CN108398884A - A kind of adaptive fusion method of the Uncertain time-delayed systems based on sliding formwork - Google Patents
A kind of adaptive fusion method of the Uncertain time-delayed systems based on sliding formwork Download PDFInfo
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Abstract
The invention discloses a kind of adaptive fusion methods of the Uncertain time-delayed systems based on sliding formwork.Consider that actuator failures, combining adaptive control and sliding formwork control occur there are input delay and external disturbance for quadrotor, proposes a kind of fault tolerant control method.Time lag look-ahead device is devised to handle the input delay of system.Actuator failures are solved the problems, such as using the full order decomposition method of matrix and the method for design sliding-mode surface.Adaptive sliding mode controller replaces fault detect and isolation mech isolation test to automatically update the influence for compensating actuator failures.Pass through adaptive H2The asymptotic stability of performance guarantee closed-loop system.The method of the present invention is by designing adaptive sliding mode controller, the on-line tuning of controller gain may be implemented, so that carried control law is optimal, it is effectively improved the control accuracy and response speed of quadrotor flight, fault controller foundation can be provided for the complicated quadrotor with actuator failures.The present invention is used for the faults-tolerant control of the quadrotor with input delay.
Description
Technical field
The present invention relates to a kind of adaptive fusion methods of the quadrotor based on sliding formwork, belong to aircraft control
Field processed.
Background technology
Typical four-rotor helicopter, four rotors are in crossing distribution in front, rear, left and right four direction.Each rotor
A direct current generator is all connected, control law controls the rotating speed of rotor by adjusting the rotating speed of direct current generator, to adjust four
The lift on direction vertex.In order to offset the reaction torque of rotor wing rotation generation, front and back is one group, and left and right is one group, and two groups of rotors are pressed
Anti- direction of taking a picture rotates, therefore by tail-rotor need not eliminate torque as conventional single rotor helicopter.Quadrotor is gone straight up to
Machine is a complicated controlled device, has the various complexity such as multiple-input and multiple-output and non-linear, close coupling, time lag
Problem, and the uncertain factors such as disturbance, engine luggine can be inevitably encountered in flight course, lack personnel's in addition
Real time management, helicopter once break down, it will cause serious consequence.Therefore fault-tolerant controller needs in the presence of system
Still has stronger robust Fault-Tolerant ability in the case of stagnant and uncertain.
Active tolerant control and passive fault tolerant control are broadly divided into the fault tolerant control method of quadrotor at present, by
There is prodigious advantage in design in passive fault tolerant control, since the structure and parameter of controller is fixed, there is no need to outer
The auxiliary of other hardware of boundary can obtain fault message by these known posterior infromations, be not necessarily to fault diagnosis link, because
This can accomplish dramatically cost-effective, while show good instantaneity, realisation and practicability.Passive fault-tolerant control control
System is not usually required to fault detection and diagnosis unit, only need to be by designing fixed controller, the failure that may occur to system
Leave certain nargin so that certain failures can not impact closed-loop system, can be achieved with fault-tolerant, reach final need
It asks.
It is non-since the sliding mode of sliding formwork control has complete adaptivity to systematic parameter perturbation and additional interference
Often it is suitble to the passive fault tolerant control problem of processing four-rotor helicopter flight control system.Its control is discontinuous, controls process
In, the structure of closed-loop system ceaselessly changes, and system mode is forced to be moved along pre-designed sliding-mode surface, gradually " cunning " to
State balance point, i.e. Asymptotic Stability.Its most important advantage is once system state amount reaches sliding-mode surface, and system is not just by parameter
The influence of variation and external disturbance.Sliding formwork control is widely used in flight control system, is the faults-tolerant control of flight control system
Provide new approaches.
In order to which time lag present in quadrotor flight control system and uncertainty is effectively treated, leaf thinks meaningful proposition
A kind of robust Fault-Tolerant Control algorithm.Sun Xinzhu proposes a kind of reliable tracking for the uncertain system for being unsatisfactory for matching condition
Controller, Jia Xinchun then have studied the reliable guaranteed cost problem of uncertain linear time-delay system.But existing method is mostly that structure is solid
The passive fault tolerant control of order one is difficult to have good control effect, therefore the present invention has very to complicated flight control system
Good practicability.
Invention content
Goal of the invention：For the above-mentioned prior art, a kind of adaptive appearance of the Uncertain time-delayed systems based on sliding formwork is proposed
Wrong control method devises time lag look-ahead device and handles the input delay of system.Using the full order decomposition method of matrix and
The method of sliding-mode surface is designed to solve the problems, such as actuator failures.Adaptive sliding mode controller replaces fault detect and isolation mech isolation test certainly
The influence of dynamic update compensation actuator failures.
