CN108345212A - A kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method - Google Patents
A kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method Download PDFInfo
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- CN108345212A CN108345212A CN201710063923.5A CN201710063923A CN108345212A CN 108345212 A CN108345212 A CN 108345212A CN 201710063923 A CN201710063923 A CN 201710063923A CN 108345212 A CN108345212 A CN 108345212A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
Abstract
The robust H of the invention discloses a kind of Three Degree Of Freedom helicopter based on sliding formwork∞Control method.Consider time lag and Bounded uncertainties existing for Three Degree Of Freedom Helicopter Flight Control System, is disturbed for its inside and outside, in conjunction with sliding-mode control, propose a kind of robust H∞Control method.Integral form sliding-mode surface is devised, if system provides the adequate condition of standard sliding mode asymptotically stability without external disturbance, such as there is external disturbance, then system meets robust H∞Index, in conjunction with sliding formwork control and adaptive boundary method of estimation, design control law makes system be moved along standard sliding-mode surface.The method of the present invention is by constructing integral form sliding-mode surface, so that system is regardless of whether can meet certain performance indicator there are external disturbance, by designing adaptive law and sliding mode controller, system can be made to be moved along standard sliding-mode surface, the stability of Three Degree Of Freedom helicopter is effectively increased, foundation can be provided for the complicated Three Degree Of Freedom Helicopter Flight Control System robust Controller Design with inside and outside disturbance.The present invention is used for the robust control with permanent time lag and the probabilistic Three Degree Of Freedom helicopter of modeling.
Description
Technical field
The robust H of the present invention relates to a kind of Three Degree Of Freedom helicopter based on sliding formwork∞Control method belongs to aircraft robust
Control field.
Background technology
Small-sized depopulated helicopter is that one kind can VTOL, rotary wind type autonomous control aircraft.According to the position of rotor
And quantity, multirotor helicopter can be divided mainly into four kinds of single rotor, series connection DCB Specimen, coaxial double-rotary wing and quadrotor.Rotor flies
Row utensil has and quick change of flight posture, any direction can fly in the air, VTOL, aerial spot hover, shape
Size is small, radar emission area is small, and flight safety is high, takes off and land requirement condition is simple, and erection and receiving time are short etc.
The advantages of many Fixed Wing AirVehicles do not have, succour in battlefield surveillance, tactics guiding, military surveillance, agricultural production, fire-fighting,
Scientific research etc. is widely used and receives research institution of various countries, the more and more concerns of the military and government.
The control problem of heligyro is a very challenging task.It is inherently unstable that it is related to helicopter
Dynamically, the various challenges such as multivariable, non-linear, close coupling, open-cycle controller saturation, and the meeting in flight course
Inevitably encounter wind disturb, a variety of uncertain factors such as engine luggine, therefore, for the robust control skill of heligyro
The research of art becomes the urgent task for improving its safety and reliability.
As shown in Fig. 2, Three Degree Of Freedom helicopter can be applied to the Hardware-in-loop Simulation Experimentation and property of flight control system
The occasions such as energy test, to simulate side-by-side helicopter, i.e. the helicopter state of gyroplane.Therefore in the lab, Ke Yitong
Three Degree Of Freedom helicopter is crossed to simulate the robust control of quadrotor.
The emphasis studied in control system theory is related to robustness problem：Time control is had differences in real system and model
Device processed has the ability to keep stability and performance indicator.It is H in the Typical Representative of linear field control, robust control∞Control theory
With μ methods；It is Sliding mode variable structure control in the Typical Representative of field of non-linear control, robust control.Sliding mode variable structure control is
At present nonlinear control system it is relatively universal, compared with a kind of integrated approach of system.Its outstanding advantages are sliding modes for parameter
The uncertain factors such as perturbation and external disturbance have insensitivity, and the dynamic quality of sliding mode is can be pre-designed
's.This excellent performance is highly important to control system, has been widely used in flight control system at present.Structure changes control
Method processed is with the heat that its design is simple and there is this unique advantage of superior robustness to form theoretical area research in order to control
One of point.
However, existing method cannot consider that real system time lag that may be present, uncertainty, disturbance etc. are each comprehensively
Kind factor, is difficult to have good control effect, therefore the present invention has good practicability to complicated flight control system.
Invention content
Goal of the invention：For the above-mentioned prior art, a kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork is proposed∞Control
Method processed, the negative effect that can be effectively eliminated time lag and be brought by external disturbance keep system uncertain for modeling
It is insensitive so that aircraft can remain good state of flight.
