CN108490783A - Rigid aerospace vehicle finite time self-adaptive fault-tolerant control method based on enhanced double-power approach law and fast terminal sliding mode surface - Google Patents

Rigid aerospace vehicle finite time self-adaptive fault-tolerant control method based on enhanced double-power approach law and fast terminal sliding mode surface Download PDF

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CN108490783A
CN108490783A CN201810326974.7A CN201810326974A CN108490783A CN 108490783 A CN108490783 A CN 108490783A CN 201810326974 A CN201810326974 A CN 201810326974A CN 108490783 A CN108490783 A CN 108490783A
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陈强
陶玫玲
何熊熊
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Zhejiang University of Technology ZJUT
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Abstract

A finite-time self-adaptive fault-tolerant control method for a rigid aerospace vehicle based on an enhanced double-power approximation law and a fast terminal sliding mode surface is used for designing a self-adaptive fast terminal sliding mode composite control scheme by utilizing a sliding mode control method based on the enhanced double-power approximation law and combining self-adaptive control aiming at the problem of attitude stability of an aircraft actuator with centralized uncertainty under the fault. According to the scheme, on one hand, the uncertain and disturbed upper bound is estimated and compensated by using a self-adaptive technology, and on the other hand, the finite time attitude stability of the aircraft system is realized by using the rapidity and the strong robustness of a rapid terminal sliding mode. The invention provides a control method which can reduce the buffeting problem of a sliding mode surface and control moment, and can realize the consistency of limited time of a system and final bounding under the condition that the system has uncertainty and interference.

Description

Rigid space travel based on enhanced double power Reaching Laws and fast terminal sliding-mode surface Device finite time adaptive fusion method
Technical field
The present invention relates to a kind of rigid aerospace crafts based on enhanced double power Reaching Laws and fast terminal sliding-mode surface Finite time adaptive fusion method, is especially in the presence of external interference and the probabilistic aircraft of rotator inertia matrix is held Attitude control method under row device failure.
Background technology
Whether attitude control system works normally and will directly determine as one of spacecraft important subsystem, its reliability Can determine spacecraft normally complete set space mission.However the severe factors such as space environment and components aging cause spacecraft Component inevitably breaks down.If Spacecraft malfunction cannot in time, correctly be detected, positions, be isolated and carry out phase Fault-tolerant processing is answered, then gesture stability performance will be remarkably decreased or system stability will be destroyed, and will cause entirely to navigate when serious Its mission failure.Therefore the autonomous Fault Tolerance Control Technology of spacecraft attitude control system failure is the base of spacecraft autonomous operation technology Plinth, it has become current aerospace engineering field one of project urgently to be resolved hurrily, has to raising spacecraft task completion rate great Theoretical and realistic meaning.
Variable-structure control thought is a kind of comprehensive designing method of modern control theory.Structure changes are with its unique robustness The advantages that, provide a kind of promising control system synthesis method for uncertain system.It is proposed based on sliding mode control theory The concept of " Reaching Law " includes mainly：Constant speed Reaching Law, exponentially approaching rule, power Reaching Law.Sliding formwork control is broadly divided into two Step：1) design control law enables system mode to be reached in finite time on designed sliding surface；2) work as system mode After reaching sliding surface, which can make state not leave sliding surface and can slide into origin along sliding surface.In recent years Come, domestic and foreign scholars have carried out it extensive research.
Self adaptive control as adapts to uncertainty plant and interferes the variation of dynamic characteristic, control system that can move The characteristic of oneself is voluntarily corrected in the process.The elementary object of self adaptive control is when object is in the presence of uncertain or parameter unknown When variation, remain to keep reliable system performance.Self adaptive control is divided into Indirect adaptive control and direct adaptive control two Major class.Indirect adaptive control needs systematic parameter on-line identification, then designs suitable control law on this basis；Directly from Suitable solution is not necessarily to Parameter identification, and controller parameter can directly update.Most common self adaptive control mode is to pass through Real time correction parameter achievees the purpose that adaptation parameter adaptive control.Robust control can also handle the uncertain of model parameter Property, there is learning ability difference lies in self adaptive control with adaptive, during adaptive, adaptive controller can not It is disconnected to improve the performance of itself.The complex control that some conventional control methods cann't be solved can be solved using self adaptive control to ask Topic, can significantly lifting system lasting accuracy and tracking accuracy.
