1, the method comprise the steps that
S1, it sets around X, Y, Z axis rotates to x, and the Eulerian angles vector of y, z are [φ θ ψ] respectively according to X, Y, the sequence of Z axis
Carry out Space Rotating variation；Wherein φ is roll angle, i.e. the angle that rotates through around itself X-axis of body；θ is pitch angle, i.e. body
The angle rotated through around itself Y-axis；ψ is yaw angle, i.e. the angle that rotates through around itself Z axis of body coordinate system；By quadrotor without
Man-machine movement is considered as rigid motion, and the center of quadrotor drone is located at body coordinate origin, and there is only dry for foundation
Disturb the kinetic model of the quadrotor drone of situation:Wherein, l is each rotor to unmanned plane matter
The distance of the heart；diIt (i=1,2,3) is unknown external disturbance, and di≤||d||；KiIt (i=1,2,3) is resistance coefficient；Ix, Iy, Iz
Respectively three axis rotary inertias of aircraft body；u1, u2, u3The control of respectively roll angle φ, pitching angle theta and yaw angle ψ is defeated
Enter amount.
Then, kinetic model is converted to second order model, comprising steps of
Firstly, defining the state variable of quadrotor drone state spaceThen, quadrotor is defined
The control variable U=[u of unmanned plane1u2u3]T, it is based on kinetic modelAnd state variableObtain the state-space model of quadrotor drone are as follows:
Wherein,Finally, choosing
One in roll angle φ, pitching angle theta or yaw angle ψ by kinetic modelIn corresponding model change
For second order model:With the kinetic model expression formula of roll angle φFor
Example is illustrated, then can be obtainedFor the state of system,B=[0 1]T, u=u1It is inputted for control,
D=[0 d1]TFor unknown input disturbances, d1Bounded and d1≤ | | d | |, C=[c 0], D are unit matrix, and c is constant, and y is to be
The output of system, E=[0 1]；Construct the thought of the second order model of the kinetic model expression formula of depression angle θ or yaw angle ψ
Principle is consistent with using the principle of roll angle φ, is not being repeated herein.
S2, referring to Fig.2, being illustrated as the design drawing of Proportional integral observer in the present embodiment, the present invention is based respectively on rolling
The second order model of angle φ, pitching angle theta and yaw angle ψ construct corresponding Proportional integral observer the specific steps are, with rolling
It is illustrated for corner φ:
Based on roll angle φ state variable modelBuilding ratio
Integral observer:Wherein,Indicate the observation to system mode x,It indicates
To the observation of system output yKp, kIRespectively represent the proportional gain matrix and integral coefficient of Proportional integral observer.
Construct the corresponding Proportional integral observer of second order model of depression angle θ or yaw angle ψ principle and thought with
It constructs the roll angle φ second order model and constructs the principle of corresponding Proportional integral observer as thought, herein equally
It is no longer repeated, specifically sees the above-mentioned building to the corresponding Proportional integral observer of roll angle φ second order model structure
Process.
Meanwhile in order to which the Proportional integral observer for proving that the present invention constructs is with good stability, the present invention also passes through
Lyapunov Theory of Stability, which constructs Lyapunov function, proves the stability of Proportional integral observer, specifically includes: firstly, fixed
The state estimation error of adopted Proportional integral observer isIt willConversion are as follows:
Wherein,And it will
It is converted intoWherein,
Then, based on Li Yapu love theory for Li Yapu love function V (ef), existIt is negative definite, then illustrates ratio
Integral observer is asymptotically stability.
Wherein, the tool of Proportional integral observer asymptotically stability in the suitable Li Yapu love function declaration present invention is obtained
Body process are as follows: enableAnd it sets just into definite quadratic form functionAs Li Yapu love function, then
It can obtain:
IfKnown a, b are constant；λmax(P)For the maximum eigenvalue of matrix P；Cause
This can be by formula:It is obtained by integral:
And becauseSoBecauseFor constant, soIt follows that this
Proportional integral observer has asymptotically stability characteristic in invention.
Simultaneously as P is positive definite symmetrical matrix, then formulaMiddle AeMeet Hurwitz conditioned matrix, according to
The property of Hurwitz matrix: Hurwitz matrix indicate multinomial be it is stable, i.e., polynomial all have negative real part,
Know its characteristic value in left negative half-plane；Thus K can be releasedP,kIRange.
