CN116873226A - Spacecraft attitude control and RCS optimal allocation method - Google Patents
Spacecraft attitude control and RCS optimal allocation method Download PDFInfo
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Abstract
The invention discloses a spacecraft attitude control and RCS (radar cross section) optimal allocation method, and relates to the technical field of spacecraft control. Acquiring spacecraft parameters and spacecraft attitude control moment instructions; constructing a spacecraft attitude dynamics model; constructing a state space equation according to the spacecraft attitude dynamics model; obtaining an estimated value of external disturbance moment born by the spacecraft according to a state space equation; constructing an error conversion state space equation according to the finite time performance function and the external disturbance moment estimation value of the spacecraft; constructing a supercoiled sliding mode controller according to an error conversion state space equation; constructing a spacecraft attitude dynamics model after buffeting is restrained according to the supercoiled sliding mode controller and the saturation function; and obtaining an RCS optimal allocation result according to the spacecraft attitude control moment command and the spacecraft attitude dynamics model after buffeting is inhibited. The invention realizes the precise tracking control of the spacecraft attitude in the limited time, and optimizes the control distribution with minimum instruction error and comprehensive optimal energy consumption.
Description
Technical Field
The invention relates to the technical field of spacecraft control, in particular to a spacecraft attitude control and RCS optimal allocation method.
Background
Along with the rapid development of science and technology, the requirements of people for the detection of the outer space field are continuously increased, and more researches and developments need the precise control of the spacecraft. The attitude control subsystem is one of the most important systems of the spacecraft, and stable and accurate attitude control needs to be provided for the spacecraft so that the spacecraft can complete various space tasks, and the development of national aerospace industry is promoted.
In theory, the convergence time of the traditional spacecraft attitude control method is infinite, and the final attitude tracking error range cannot be determined, which is obviously not suitable for practical application of engineering and can bring difficulty and challenges to on-orbit operation of the spacecraft. Meanwhile, in order to cope with larger disturbance in the traditional attitude control method, a larger controller gain is often set, which undoubtedly aggravates the influence of the buffeting problem. Most of researches on attitude control of spacecraft do not consider the problem of control instruction distribution, and the attitude control of many spacecraft needs a plurality of groups of reaction control systems (reaction control system, RCS) to realize, so how to realize the optimal control distribution of the RCS is also a problem faced in current engineering practice.
Disclosure of Invention
The embodiment of the invention aims to provide a spacecraft attitude control and RCS optimal allocation method, which realizes accurate tracking control of spacecraft attitude in a limited time, optimizes control allocation with minimum instruction error and comprehensive optimal energy consumption.
In order to achieve the above object, the embodiment of the present invention provides the following solutions:
the spacecraft attitude control and RCS optimal allocation method is operated based on preset performances of a spacecraft and comprises the following steps:
acquiring spacecraft parameters and spacecraft attitude control moment instructions; the spacecraft parameters at least comprise an inertia matrix;
constructing a spacecraft attitude dynamics model according to the spacecraft parameters;
constructing a state space equation according to the spacecraft attitude dynamics model; designing an interference observer according to the state space equation, and observing to obtain an estimated value of external interference moment borne by the spacecraft;
constructing a finite time performance function according to the required control performance index; constructing an error conversion state space equation according to the finite time performance function and an external disturbance moment estimated value borne by the spacecraft;
constructing a supercoiled sliding mode controller according to the error conversion state space equation;
constructing a saturation function according to the sliding mode surface; constructing a spacecraft attitude dynamics model after buffeting is restrained according to the supercoiled sliding mode controller and the saturation function;
obtaining an RCS optimal allocation result according to the spacecraft attitude control moment command and the buffeting-inhibited spacecraft attitude dynamics model; the RCS optimal allocation result comprises the on-off state of any RCS thruster.
Optionally, constructing a spacecraft attitude dynamics model according to the spacecraft parameters, specifically including:
wherein , representing roll in inertial frame, ψ represents pitch in inertial frame, γ represents yaw angle in inertial frame, θ εR 3×1 Representing spacecraft attitude angle, < >>Represents the first derivative of θ, ++>Represents the first derivative of ω, ω εR 3×1 The attitude angular speed of the spacecraft is represented, and M is the triaxial moment born by the spacecraft;
according to the spacecraft attitude dynamics model, a state space equation is constructed, and the method specifically comprises the following steps:
A＝-J -1 ω×J；
B＝J -1 ；
wherein ,x1 ＝θ，x 2 =ω, a and B represent the sign of the equation,represents x 2 First derivative of>Represents x 2 U e R 3×1 Representing control moment D.epsilon.R 3×1 And representing the estimated value of the external disturbance moment borne by the spacecraft.