Invention content
In order to solve the nonlinear problem in existing attitude of flight vehicle kinematics and dynamics and realize external disturbance Inhibit control, and reduce and buffet problem present in sliding formwork control, the present invention provides a kind of based on enhanced double power Reaching Laws It is and not true in system presence with the rigid aerospace craft finite time adaptive fusion method of fast terminal sliding-mode surface In the case of qualitative and interference, the control method of the finite time uniform ultimate bounded of system is realized.
In order to solve the above-mentioned technical problem the technical solution proposed is as follows：
A kind of rigid aerospace craft finite time based on enhanced double power Reaching Laws and fast terminal sliding-mode surface from Fault tolerant control method is adapted to, is included the following steps：
Step 1, establish the kinematics and dynamics modeling of attitude of flight vehicle fault-tolerant control system, initialization system mode with And control parameter, process are as follows：
The kinetic model expression-form of 1.1 aircraft manufacturing technology systems is：
Wherein, ω,It is the angular speed and angular acceleration of aircraft respectively；Ω∈RnIt is the angle speed of counteraction flyback Degree；×It is oeprator, by oeprator×Applied to a=[a1,a2,a3]TObtain a×=[0 ,-a3,a2；a3,0,-a1；-a2,a1, 0]；J∈R3×3It is the rotator inertia matrix of aircraft；Jω=diag ([Jω1；Jω2,...,Jωn])∈Rn×nIt is counteraction flyback Rotator inertia matrix；D∈RnIt is counteraction flyback control moment allocation matrix and row full rank；u∈R3With d (t) ∈ R3It is control Input and external disturbance；
The kinematics model expression-form of 1.2 aircraft manufacturing technology systems is：
Wherein, unit quaternionIt is attitude of flight vehicle quaternary number and expires Foot It is q respectively0And qvDerivative；I3∈R3×3It is 3 × 3 unit matrixs；
1.3 assume rotator inertia matrix J=J0+ Δ J, wherein J0The nominal section of J and uncertain portion are indicated respectively with Δ J Point；And list-directed input list is shown asWherein E (t)=diag ([e1(t),e2(t),...,en (t)])∈Rn×nIt is actuator control efficiency matrix；0≤ei(t)≤1 it is the efficiency factor of i-th of counteraction flyback；It is additional actuators fault vector；uc=[uc1,uc2,...,ucn]T∈RnIt is n-th of actuator Control moment vector；Then formula (1) is write as again：
1.4 enablingSubstitution formula (2), obtains：
Wherein,
Differential is carried out to formula (5), is obtained：
Wherein,Respectively P and qvFirst derivative and second dervative；
After formula (5), formula (6) are substituted into formula (4), in both members while premultiplication PTIt obtains：
Wherein, J*=PTJ0P and due to rotator inertia matrix J*Skew symmetry positive definite matrix, then matrixMeet with Oblique symmetric relation：
J simultaneously*Meet with lower inequality：
Wherein, JminAnd JmaxIt is normal number, indicates lower bound and the upper bound of J*； It is interference and probabilistic set, meets | | Td||≤υ0Φ, Φ=1+ | | ω | |+ ||ω||2And υ0It is normal number；
Step 2, in the case where not known there are rotary inertia and external disturbance, the gesture stability system based on aircraft System, the sliding-mode surface of design, process are as follows：
2.1 selection fast terminal sliding-mode surface s ∈ R3For：
Wherein, λ1＞ 0；λ2＞ 0；a1＞ a2＞ 1；Function sig (x)r=[| x1|rsign(x1),|x2|rsign(x2),|x3 |rsign(x3)]T；Sign () is sign function；
To formula (10) derivation, obtain：
Wherein,For the first derivative of s；|α(qv) | it is α (qv) absolute value；
If α (qv)=0 and β (qv) ≠ 0, due to bearing fractional powerPresence will produce singularity, it is unusual to avoid The generation of property, the first derivative of s are changed into：
Wherein, qve∈R3It is defined as：