S3, corresponding sliding formwork appearance designed according to the Proportional integral observer of roll angle φ, pitching angle theta and yaw angle ψ respectively
State controller, to calculate separately quadrotor drone in roll angle φ, pitching angle theta and yaw angle by Sliding Mode Attitude controller
The control rate in tri- directions ψ；
Firstly, choose roll angle φ, in pitching angle theta and yaw angle ψ one combine Proportional integral observer
And the state variable model of roll angle φ, pitching angle theta and yaw angle ψAnd equationConstruct roll angle φ, pitching angle theta and yaw
Angle ψ respectively corresponds Sliding Mode Attitude controller,The present embodiment by taking roll angle φ as an example into
Row explanation, then can obtain y1=cx1+ d,The integral action introduced for roll angle φ；Wherein, to bow
View angle theta or the principle of yaw angle ψ are consistent with using the principle of roll angle φ, are not being repeated herein；Then, according to obtaining
Sliding Mode Attitude controllerDesign sliding formwork function c1>
0, it realizesxdFor roll angle φ desired value, kP,kIRespectively represent the proportional gain matrix and product of Proportional integral observer
Divide coefficient；It is directed to roll angle φ subsystem are as follows:Finally, setting b1It is 1,
Then it is based on subsystemThe sliding formwork control of quadrotor drone can be acquired
Rate are as follows:Wherein,
In embodiments of the present invention, the corresponding Sliding Mode Attitude control of Proportional integral observer of depression angle θ or yaw angle ψ is constructed
The principle of the principle and thought of device processed Sliding Mode Attitude controller corresponding with the roll angle φ Proportional integral observer is constructed and
Thought is the same, is equally no longer repeated herein, specifically sees above-mentioned to the corresponding cunning of roll angle φ Proportional integral observer
The design process of mould attitude controller.
Likewise, in order to guarantee that present invention quadrotor drone after combining Proportional integral observer and sliding mode controller has
There is good stability, the present invention is proved also with Lyapunov Theory of Stability building Lyapunov function, detailed process
Are as follows:
According to subsystem expression formula
It obtains:And take Li Yapu love function are as follows:In conjunction withWith Li Yapu love functionIt can obtain:
It is managed based on Lyapunov stability
Prove bright s1The convergence of index, if convergence, demonstrates quadrotor drone stability, otherwise, quadrotor drone is unstable
It is fixed.
Embodiment two
Refering to Fig. 3~Fig. 9, in the environment of MATLAB2016, select quadrotor drone to base designed by the present invention
Simulating, verifying test is carried out in the sliding-mode control of Proportional integral observer:
Firstly, building emulation module in MATLAB carries out entire quadrotor drone emulation experiment, quadrotor drone
The relevant parameter of used Parameters in Mathematical Model and Proportional integral observer are as follows:
The original state of system state variables are as follows: initial Eulerian angles are (0.4,0.2,0) rad；It is expected that Eulerian angles be (1.2,
1,0.5)rad.Initial Euler angle rate is (0,0,0) rad/s.
In the present invention, the sliding mode controller parameter based on Proportional integral observer design has the performance of flight control system
It is direct to influence；Parameter value acquirement is bigger, and control ability is stronger, but can also cause biggish control error simultaneously, if parameter is too
Small, then system is easy to appear concussion；In conjunction with the control ability of quadrotor drone executing agency and the requirement of control performance, then plus
Theory deduction before upper as a result, the attitude angle control parameter of final selection is respectively as follows:
The output of roll angle φ, pitching angle theta and yaw angle ψ in motion model are obtained, in conjunction with Fig. 2, it can be seen that, quadrotor
The attitude angle of unmanned plane is stable near desired attitude angle, and error is minimum；And as can be seen from the figure quadrotor drone
Response time reached stable state in 1 second；The angular speed at each angle of quadrotor drone is in cases of a disturbance
The comparison of true value and observation, the comparison diagram 6 of the true value and estimated value of combinable Fig. 3, Fig. 4 and Fig. 5 and interference value,
Fig. 7 and Fig. 8, it follows that can guarantee to control in the Sliding Mode Attitude to quadrotor drone by means of the present invention
When, quadrotor drone can be adjusted to stable state in 1 second or so time, and illustrate Proportional integral observer of the invention
With good observation effect.
Quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer of the invention, by the way that ratio is long-pending
Observer is divided to combine with Sliding Mode Attitude controller, by introducing integral term in proportional integration state observer, so as to pass through
Partial feedback estimates the state of quadrotor drone, and also can be simultaneously to quadrotor drone unknown input disturbances
Estimated, to improve the steady-state tracking precision of proportional integration state observer；Meanwhile in conjunction with Sliding Mode Attitude controller, no
Only there is stronger robustness and anti-interference to the uncertain factor of quadrotor drone, and sliding mode control can be passed through
The design of device processed is so that quadrotor drone obtains satisfied dynamic quality, and Proportional integral observer observer is for compensating
Unknown disturbances can eliminate chattering phenomenon existing for traditional sliding formwork control, achieve the effect that eliminate disturbing influence；With prior art phase
Than the entire quadrotor drone design of the present invention and calculating are simple, and manufacturing cost is lower, is also easy to realize in engineering, is easy to push away
Wide application.
The foregoing is merely a prefered embodiment of the invention, is not intended to limit the scope of the patents of the invention, although referring to aforementioned reality
Applying example, invention is explained in detail, for a person skilled in the art, still can be to aforementioned each specific
Technical solution documented by embodiment is modified, or carries out equivalence replacement to part of technical characteristic.All utilizations
The equivalent structure that description of the invention and accompanying drawing content are done directly or indirectly is used in other related technical areas, together
Reason is within the invention patent protection scope.