Technical solution：A kind of adaptive fusion method of the quadrotor based on sliding formwork control, feature exist
In：Considering quadrotor, there are input delay, external disturbance and actuator failures, and combining adaptive controls and sliding formwork control
System, proposes a kind of fault tolerant control method so that aircraft can continue to safe flight after actuator failures occur.According to being obtained
The model parameter of the aircraft taken is asked using the method for the full order decomposition method of matrix and design sliding-mode surface to solve actuator failures
Topic, is finally reached the purpose of faults-tolerant control.It comprises the following specific steps that：
Step 1) obtains the Controlling model of quadrotor：
Z (t)=C1X (t),
Y (t)=Cx (t), (1)
Wherein, x=[x1 x2 x3]TFor system state variables, by taking the control of the position of quadrotor X-direction as an example,
Indicate that position, speed and the Actuator dynamic in X-direction, u (t) input in order to control respectively, d is time lag, ω (t) ∈ RnIt is outer
Portion interferes, and z (t) is to adjust to export, and y (t) is that can survey output, and Δ A (t) is time-varying parameter uncertainties, and form isF
(x, t) does not know but for owning (x, t) ∈ Rn×RmMeet.
Step 2) devises corresponding time lag look-ahead device for the above quadrotor flight control system with input delay
Model：
To improve the accuracy of status predication, following amendment has been carried out：
Wherein, yp(t) it is the output error of real system.
Because proposing a kind of design method of advanced sliding mode controller, consider that ambiguous model is
z*(t)=C1x*(t)
y*(t)=Cx*(t) (4)
Wherein, d (x*, u, t) and it is uncertainty in system.Assuming that uncertainty d (x*, u, t) and it is bounded, it upper
Bound function dmax() can be estimated as | d (x*, u, t) |≤dmax(x*, t).
The problem of step 3) is due to faults-tolerant control, the failure that we formulate include that actuator interrupts, and loss in efficiency and are blocked.
It allowsIndicate the fault-signal of the i-th actuator in jth malfunctioning module.Then, the fault model we described is：
Wherein, WithFor unknown constant, index j indicates jth malfunctioning module, and L is malfunctioning module
Summation.For each malfunctioning module,WithThe respectively known upper bound and lower bound.usi(t) it is holding for unknown bounded time-varying
Row device blocks failure.
It willIt is defined as：
Step 4) considers actuator failures situation in Uncertain time-delayed systems, designs sliding mode controller：
uF(t)=ρ u (t)+σ us(t) (7)
Wherein, us(t)=[us1(t), us2(t) ..., usn(t)]T,
Therefore, dynamical system (4) is converted into the system with actuator failures and is：
z*(t)=C1x*(t)
y*(t)=Cx*(t) (8)
Step 5) devises the sliding mode controller based on order compensator to realize fault-tolerant target：
Wherein, AK∈Rq×q, CK∈Rq×q, BK∈Rq×l, DK∈Rq×l.Non-linear discontinuous vector v (t) is not true for handling
Determine item and actuator failures.
In conjunction with (8) and (9), obtaining closed-loop system is：
Wherein,
Wherein,For known function, k1＜ 1.
The main purpose of research is to ensure closed-loop system Asymptotic Stability under actuator failures and perturbation action.It is dry from outside
Disturb ω0(t) it arrives and adjusts output z0(t), inequality below is set up：
Wherein, γ0Known to ＞ 0.
Step 6) combining step 2) and step 3), design complete faults-tolerant control rule：
Step 6.1) designs sliding-mode surface first according to sliding mode controller design method：
ξ=0 α=F (13)
Wherein, matrix F ∈ Rq×q.It can be proved that the system sliding mode on the sliding-mode surface is asymptotically stability.
Step 6.2) defines Φ0∈Rn×(n-l),
Wherein, Φ0B2v=0,ζ1(t)∈Rq, ζ2(t)∈Rn,
It obtains
Lemma and equivalent control method are mended using Schur, obtaining Equivalent control law is：
Design dynamic compesated control rule as follows：
Wherein,
∈ is the positive scalar of design, parameterWithThe upper bound for being failure impact factor σ respectively and blocking failureAssuming that α
=0 v (t)=0 is suitable for control methods.
Wherein,
It illustrates, adaptive law is：
Wherein,And σsi0Respectively in initial valueWithLocate bounded.Constant and adaptive law gain are to be based on actually answering
Design.