Wherein, ∈ is the constant of very little；| ∈ | it is the absolute value of ∈；
Then, it is obtained by formula (7), formula (10) and formula (12)：
Wherein,
Step 3, enhanced double power Reaching Laws are designed, process is as follows：
3.1, which define enhanced double power Reaching Laws, is：
Wherein, r1＞ r2＞ 1；k1＞ 0；k2＞ 0；0 ＜ p ＜ 1； | | s | | it is the norm of s；
Step 4, finite time adaptive sliding mode controller is designed, process is as follows：
4.1 consideration finite time adaptive sliding mode controllers are designed to：
Wherein, | | P | | it is the norm of P；| | F | | it is the norm of F；| | Ps | | it is the norm of Ps；| | s | | it is the norm of s；Positive definite matrix DEDTMeet：0 ＜ e0≤min{λmin(DEDT),1}；λmin() indicates square The minimal eigenvalue of battle array；e0It is a normal number；For γiEstimation；I=0,1,2；
The more new law of 4.2 design auto-adaptive parameters：
Wherein, ciAnd εiIt is normal number；ForFirst derivative；I=0,1,2；
4.3 design liapunov functions：
Wherein,sTIt is the transposition of s；
Derivation is carried out to formula (22), is obtained intoOrForm；Simultaneously to formula (23) Derivation is carried out, is obtainedForm；Based on result above, decision-making system is that finite time is consistent Ultimate boundness；Wherein,
Based on the above analysis, sliding-mode surface s, attitude of flight vehicle quaternary number qvWith angular velocity omega be local finite time consistency most Whole bounded.
The present invention is based under the factor of aircraft actuator failures, rotator inertia matrix uncertainty and external interference The rigid aerospace craft finite time adaptive fusion method of enhanced double power Reaching Laws and fast terminal sliding-mode surface, Realization system stability contorting reduces the buffeting of sliding formwork control, ensures that system realizes finite time uniform ultimate bounded.
The present invention technical concept be：For with the attitude stabilization concentrated under probabilistic aircraft actuator failures Problem is designed a kind of adaptive using the sliding-mode control based on enhanced double power Reaching Laws in conjunction with self adaptive control The compound faults-tolerant control scheme of fast terminal sliding formwork.The program on the one hand using adaptive technique to the upper bound that is uncertain and disturbing into Row estimation and compensation, on the other hand, using the rapidity and strong robustness of fast terminal sliding formwork, to realize aerocraft system Finite time attitude stabilization.The accurate estimation of adaptive technique and the application of enhanced double power Reaching Laws effectively inhibit sliding formwork Buffeting problem in control.The present invention provides a kind of buffeting problem that can reduce sliding-mode surface and control moment, and in system In the case of in the presence of uncertain and interference, the control method of the finite time uniform ultimate bounded of system is realized.
Advantages of the present invention is：It reduces and buffets, it is uncertain and extraneous in aircraft actuator failures, rotator inertia matrix In the case of interference, the finite time uniform ultimate bounded of system is realized.
Description of the drawings
Fig. 1 is the sliding-mode surface schematic diagram of the present invention.
Fig. 2 is the control moment schematic diagram of the present invention.
Fig. 3 is the attitude of flight vehicle quaternary number schematic diagram of the present invention.
Fig. 4 is the angular speed schematic diagram of the present invention.
Fig. 5 is the parameter Estimation schematic diagram of the present invention.
Fig. 6 is the control flow schematic diagram of the present invention.
Specific implementation mode
The present invention will be further described below in conjunction with the accompanying drawings.