Optionally, designing a disturbance observer according to the state space equation, and observing to obtain an estimated value of external disturbance moment borne by the spacecraft, including:
wherein ,LA ＝diag(L A1 L A2 L A3 )＞0；k Ai ＝diag(k Ai1 k Ai2 k Ai3 )，i＝1,...,4；κ Ai ，α A Are all expected parameters; e, e x2 ＝x 2 -x 2d ；x 1d Representing the spacecraft attitude control moment command x 1 Instruction value of (2); x is x 2d Representing the spacecraft attitude control moment command x 2 Instruction value of (2); function sig r (x)＝|x| r ·sgn(x)；
Parameter σ=diag (σ) 1 σ 2 σ 3 ) The definition is as follows:
wherein ,TAj Is a direct switching time parameter.
Optionally, constructing a finite time performance function according to the required control performance index specifically includes:
ρ fV (t)＝a V3 t 4 +a V2 t 3 +a V1 t 2 +c Vρr t+c Vρ0 ；
wherein ,aV3 、a V2 And a V1 The expressions of (2) are respectively:
wherein parameter c Vρ0 、c Vρr 、ρ fV∞ And T is fV Are all expected parameters, and t represents time; c Vρ0 Is positive, represents an initial margin of error, c Vρr Representing the initial change direction of the performance function ρ fV∞ Characterization function ρ fV Steady state convergence value of (T), T fV Representation ρ fV (t) convergence to a steady state value ρ fV∞ Is set for a predetermined time period.
Optionally, constructing an error conversion state space equation according to the finite time performance function and the external disturbance moment estimation value suffered by the spacecraft, which specifically includes:
where xi represents the conversion error,representing the first derivative of xi +.> Representation->Q and P represent the sign of the equation, +.>The upper limit coefficient of the finite time performance function error is obtained, and delta is obtained as the lower limit coefficient of the finite time performance function error;
according to the error conversion state space equation, constructing a supercoiled sliding mode controller, which specifically comprises the following steps:
wherein ,x'1 ＝ξ，Represents x' 1 First derivative of> Represents x' 2 First derivative of>Representing a diagonal matrix of vectors Q +.>Represents x 1d Is a second derivative of (c).
Alternatively, the process may be carried out in a single-stage,
the sliding mode surface s in the supercoiled sliding mode controller is as follows:
s＝Cx' 1 +x' 2 ；
super-spiral approach lawThe method comprises the following steps:
wherein ,is the first derivative of s, C is the predicted parameter, x' 1 、x′ 2 And v is the equation sign; k (K) 1 ，K 2 For the controller gain, +>Is the first derivative of v; u (u) d Representing control output instruction, ++>Representing the total disturbance observed by the disturbance observer;
constructing a saturation function according to the sliding mode surface, wherein the method specifically comprises the following steps of:
wherein delta is a preset parameter.