Step 7) selects suitable parameter according to the state of flight of quadrotor, completes to its faults-tolerant control.Have
Beneficial effect：A kind of adaptive fusion method of quadrotor based on sliding formwork proposed by the present invention, devises time lag
Look-ahead device handles the input delay of system, is solved using the full order decomposition method of matrix and the method for design sliding-mode surface
Actuator failures problem, adaptive sliding mode controller substitution fault detect and isolation mech isolation test automatically update compensation actuator failures
It influences, finally constitutes complete fault-tolerant controller.
It has the following advantages that：
(1) there is the adaptive sliding mode fault tolerant control method that sliding formwork switches item by design so that flight control system has
There is better robustness；
(2) input delay of system is handled using time lag look-ahead device, fully takes into account quadrotor
The case where there may be time lags during practical flight so that the design of controller has better practicability；
(3) fault detect and isolation mech isolation test is replaced to automatically update compensation quadrotor using adaptive sliding mode controller
The parameter of the influence of actuator failures, faults-tolerant control rule automatically updates so that security of system higher, control effect is more preferably.
Method therefor of the present invention has certain practical application valence as a kind of fault tolerant control method of quadrotor
Value, it is easy to accomplish, fault-tolerant ability is strong, can effectively improve the flight safety of quadrotor.This method operability is strong,
Application is wide.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the quadrotor simulating experimental system of Quanser；
Fig. 3 is quadrotor attitude motion schematic diagram；
Fig. 4 is four-rotor aircraft control system functional block diagram；
Fig. 5 is the dynamic respond curve of X-direction；
Fig. 6 is the velocity-response curve of X-direction；
Fig. 7 is Actuator dynamic response curve；
Fig. 8 is control input response curve；
Fig. 9 is simulink analogous diagrams.
Specific implementation mode
Further explanation is done to the present invention below in conjunction with the accompanying drawings.
As shown in Figure 1, consider quadrotor in the case that actuator occurs there are input delay and external disturbance therefore
Barrier, combining adaptive control and sliding formwork control, propose a kind of fault tolerant control method so that aircraft is after occurring actuator failures
It can continue to safe flight.Actuator failures, adaptive sliding mode control are solved using the full order decomposition method of matrix and sliding-mode surface design method
Device substitution fault detect processed and isolation mech isolation test automatically update the influence of compensation actuator failures, are finally reached the mesh of faults-tolerant control
's.It comprises the following specific steps that：
Step 1) obtains the Controlling model of quadrotor：
Z (t)=C1X (t),
Y (t)=Cx (t), (1)
Wherein, x=[x1 x2 x3]TFor system state variables, by taking the control of the position of quadrotor X-direction as an example,
Indicate that position, speed and the Actuator dynamic in X-direction, u (t) input in order to control respectively, d is time lag, ω (t) ∈ RnIt is outer
Portion interferes, and z (t) is to adjust to export, and y (t) is that can survey output, and Δ A (t) is time-varying parameter uncertainties, and form isF
(x, t) does not know but for owning (x, t) ∈ Rn×RmMeet.
Step 2) devises corresponding time lag look-ahead device for the above quadrotor flight control system with input delay
Model：
To improve the accuracy of status predication, following amendment has been carried out：
Wherein, yp(t) it is the output error of real system.
Because proposing a kind of design method of advanced sliding mode controller, consider that ambiguous model is
z*(t)=C1x*(t)
y*(t)=Cx*(t) (4)
Wherein, d (x*, u, t) and it is uncertainty in system.Assuming that uncertainty d (x*, u, t) and it is bounded, it upper
Bound function dmax() can be estimated as | d (x*, u, t) |≤dmax(x*, t).
The problem of step 3) is due to faults-tolerant control, the failure that we formulate include that actuator interrupts, and loss in efficiency and are blocked.
It allowsIndicate the fault-signal of the i-th actuator in jth malfunctioning module.Then, the fault model we described is：
Wherein, WithFor unknown constant, index j indicates jth malfunctioning module, and L is malfunctioning module
Summation.For each malfunctioning module,WithThe respectively known upper bound and lower bound.usi(t) it is holding for unknown bounded time-varying
Row device blocks failure.
It willIt is defined as：
Step 4) considers actuator failures situation in Uncertain time-delayed systems, designs sliding mode controller：
uF(t)=ρ u (t)+σ us(t) (7)
Wherein, us(t)=[us1(t), us2(t) ..., usn(t)]T,
Therefore, dynamical system (4) is converted into the system with actuator failures and is：
z*(t)=C1x*(t)
y*(t)=Cx*(t) (8)
Step 5) devises the sliding mode controller based on order compensator to realize fault-tolerant target：
Wherein, AK∈Rq×q, CK∈Rq×q, BK∈Rq×l, DK∈Rq×l.Non-linear discontinuous vector v (t) is not true for handling
Determine item and actuator failures.