Referring to Fig.1~Fig. 6, a kind of rigid space travel based on enhanced double power Reaching Laws and fast terminal sliding-mode surface Device finite time adaptive fusion method, includes the following steps：
Step 1, establish the kinematics and dynamics modeling of attitude of flight vehicle fault-tolerant control system, initialization system mode with And control parameter, process are as follows：
The kinetic model expression-form of 1.1 aircraft manufacturing technology systems is：
Wherein,It is the angular speed and angular acceleration of aircraft respectively；Ω∈RnIt is the angle speed of counteraction flyback Degree；×It is oeprator, by oeprator×Applied to a=[a1,a2,a3]TObtain a×=[0 ,-a3,a2；a3,0,-a1；-a2,a1, 0]；J∈R3×3It is the rotator inertia matrix of aircraft；Jω=diag ([Jω1；Jω2,...,Jωn])∈Rn×nIt is counteraction flyback Rotator inertia matrix；D∈RnIt is counteraction flyback control moment allocation matrix and row full rank；u∈R3With d (t) ∈ R3It is control Input and external disturbance；
The kinematics model expression-form of 1.2 aircraft manufacturing technology systems is：
Wherein, unit quaternionIt is attitude of flight vehicle quaternary number and expires Foot It is q respectively0And qvDerivative；I3∈R3×3It is 3 × 3 unit matrixs；
1.3 assume rotator inertia matrix J=J0+ Δ J, wherein J0The nominal section of J and uncertain portion are indicated respectively with Δ J Point；And list-directed input list is shown asWherein E (t)=diag ([e1(t),e2(t),...,en (t)])∈Rn×nIt is actuator control efficiency matrix；0≤ei(t)≤1 it is the efficiency factor of i-th of counteraction flyback；It is additional actuators fault vector；uc=[uc1,uc2,...,ucn]T∈RnIt is n-th of actuator Control moment vector；Then formula (1) is write as again：
1.4, in order to more easily describe the attitude dynamics controller design of aircraft, enable Substitution formula (2), obtains：
Wherein,
Differential is carried out to formula (5), is obtained：
Wherein,Respectively P and qvFirst derivative and second dervative；
After formula (5), formula (6) are substituted into formula (4), in both members while premultiplication PTIt obtains：
Wherein, J*=PTJ0P and since rotator inertia matrix J * is skew symmetry positive definite matrix, then matrixMeet with Oblique symmetric relation：
J* meets with lower inequality simultaneously：
Wherein, JminAnd JmaxIt is normal number, indicates lower bound and the upper bound of J*；
It is interference and probabilistic set, expires Foot | | Td||≤υ0Φ, Φ=1+ | | ω | |+| | ω | |2And υ0It is normal number；
Step 2, in the case where not known there are rotary inertia and external disturbance, the gesture stability system based on aircraft System, the sliding-mode surface of design, process are as follows：
2.1 selection fast terminal sliding-mode surface s ∈ R3For：
Wherein, λ1＞ 0；λ2＞ 0；a1＞ a2＞ 1；Function sig (x)r=[| x1|rsign(x1),|x2|rsign(x2),|x3 |rsign(x3)]T；Sign () is sign function；
To formula (10) derivation, obtain：
Wherein,For the first derivative of s；|α(qv) | it is α (qv) absolute value；
If α (qv)=0 and β (qv) ≠ 0, due to bearing fractional powerPresence will produce singularity, it is unusual to avoid The generation of property, the first derivative of s are changed into：
Wherein, qve∈R3It is defined as：
Wherein, ∈ is the constant of very little；| ∈ | it is the absolute value of ∈；
Then, it is obtained by formula (7), formula (10) and formula (12)：
Wherein,
Step 3, enhanced double power Reaching Laws are designed, process is as follows：
3.1, which define enhanced double power Reaching Laws, is：
Wherein, r1＞ r2＞ 1；k1＞ 0；k2＞ 0；0 ＜ p ＜ 1； | | s | | it is the norm of s；
Step 4, finite time adaptive sliding mode controller is designed, process is as follows：
4.1 considering that finite time adaptive sliding mode controller is designed to：
Wherein, | | P | | it is the norm of P；| | F | | it is the norm of F；| | Ps | | it is the norm of Ps；| | s | | it is the norm of s； γ0=υ0；Positive definite matrix DEDTMeet：0 ＜ e0≤min{λmin(DEDT),1}；λmin() indicates The minimal eigenvalue of matrix；e0It is a normal number；For γiEstimation；I=0,1,2；
The more new law of 4.2 design auto-adaptive parameters：
Wherein, ciAnd εiIt is normal number；ForFirst derivative；I=0,1,2；
4.3 design liapunov functions：
Wherein,sTIt is the transposition of s；
Based on the above analysis, sliding-mode surface s, attitude of flight vehicle quaternary number qvWith angular velocity omega be local finite time consistency most Whole bounded.