Alternatively, the process may be carried out in a single-stage,
obtaining an RCS (radar cross section) optimal allocation result according to the spacecraft attitude control moment command and the spacecraft attitude dynamics model after buffeting inhibition, wherein the RCS optimal allocation result comprises the following steps of:
M RCS ＝F I R；
wherein ,MRCS Indicating the moment provided by RCS, M d Representing the spacecraft attitude control moment command, wherein alpha is a weight coefficient, Q 1 ∈R 3×3 and Q2 ∈R m×m Setting a matrix for a preset; f (F) I Coefficient matrix representing torque provided by RCS, R= [ R ] 1 ,r 2 ,...,r m ] T Represents the on-off state of m RCS thrusters, r i Can only take 0 or 1 。
In the embodiment of the invention, a finite time performance function is constructed, and an error conversion state space equation is constructed according to the finite time performance function and an external disturbance moment estimated value borne by a spacecraft; the control method of the preset performance can finally meet some set control performance indexes by converting the original tracking error into the unconstrained error, and can realize accurate tracking control of the spacecraft in the limited time. Constructing a supercoiled sliding mode controller according to the error conversion state space equation; the supercoiled sliding mode control can effectively cope with larger interference and does not bring serious buffeting phenomenon, and can simultaneously realize the control allocation optimization with minimum instruction error and comprehensive optimal energy consumption.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow chart of a spacecraft attitude control and RCS optimization allocation method provided by an embodiment of the invention;
FIG. 2 is a schematic diagram of an implementation flow of a spacecraft attitude control and RCS optimization allocation method based on predetermined performance according to an embodiment of the invention;
FIG. 3 is a graph of roll angle tracking error without regard to control distribution provided by an embodiment of the present invention;
FIG. 4 is a graph of pitch tracking error without regard to control distribution provided by an embodiment of the present invention;
FIG. 5 is a graph of yaw angle tracking error without regard to control distribution provided by an embodiment of the present invention;
FIG. 6 is a graph of spacecraft X-axis moment curves without regard to control distribution provided by an embodiment of the invention;
FIG. 7 is a graph of a spacecraft Y-axis torque curve without regard to control distribution provided by an embodiment of the invention;
FIG. 8 is a graph of Z-axis moment of a spacecraft without regard to control distribution, provided by an embodiment of the invention;
FIG. 9 is a graph of roll angle tracking error under consideration control distribution provided by an embodiment of the present invention;
FIG. 10 is a graph of pitch tracking error under consideration control distribution provided by an embodiment of the present invention;
FIG. 11 is a graph of yaw angle tracking error under consideration control distribution provided by an embodiment of the present invention;
FIG. 12 is a graph of spacecraft X-axis moment under consideration control distribution provided by an embodiment of the invention;
FIG. 13 is a graph of a spacecraft Y-axis moment under consideration control distribution provided by an embodiment of the invention;
fig. 14 is a graph of a moment curve of a spacecraft Z-axis under consideration control distribution provided by an embodiment of the invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a spacecraft attitude control and RCS (remote control system) optimal allocation method for solving the problems of low tracking control accuracy, large instruction error and low control accuracy caused by large energy consumption of the existing spacecraft attitude in a limited time.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Fig. 1 and 2 illustrate an exemplary flow of the above-described spacecraft attitude control and RCS optimal allocation method, which operates based on predetermined performance of the spacecraft. The steps are described in detail below.
Step 1: acquiring spacecraft parameters and spacecraft attitude control moment instructions; the spacecraft parameters at least comprise an inertia matrix;
step 2: according to the spacecraft parameters, constructing a spacecraft attitude dynamics model, which specifically comprises the following steps:
wherein , representing roll in inertial frame, ψ represents pitch in inertial frame, γ represents yaw angle in inertial frame, θ εR 3×1 Representing spacecraft attitude angle, < >>Represents the first derivative of θ, ++>Represents the first derivative of ω, ω εR 3×1 The attitude angular speed of the spacecraft is represented, and M is the triaxial moment born by the spacecraft;
in one example, the inertia matrix is J.
Step 3: constructing a state space equation according to the spacecraft attitude dynamics model; designing an interference observer according to the state space equation, and observing to obtain an estimated value of external interference moment borne by the spacecraft; the method specifically comprises the following steps:
A＝-J -1 ω×J；
B＝J -1 ；
wherein ,x1 ＝θ，x 2 =ω, a and B represent the sign of the equation,represents x 2 First derivative of>Represents x 2 U e R 3×1 Representing control moment D.epsilon.R 3×1 And representing the estimated value of the external disturbance moment borne by the spacecraft.
Designing an interference observer according to the state space equation, and observing to obtain an estimated value of external interference moment borne by the spacecraft, wherein the method specifically comprises the following steps:
wherein ,LA ＝diag(L A1 L A2 L A3 )＞0；k Ai ＝diag(k Ai1 k Ai2 k Ai3 )，i＝1,...,4；κ Ai ，α A Are all expected parameters; e, e x2 ＝x 2 -x 2d ；x 1d Representing the spacecraft attitude control moment command x 1 Instruction value of (2); x is x 2d Representing the spacecraft attitude control moment command x 2 Instruction value of (2); function sig r (x)＝|x| r ·sgn(x)；
Parameter σ=diag (σ) 1 σ 2 σ 3 ) The definition is as follows:
wherein ,TAj Is a direct switching time parameter.