In conjunction with (8) and (9), obtaining closed-loop system is：
Wherein,
Wherein,For known function, k1＜ 1.
The main purpose of research is to ensure closed-loop system Asymptotic Stability under actuator failures and perturbation action.It is dry from outside
Disturb ω0(t) it arrives and adjusts output z0(t), inequality below is set up：
Wherein, γ0Known to ＞ 0.
Step 6) combining step 2) and step 3), design complete faults-tolerant control rule：
Step 6.1) designs sliding-mode surface first according to sliding mode controller design method：
ξ=0 α=F (13)
Wherein, matrix F ∈ Rq×q.It can be proved that the system sliding mode on the sliding-mode surface is asymptotically stability.
Step 6.2) defines Φ0∈Rn×(n-l),
Wherein, Φ0B2v=0,ζ1(t)∈Rq, ζ2(t)∈Rn,
It obtains
Lemma and equivalent control method are mended using Schur, obtaining Equivalent control law is：
Design dynamic compesated control rule as follows：
Wherein,
∈ is the positive scalar of design, parameterWithThe upper bound for being failure impact factor σ respectively and blocking failureAssuming that α
=0 v (t)=0 is suitable for control methods.
Wherein,
It illustrates, adaptive law is：
Wherein,WithRespectively in initial valueWithLocate bounded.Constant and adaptive law gain are to be based on actually answering
Design.
Step 7) selects suitable parameter according to the state of flight of quadrotor, completes to its faults-tolerant 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, without departing from the principle of the present invention, several improvement and polishing can also be made, these are improved and polishing is also answered
It is considered as protection scope of the present invention,
Illustrate the validity of embodiment with real case emulation below.
Using the Qball-X4 four-rotor helicopter semi-physical simulation platforms of Canadian quanser companies production as specific
Algorithm experimental simulation object.Fig. 2 is the quadrotor simulating experimental system of Quanser, and Fig. 3 is quadrotor appearance
State moves schematic diagram.As seen from Figure 3, quadrotor relative to ground there are six dimension variables (X, Y, Z, ψ, θ,
φ), wherein first three variable is location variable, the i.e. position relative to inertial system center.Three variables are gone straight up to for quadrotor afterwards
The posture Eulerian angles of machine：Yaw ψ, pitching θ, rolling φ.As can be seen that quadrotor has 6 controlled volumes and 4 controls
Amount, thus be a typical underactuated control system, i.e., each control component can have effect to different controlled volumes simultaneously, couple
Degree is higher, therefore its stability is poor, and control difficulty is also larger.Without loss of generality, the displacement of X-direction, speed are selected here
Quantity of state with Actuator dynamic as system carries out emulation experiment to it.
The state-space model of quadrotor is as follows：
Write as the state-space expression of canonical form：
Wherein, it inputs, is exported as axial displacement amount in order to control.In view of quadrotor is one typical complicated controlled
Object since control law calculates complexity, while being limited by factors such as communication speed, remote control and network transmissions again, because
This its quantity of state existence time postpones.Quadrotor is considered further that in flight course, its execution is led to by various factors
Device breaks down, and introduces actuator failures and indicates that actuator input changes, then complete quadrotor position control
Model is：
Z (t)=C1X (t),
Y (t)=Cx (t),
The organism parameter value of the quadrotor is as shown in table 1：
1 organism parameter numerical tabular of table
| Parameter | It is worth unit |
| K | 120N |
| ω | 15rad/sec |
| M | 1.4kg |
Then it is as follows that each coefficient matrix in system can be obtained：
It is measured according to experiment, time lag d is set as 2s.Assuming that quadrotor encounters the prominent of following form in flight course
Send out failure：
The quantity of state vector of initial time system is taken to be：
x0=[x1 x2 x3]T=[0.05 1 0.25]T
According to the method for the present invention, faults-tolerant control is carried out to the quadrotor that actuator failures occur, Fig. 5 is fault-tolerant control
Result processed.It is the response curve of X-direction displacement, speed and Actuator dynamic respectively in Fig. 5, Fig. 6 is the curve of control input.
As shown in Figure 5, when system occur actuator failures after, the present invention faults-tolerant control under, the displacement of aircraft X-axis and
Speed can tend towards stability in a relatively short period of time, and fast response time, and overshoot is small, that is to say, that after system jam
Aircraft remains able to maintain original state of flight, avoids the generation of accident.When there are time lags and actuator failures for system
When, adaptive sliding mode faults-tolerant control restrains amplitude of variation very little, i.e. faults-tolerant control rule can ensure the control of aircraft well
Precision and safety.