For the validity of verification institute extracting method, The present invention gives based on enhanced double power Reaching Laws and fast terminal cunning The rigid aerospace craft finite time adaptive fusion method simulating, verifying of die face, it is as follows：
Reaching Law relevant parameter is：k1=10, k2=0.5, r1=1.5, r2=0.1, μ=0.01, χ=5,P= 0.9,System external disturbance is：D (t)=0.01 × [sin (0.8t), cos (0.5t), cos (0.3t)]TN·m；Sliding formwork Face parameter is：a1=2, a2=1.1, λ1=0.35, λ2=0.01；Adaptive updates rule parameter be：ε0=0.01, ε1= 0.001, ε2=0.001,c0=0.05, c1=0.25, c2=0.5； Attitude of flight vehicle system actual parameter is：Jω=0.015I4kg·m2, J0=diag ([140,120,130]) kgm2, Δ J= diag[sin(0.1t),2sin(0.2t),3sin(0.3t)]kg·m2, ω (0)=[0,0,0]TRad/s, qv(0)=[0.3 ,- 0.3,0.2]T, q0(0)=0.8832；Actuator Fault-tolerant Model is：Additional moment of first reagentia wheel after 25 seconds：Second reagentia wheel is original normal control torque efficiencies after 5 seconds 50%；Third reagentia wheel reduced by 60% efficiency at 5 seconds to 30 seconds, and after 35 seconds, there are additional moments to be：4th reagentia wheel fails between 10 seconds to 30 seconds；In order to avoid The discontinuous term of formula (17) and formula (18)WithCaused by buffet problem, in simulations apply continuous itemsWithIt replaces, wherein ξ is normal number, ξ=0.002.
Fig. 1 and Fig. 2 is based respectively on sliding-mode surface and control moment response schematic diagram under the present invention.The convergence time of sliding-mode surface is 10 seconds, the buffeting range of control moment was in 0.05Nm.
Attitude of flight vehicle quaternary number and angular speed response schematic diagram difference based on the present invention are as shown in Figure 3 and Figure 4.Posture The convergence time of quaternary number is 12 seconds, and the convergence time of angular speed is 12 seconds.The result shows that this method can realize finite time one Cause ultimate boundness.
Parameter Estimation response schematic diagram based on the present invention is as shown in Figure 5.
In conclusion the method for the present invention can realize good control performance, and gathered around on sliding-mode surface and control moment There is the ability for preferably reducing and buffeting.
Described above is the excellent effect of optimization that one embodiment that the present invention provides is shown, it is clear that the present invention is not only It is limited to above-described embodiment, in the premise without departing from essence spirit of the present invention and without departing from range involved by substantive content of the present invention Under it can be made it is various deformation be implemented.

Claims (1)

1. a kind of rigid aerospace craft finite time based on enhanced double power Reaching Laws and fast terminal sliding-mode surface is adaptive Answer fault tolerant control method, it is characterised in that：The control method includes the following steps：
Step 1, the kinematics and dynamics modeling of attitude of flight vehicle fault-tolerant control system is established, system mode and control are initialized Parameter processed, process are as follows：
The kinetic model expression-form of 1.1 aircraft manufacturing technology systems is：
Wherein, ω,It is the angular speed and angular acceleration of aircraft respectively；Ω∈RnIt is the angular speed of counteraction flyback；× Oeprator, by oeprator × be applied to a=[a1,a2,a3]TObtain a×=[0 ,-a3,a2；a3,0,-a1；-a2,a1,0]；J ∈R3×3It is the rotator inertia matrix of aircraft；Jω=diag ([Jω1；Jω2,...,Jωn])∈Rn×nIt is turning for counteraction flyback Dynamic inertial matrix；D∈RnIt is counteraction flyback control moment allocation matrix and row full rank；u∈R3With d (t) ∈ R3It is control input And external disturbance；
The kinematics model expression-form of 1.2 aircraft manufacturing technology systems is：
Wherein, unit quaternionIt is attitude of flight vehicle quaternary number and satisfaction It is q respectively0And qvDerivative；I3∈R3×3It is 3 × 3 unit matrixs；