Technical solution：A kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method, it is characterised in that：Consider
Time lag and Bounded uncertainties existing for Three Degree Of Freedom Helicopter Flight Control System are disturbed for its inside and outside, in conjunction with sliding formwork
Control method proposes a kind of robust H∞Control method so that aircraft can have good flight quality always.Devise product
Parting sliding-mode surface, if system provides the adequate condition of standard sliding mode asymptotically stability, such as disturbed in the presence of outside without external disturbance
Dynamic, then system meets robust H∞Index, in conjunction with sliding formwork control and adaptive boundary method of estimation, design control law makes system edge
The movement of standard sliding-mode surface.It comprises the following specific steps that：
Step 1) establishes the mathematical model of Three Degree Of Freedom helicopter：
Wherein x ∈ RnFor system state variables, u (t) is the difference of two propeller controls of helicopter input, and y is defeated for that can survey
Go out, τ is constant, represents fixed time lag size, Δ A (t) and Δ Ad(t) it is that modeling is uncertain, g (x, t) is external disturbance,
F (x, t) is internal disturbance.
Step 2) is directed to above-mentioned Helicopter Flight Control System, carries out Integral Sliding Mode face design：
Design following Integral Sliding Mode face：
Matrix G ∈ Rm×nMeet the nonsingular conditions of GB, K ∈ Rm×nIt is undetermined constant matrix.
It enablesSolve Equivalent control law：
ueq=-(GB)-1G (g (x, t)+Δ A (t) x (t)+Δ Ad(t) x (t- τ))-Kx (t)-f (x, t) (3)
Equivalent control law is brought into original system (1), so that it may to obtain following standard sliding mode：
If step 2.1) exterior disturbs g=0, can provide standard sliding mode asymptotically stability one is abundant
Condition.
It can be proved that if there is matrix Y ∈ Rm×n, positive definite matrix X ∈ Rn×nWith normal number ε1, ε2, ε3Make linear moment
Battle array inequality (5) is set up, then standard sliding mode (4) of the system (1) on sliding-mode surface (2) is asymptotically stable.
More than,And the undetermined coefficient matrix K of sliding-mode surface (2)
=YX-1。
If step 2.2) external disturbance g ≠ 0：
An interference attenuation index γ ＞ 0 is given, as long as then above-mentioned linear matrix inequality (5) is set up, then system is defeated
Go out to meet robust H∞Index γ.
Step 3) designs the continuous part control of sliding formwork control：
According to the design method of sliding formwork control, even all modeling uncertainty and disturbance of continuous part original system is
Zero, the nominal system of absolute standard is obtained, then solve Equivalent control law at this time, is the continuous portion in complete control law
Point, according to Equivalent control law (3), it is 0 to enable uncertain and inside and outside disturbance therein, then can obtain the company of sliding formwork control ratio
Continuous part is as follows：
ucon(t)=- Kx (t) (6)
The form is a kind of STATE FEEDBACK CONTROL.
Step 4) designs the discontinuous section in sliding formwork control：
Discontinuous section is generating discontinuous signal so that system can be moved along sliding-mode surface (2).
First, adaptive law is designed to estimate the size of internal disturbance：
Then the discontinuous portion of faults-tolerant control rule is divided into：
Wherein η is a small normal number.
Convolution (6) and (8) can obtain complete robust H∞Control law is as follows：
Step 5) selects suitable parameter according to the state of flight of quadrotor, completes to its robust H∞Control.
Advantageous effect：The present invention proposes a kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method considers Three Degree Of Freedom
Time lag and Bounded uncertainties existing for Helicopter Flight Control System are disturbed for its inside and outside, in conjunction with sliding-mode control,
It is proposed a kind of robust H∞Control method.
It has the following advantages that：
(1) by designing a kind of integral form sliding-mode surface, the buffeting of system is effectively reduced, the influence that time lag is brought is reduced；
(2) system asymptotically stability adequate condition is provided using linear matrix inequality so that the design of controller has more
Good practicability；
(3) an interference attenuation index is designed so that when system has external disturbance, ensure that service system output meets Shandong
Stick H∞Index；
(4) method for introducing adaptive boundary estimation estimates the size of internal disturbance so that system conservative smaller, Shandong
Stick is stronger.
Method therefor of the present invention has certain practical application as a kind of robust control method of Three Degree Of Freedom helicopter
Value, it is easy to accomplish, strong robustness can effectively improve the flight stability of quadrotor.This method operability is strong,
Using convenient, reliable.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the 3DOF Three Degree Of Freedom helicopter simulating experimental systems of Quanser；
Fig. 3 is condition curve in the case of no external disturbance；
Fig. 4 is controlling curve in the case of no external disturbance；
Fig. 5 is that have external disturbance condition lower curve；
Specific implementation mode
Further explanation is done to the present invention below in conjunction with the accompanying drawings.