Claims (1)
1. a kind of adaptive fusion method of the quadrotor based on sliding formwork control, it is characterised in that：Consider four rotations
There are input delay, external disturbance and actuator failures for rotor aircraft, and combining adaptive controls and sliding formwork control, proposes a kind of appearance
Wrong control method so that aircraft can continue to safe flight after actuator failures occur.According to acquired aircraft
Model parameter solves actuator failures, adaptive sliding mode controller substitution using the full order decomposition method of matrix and sliding-mode surface design method
Fault detect and isolation mech isolation test automatically update the influence of compensation actuator failures, are finally reached the purpose of faults-tolerant control.Including such as
Lower specific steps：
Step 1) obtains the Controlling model of quadrotor：
Wherein, x=[x1 x2 x3]TFor system state variables, by taking the control of the position of quadrotor X-direction as an example, difference
Indicate that position, speed and the Actuator dynamic in X-direction, u (t) input in order to control, d is time lag, ω (t) ∈ RnIt is dry for outside
It disturbs, z (t) is to adjust to export, and y (t) is that can survey output, and Δ A (t) is time-varying parameter uncertainties, and form isF (x,
T) do not know but for owning (x, t) ∈ Rn×RmMeet.
Step 2) devises corresponding time lag look-ahead device mould for the above quadrotor flight control system with input delay
Type：
To improve the accuracy of status predication, following amendment has been carried out：
Wherein, yp(t) it is the output error of real system.
Because proposing a kind of design method of advanced sliding mode controller, consider that ambiguous model is
Wherein, d (x*, u, t) and it is uncertainty in system.Assuming that uncertainty d (x*, u, t) and it is bounded, its upper bound letter
Number dmax() can be estimated as | d (x*, u, t) |≤dmax(x*, t).
The problem of step 3) is due to faults-tolerant control, the failure that we formulate include that actuator interrupts, and loss in efficiency and are blocked.It allows
Indicate the fault-signal of the i-th actuator in jth malfunctioning module.Then, the fault model we described is：
Wherein, WithFor unknown constant, index j indicates jth malfunctioning module, and L is the total of malfunctioning module
With.For each malfunctioning module,WithThe respectively known upper bound and lower bound.usi(t) be unknown bounded time-varying actuator
Block failure.
It willIt is defined as：
Step 4) considers actuator failures situation in Uncertain time-delayed systems, designs sliding mode controller：
uF(t)=ρ u (t)+σ us(t) (7)
Wherein, us(t)=[us1(t), us2(t) ..., usn(t)]T,
Therefore, dynamical system (4) is converted into the system with actuator failures and is：
Step 5) devises the sliding mode controller based on order compensator to realize fault-tolerant target：
Wherein, AK∈Rq×q, CK∈Rq×q, BK∈Rq×l, DK∈Rq×l.Non-linear discontinuous vector v (t) is for handling indeterminate
And actuator failures.
In conjunction with (8) and (9), obtaining closed-loop system is：
Wherein,
Wherein,For known function, k1＜ 1.
The main purpose of research is to ensure closed-loop system Asymptotic Stability under actuator failures and perturbation action.From external disturbance ω0
(t) it arrives and adjusts output z0(t), inequality below is set up：
Wherein, γ0Known to ＞ 0.
Step 6) combining step 2) and step 3), design complete faults-tolerant control rule：
Step 6.1) designs sliding-mode surface first according to sliding mode controller design method：
ξ=0 α=F (13)
Wherein, matrix F ∈ Rq×q.It can be proved that the system sliding mode on the sliding-mode surface is asymptotically stability.
Step 62) defines Φ0∈Rn×(n-l),
Wherein, Φ0B2v=0,ζ1(t)∈Rq, ζ2(t)∈Rn,
It obtains
Lemma and equivalent control method are mended using Schur, obtaining Equivalent control law is：
Design dynamic compesated control rule as follows：
Wherein,
∈ is the positive scalar of design, parameterWithThe upper bound for being failure impact factor σ respectively and blocking failureAssuming that α=0 item v
(t)=0 it is suitable for control methods.
Wherein,
It illustrates, adaptive law is：
Wherein,And σsi0Respectively in initial valueWithLocate bounded.Constant and adaptive law gain are based on practical application
Design.
Step 7) selects suitable parameter according to the state of flight of quadrotor, completes to its faults-tolerant control.
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