1.3 assume rotator inertia matrix J=J0+ Δ J, wherein J0The nominal section of J and uncertain part are indicated respectively with Δ J；And List-directed input list is shown asWherein E (t)=diag ([e1(t),e2(t),...,en(t)])∈Rn×nIt is Actuator control efficiency matrix；0≤ei(t)≤1 it is the efficiency factor of i-th of counteraction flyback；It is Additional actuators fault vector；uc=[uc1,uc2,...,ucn]T∈RnIt is the control moment vector of n-th of actuator；Then formula (1) Again it is write as：
1.4 enablingSubstitution formula (2), obtains：
Wherein,
Differential is carried out to formula (5), is obtained：
Wherein,Respectively P and qvFirst derivative and second dervative；
After formula (5), formula (6) are substituted into formula (4), in both members while premultiplication PTIt obtains：
Wherein, J*=PTJ0P and since rotator inertia matrix J * is skew symmetry positive definite matrix, then matrixMeet with oblique Symmetric relation：
J simultaneously*Meet with lower inequality：
Wherein, JminAnd JmaxIt is normal number, indicates J*Lower bound and the upper bound；
It is interference and probabilistic set, expires Foot | | Td||≤υ0Φ, Φ=1+ | | ω | |+| | ω | |2And υ0It is normal number；
Step 2, in the case where not known there are rotary inertia and external disturbance, the attitude control system based on aircraft, if Sliding-mode surface needed for meter, process are as follows：
2.1 selection fast terminal sliding-mode surface s ∈ R3For：
Wherein, λ1＞ 0；λ2＞ 0；a1＞ a2＞ 1；Function sig (x)r=[| x1|rsign(x1),|x2|rsign(x2),|x3|rsign (x3)]T；Sign () is sign function；
To formula (10) derivation, obtain：
Wherein,For the first derivative of s；For α (qv) absolute value；
If α (qv)=0 and β (qv) ≠ 0, due to bearing fractional powerPresence will produce singularity, to avoid singularity It generates, the first derivative of s is changed into：
Wherein, qve∈R3It is defined as：
Wherein, ∈ is the constant of very little；| ∈ | it is the absolute value of ∈；
Then, it is obtained by formula (7), formula (10) and formula (12)：
Wherein,
Step 3, enhanced double power Reaching Laws are designed, process is as follows：
3.1, which define enhanced double power Reaching Laws, is：
Wherein, r1＞ r2＞ 1；k1＞ 0；k2＞ 0；0 ＜ p ＜ 1；θ ＞ 0；| | s | | it is the norm of s；
Step 4, finite time adaptive sliding mode controller is designed, process is as follows：
4.1 consideration finite time adaptive sliding mode controllers are designed to：
Wherein, | | P | | it is the norm of P；| | F | | it is the norm of F；| | Ps | | it is the norm of Ps；| | s | | it is the norm of s；
Positive definite matrix DEDTMeet：0 ＜ e0≤min{λmin(DEDT),1}；λmin() table Show the minimal eigenvalue of matrix；e0It is a normal number；For γiEstimation；I=0,1,2；
The more new law of 4.2 design auto-adaptive parameters：
Wherein, ciAnd εiIt is normal number；ForFirst derivative；I=0,1,2；
4.3 design liapunov functions：
Wherein,sTIt is the transposition of s；
Derivation is carried out to formula (22), is obtained intoOrForm；Formula (23) are carried out simultaneously Derivation obtainsForm；Based on result above, decision-making system is that finite time is unanimously final Bounded；Wherein,
Based on the above analysis, sliding-mode surface s, attitude of flight vehicle quaternary number qvWith angular velocity omega being local finite time consistency finally has Boundary.
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CN109062034A (en) * 2018-09-28 2018-12-21 东北大学 A kind of tight feedback system control method of three ranks for improving double power Reaching Law sliding formworks
CN110471440A (en) * 2018-09-28 2019-11-19 浙江工业大学 A kind of calm method of the rigid-body spacecraft set time posture considering actuator constraints problem
CN108958043A (en) * 2018-09-28 2018-12-07 浙江工业大学 A kind of set time Adaptive Attitude fault tolerant control method of rigid aircraft
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CN113050427A (en) * 2021-03-25 2021-06-29 南京航空航天大学 Rapid terminal sliding mode fault-tolerant control method for nonlinear system under actuator fault
CN113433823A (en) * 2021-05-10 2021-09-24 北京仿真中心 Improved adaptive double power approach law method, device and storage medium

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