As shown in Figure 1, considering quadrotor, there are time lags and actuator failures, in conjunction with optimum control and sliding formwork control
System proposes a kind of optimal fault tolerant control method so that aircraft can continue to safe flight after actuator failures occur, and protect
Demonstrate,prove good flight quality.According to the model parameter of acquired aircraft, a kind of Integral Sliding Mode with time lag compensation is designed
The influence of time lag is eliminated in face, and quadratic optimal performance index is designed for nominal system, obtains optimal ideal sliding mode, into
And corresponding sliding formwork control ratio is designed, finally constitute optimal fault-tolerant controller.It comprises the following specific steps that：
Step 1) establishes the mathematical model of Three Degree Of Freedom helicopter：
Wherein x ∈ RnFor system state variables, u (t) is the difference of two propeller controls of helicopter input, and y is defeated for that can survey
Go out, τ is constant, represents fixed time lag size, Δ A (t) and Δ Ad(t) it is that modeling is uncertain, g (x, t) is external disturbance,
F (x, t) is internal disturbance.
Step 2) is directed to above-mentioned Helicopter Flight Control System, carries out Integral Sliding Mode face design：
Design following Integral Sliding Mode face：
Matrix G ∈ Rm×nMeet the nonsingular conditions of GB, K ∈ Rm×nIt is undetermined constant matrix.
It enablesSolve Equivalent control law：
ueq=-(GB)-1G (g (x, t)+Δ A (t) x (t)+Δ Ad(t) x (t- τ))-Kx (t)-f (x, t) (3)
Equivalent control law is brought into original system (1), so that it may to obtain following standard sliding mode：
If step 2.1) exterior disturbs g=0, can provide standard sliding mode asymptotically stability one is abundant
Condition.
It can be proved that if there is matrix Y ∈ Rm×n, positive definite matrix X ∈ Rn×nWith normal number ε1, ε2, ε3Make linear moment
Battle array inequality (5) is set up, then standard sliding mode (4) of the system (1) on sliding-mode surface (2) is asymptotically stable.
More than,And the undetermined coefficient matrix K of sliding-mode surface (2)
=YX-1。
If step 2.2) external disturbance g ≠ 0：
An interference attenuation index γ ＞ 0 is given, as long as then above-mentioned linear matrix inequality (5) is set up, then system is defeated
Go out to meet robust H∞Index γ.
Step 3) designs the continuous part control of sliding formwork control：
According to the design method of sliding formwork control, even all modeling uncertainty and disturbance of continuous part original system is
Zero, the nominal system of absolute standard is obtained, then solve Equivalent control law at this time, is the continuous portion in complete control law
Point, according to Equivalent control law (3), it is 0 to enable uncertain and inside and outside disturbance therein, then can obtain the company of sliding formwork control ratio
Continuous part is as follows：
ucon(t)=- Kx (t) (6)
The form is a kind of STATE FEEDBACK CONTROL.
Step 4) designs the discontinuous section in sliding formwork control：
Discontinuous section is generating discontinuous signal so that system can be moved along sliding-mode surface (2).
First, adaptive law is designed to estimate the size of internal disturbance：
Then the discontinuous portion of faults-tolerant control rule is divided into：
Wherein η is a small normal number.
Convolution (6) and (8) can obtain complete robust H∞Control law is as follows：
Step 5) selects suitable parameter according to the state of flight of quadrotor, completes to its robust H∞Control.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention,
Illustrate the validity of embodiment with real case emulation below.
It is calculated as specific using the 3DOF four-rotor helicopter semi-physical simulation platforms of Canadian quanser companies production
Method experiment simulation object.The emulation platform is by helicopter ontology, four part group of data acquisition control card, power plant and PC machine
At.The form of the composition of entire emulation platform is Virtual Controller and practical object.Fig. 2 is that the 3DOF quadrotors of Quanser are gone straight up to
Machine semi-physical simulation platform.Practical object therein is the hardware device of four-rotor helicopter, and Virtual Controller uses quanser
The special-purpose software that company provides writes program, can be C code by matlab/simulink block diagram direct compilations, pass through PCI board
Card downloads in real-time emulation system, carries out semi-physical simulation.
The mathematical model of Three Degree Of Freedom helicopter is as follows：
Wherein, each coefficient matrix is as follows：
In emulation experiment, by hard ware measure it can be found that the time lag as caused by being wirelessly transferred is generally 80-120 millis
Second, in order to prove that this chapter proposes the validity of method, it is assumed that time lag is τ=1s.
In simulation process, the model of controlled system is built with matlab simulink, can easily change control
The type of rule and failure.
Assuming that the disturbance of following form occurs in t=1s for system：
According to the method for the present invention, to occurring to carry out with the Three Degree Of Freedom helicopter of time lag, modeling uncertainty and disturbance
Robust control.According to step 1)-step 5), wherein parameter value undetermined is as follows：Sliding-mode surface coefficient matrix G=[0 0 1], a
=0.8602, ad=0.5, b=9.902, solution obtain feedback of status coefficient matrix K=[1.6263 0.5438 4.9179].