Claims (6)
1. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer, which is characterized in that the method packet
It includes:
S1, there is only the kinetic models of the quadrotor drone of disturbed condition for foundation:Wherein,
φ is roll angle, and θ is pitch angle, and ψ is yaw angle, and l is distance of each rotor to unmanned plane mass center；diIt (i=1,2,3) is unknown
External disturbance, and di≤||d||；KiIt (i=1,2,3) is resistance coefficient；Ix, Iy, IzThe respectively three axis rotation of aircraft body
Inertia；u1, u2, u3The respectively control input quantity of roll angle, pitch angle and yaw angle, and respectively by the roll angle φ, pitching
Angle θ and the corresponding kinetic model of yaw angle ψ are converted to second order model；
S2, be based respectively on the roll angle φ, pitching angle theta and yaw angle ψ convert to be formed the second order model building pair
The Proportional integral observer of the roll angle φ, pitching angle theta and yaw angle ψ that answer；
S3, the Sliding Mode Attitude that the roll angle φ, pitching angle theta and yaw angle ψ are corresponded to according to Proportional integral observer design
Controller, in conjunction with the roll angle φ, pitching angle theta and yaw angle ψ state corresponding design Sliding Mode Attitude controller quadrotor nobody
Machine, and calculate corresponding control rate.
2. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer as described in claim 1, special
Sign is, described that the kinetic model is converted to second order model in step S1, comprising:
S11, the state variable for defining quadrotor drone state space
S12, the control variable U=[u for defining quadrotor drone1 u2 u3]T, it is based on the kinetic model
And state variableObtain the state-space model of quadrotor drone
Are as follows:
Wherein,
S13, the part roll angle φ, pitching angle theta part and yaw angle ψ part in the state-space model are chosen respectively, and
It is transformed to the second order model:
3. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer as claimed in claim 2, special
Sign is that the state variable model building proportional integration for being based respectively on the roll angle φ, pitching angle theta part and yaw angle ψ is seen
Survey device:Wherein,Indicate the observation to system mode x,It indicates to system
Export the observation of yKp, kIRespectively represent the proportional gain matrix and integral coefficient of Proportional integral observer.
4. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer as claimed in claim 3, special
Sign is, in step S3, comprising:
S31, the roll angle φ, pitching angle theta part and yaw angle ψ are based respectively on and in conjunction with the corresponding ratio product of each angle
Divide observerAnd the corresponding state variable model and equation
Construct Sliding Mode Attitude controller corresponding with roll angle φ, pitching angle theta part and yaw angle ψ respectively.
5. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer as claimed in claim 4, special
Sign is, further includes proving the proportional integration using Lyapunov Theory of Stability building Lyapunov function in step S2
The stability of observer:
S21, the state estimation error for defining the Proportional integral observer areIt will
Conversion are as follows:Wherein,
And it willIt is converted intoWherein,
S22, Li Yapu love theory is based on for Li Yapu love function V (ef), existIt is negative definite, then illustrates
The Proportional integral observer is asymptotically stability.
6. the quadrotor drone Sliding Mode Attitude control method based on Proportional integral observer as claimed in claim 5, special
Sign is, further includes proving the proportional integration using Lyapunov Theory of Stability building Lyapunov function in step S3
Observer combines the stability of the rear quadrotor drone with the sliding mode controller.
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| CN110376883A (en) * | 2019-06-03 | 2019-10-25 | 济南大学 | Quadrotor drone TSM control method, system, medium and equipment |
| CN110618694A (en) * | 2019-09-10 | 2019-12-27 | 北方信息控制研究院集团有限公司 | Robust attitude control method for space interceptor |
| CN110850887A (en) * | 2019-10-10 | 2020-02-28 | 南京航空航天大学 | Composite dynamic inverse anti-interference attitude control method for quad-rotor unmanned aerial vehicle |
| CN112147894A (en) * | 2020-09-23 | 2020-12-29 | 重庆邮电大学 | Wheel type mobile robot active control method based on kinematics and dynamics model |
| CN112947518A (en) * | 2021-02-03 | 2021-06-11 | 莆田学院 | Four-rotor robust attitude control method based on disturbance observer |
| CN113049215A (en) * | 2021-03-17 | 2021-06-29 | 北京航空航天大学 | Quantitative assessment and test system for airflow interference resistance of rotor unmanned aerial vehicle position |
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| CN114489105B (en) * | 2022-01-25 | 2024-01-16 | 南京邮电大学 | Novel unmanned aerial vehicle attitude system integral sliding mode control method based on interference observer |
| CN115840367A (en) * | 2022-12-21 | 2023-03-24 | 南通大学 | Nonlinear robust control method for disturbed quadrotor unmanned aerial vehicle attitude and height system |
| CN115840367B (en) * | 2022-12-21 | 2024-04-09 | 南通大学 | Nonlinear robust control method for attitude and altitude system of disturbed four-rotor unmanned aerial vehicle |
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