Fig. 3-Fig. 5 is robust control result.Fig. 3 is the condition curve in the case of no external disturbance, and Fig. 4 is no external disturbance
In the case of control input curve, Fig. 5 is the simulation curve in the case of having external disturbance.
By Fig. 3-Fig. 5 it is found that when not having external disturbance, state is zeroed quickly, and controller output only exists
Disturbance has fluctuation when just generation, remaining period is almost a steady state value.There are external disturbance, output to have
Fluctuation, but as shown in figure 5, system is clearly that disclosure satisfy that given robustness index.Therefore, the method for the present invention can be very
Ensure the flight stability of a kind of Three Degree Of Freedom helicopter well.
Claims (1)
1. a kind of robust H of the Three Degree Of Freedom helicopter based on sliding formwork∞Control method, it is characterised in that：Consider that Three Degree Of Freedom is straight
The machine of liter is disturbed there are time lag and modeling uncertainty for its inside and outside, and the estimation of combining adaptive boundary and sliding formwork control propose
A kind of robust H∞Control method so that the undisturbed influence of helicopter keeps good flight quality.According to acquired straight
The model parameter of the machine of liter, a kind of long-pending type of design divide sliding-mode surface, weaken the influence of time lag, for the disturbance of system, design H∞Performance
Index, and then corresponding sliding formwork control ratio is designed, finally constitute robust H∞Controller.It comprises the following specific steps that：
Step 1) establishes the mathematical model of Three Degree Of Freedom helicopter：
Wherein x ∈ RnFor system state variables, u (t) is the difference of two propeller controls of helicopter input, and y is that can survey output, and τ is
Constant represents fixed time lag size, Δ A (t) and Δ Ad(t) it is that modeling is uncertain, g (x, t) is external disturbance, f (x, t)
For internal disturbance.
Step 2) is directed to above-mentioned Helicopter Flight Control System, carries out Integral Sliding Mode face design：
Design following Integral Sliding Mode face：
Matrix G ∈ Rm×nMeet the nonsingular conditions of GB, K ∈ Rm×nIt is undetermined constant matrix.
It enablesSolve Equivalent control law：
ueq=-(GB)-1G (g (x, t)+Δ A (t) x (t)+Δ Ad(t) x (t- τ))-Kx (t)-f (x, t) (3)
Equivalent control law is brought into original system (1), so that it may to obtain following standard sliding mode：
If step 2.1) exterior disturbs g=0, an abundant item of standard sliding mode asymptotically stability can be provided
Part.
It can be proved that if there is matrix Y ∈ Rm×n, positive definite matrix X ∈ Rm×nWith normal number ε1, ε2, ε3Make linear matrix inequality technique
Formula (5) is set up, then standard sliding mode (4) of the system (1) on sliding-mode surface (2) is asymptotically stable.
More than,And undetermined coefficient matrix K=YX of sliding-mode surface (2)-1。
If step 2.2) external disturbance g ≠ 0：
An interference attenuation index γ ＞ 0 is given, as long as then above-mentioned linear matrix inequality (5) is set up, then system output is full
Sufficient robust H∞Index γ.
Step 3) designs the continuous part control of sliding formwork control：
According to the design method of sliding formwork control, even all modeling uncertainty and disturbance of continuous part original system is zero, obtain
To the nominal system of absolute standard, then Equivalent control law at this time is solved, is the continuous part in complete control law, according to
Equivalent control law (3), it is 0 to enable uncertain and inside and outside disturbance therein, then can obtain the continuous part of sliding formwork control ratio
It is as follows：
ucon(t)=- Kx (t) (6)
The form is a kind of STATE FEEDBACK CONTROL.
Step 4) designs the discontinuous section in sliding formwork control：
Discontinuous section is generating discontinuous signal so that system can be moved along sliding-mode surface (2).
First, adaptive law is designed to estimate the size of internal disturbance：
Then the discontinuous portion of faults-tolerant control rule is divided into：
Wherein η is a small normal number.
Convolution (6) and (8) can obtain complete robust H∞Control law is as follows：
Step 5) selects suitable parameter according to the state of flight of quadrotor, completes to its robust H∞Control.
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| CN109116736A (en) * | 2018-09-19 | 2019-01-01 | 南京航空航天大学 | The fault tolerant control method of linear multi-agent system actuator failures based on sliding formwork |
| CN109298636A (en) * | 2018-11-21 | 2019-02-01 | 东北大学 | A kind of improved integral sliding mode control method |
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| CN113419552A (en) * | 2021-07-20 | 2021-09-21 | 中国计量大学 | Vector control method for transverse double-rotor unmanned aerial vehicle |
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| CN113419552A (en) * | 2021-07-20 | 2021-09-21 | 中国计量大学 | Vector control method for transverse double-rotor unmanned aerial vehicle |
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Application publication date: 20180731 |