In one example, a coherent disturbance observer is designed based on state space equations, and the integrated stem is estimated by the coherent disturbance observerScrambling
Parameter kappa Ai The selection is as follows:
κ A1 ＝3I 3 κ A2 ＝4.16I 3 κ A3 ＝3.06I 3 κ A4 ＝1.1I 3 ；
wherein the parameter k Ai It is necessary to guarantee polynomials s 4 +k A1j s 3 +k A2j s 2 +k A3j s+k A4j (j=1, 2, 3) satisfies the hall-effect condition, coefficient α A Is a sufficiently small positive constant.
wherein ,TAj Is a direct switching time parameter; estimation errorCan accurately converge in a fixed time> I.e. the designed disturbance observer observations.
Step 4: constructing a finite time performance function according to the required control performance index; constructing an error conversion state space equation according to the finite time performance function and an external disturbance moment estimated value borne by the spacecraft; the method specifically comprises the following steps:
ρ fV (t)＝a V3 t 4 +a V2 t 3 +a V1 t 2 +c Vρr t+c Vρ0 ；
wherein ,aV3 、a V2 And a V1 The expressions of (2) are respectively:
wherein parameter c Vρ0 、c Vρr 、ρ fV∞ And T is fV Are all expected parameters, and t represents time; c Vρ0 Is positive, represents an initial margin of error, c Vρr Representing the initial change direction of the performance function ρ fV∞ Characterization function ρ fV Steady state convergence value of (T), T fV Representation ρ fV (t) convergence to a steady state value ρ fV∞ Is set for a predetermined time period.
According to the finite time performance function and the external disturbance moment estimation value borne by the spacecraft, an error conversion state space equation is constructed, and the method specifically comprises the following steps:
where xi represents the conversion error,representing the first derivative of xi +.> Representation->Q and P represent the sign of the equation, +.>The upper limit coefficient of the finite time performance function error is obtained, and delta is obtained as the lower limit coefficient of the finite time performance function error;
in one example, the original error is converted into an unconstrained error according to a finite time performance function, specifically formulated as:
step 5: constructing a supercoiled sliding mode controller according to the error conversion state space equation; the method specifically comprises the following steps:
wherein ,x'1 ＝ξ，Represents x' 1 First derivative of> Represents x' 2 First derivative of>Representing a diagonal matrix of vectors Q +.>Represents x 1d Is a second derivative of (c).
The sliding mode surface s in the supercoiled sliding mode controller is as follows:
s＝Cx' 1 +x' 2 ；
super-spiral approach lawThe method comprises the following steps:
wherein ,is the first derivative of s, C is the predicted parameter, x' 1 、x′ 2 And v is the equation sign; k (K) 1 ，K 2 For the controller gain, +>Is the first derivative of v; u (u) d Representing control output instruction, ++>Representing the total disturbance observed by the disturbance observer;
according to the sliding mode surface, the symbol functions in the approach law are replaced by saturation functions, and the saturation functions are constructed specifically comprising:
wherein delta is a preset parameter.
Step 6: constructing a saturation function according to the sliding mode surface; constructing a spacecraft attitude dynamics model after buffeting is restrained according to the supercoiled sliding mode controller and the saturation function;
in one example, a supercoiled sliding mode controller is designed for the above-described error-transformed state space equation, and a saturation function is designed instead of a sign function to suppress buffeting.
Step 7: obtaining an RCS optimal allocation result according to the spacecraft attitude control moment command and the buffeting-inhibited spacecraft attitude dynamics model; the RCS optimal allocation result comprises the on-off state of any RCS thruster.
Obtaining an RCS (radar cross section) optimal allocation result according to the spacecraft attitude control moment command and the spacecraft attitude dynamics model after buffeting inhibition, wherein the RCS optimal allocation result comprises the following steps of:
M RCS ＝F I R；
wherein ,MRCS Indicating the moment provided by RCS, M d Representing the spacecraft attitude control moment command, wherein alpha is a weight coefficient, Q 1 ∈R 3×3 and Q2 ∈R m×m Setting a matrix for a preset; f (F) I Coefficient matrix representing torque provided by RCS, R= [ R ] 1 ,r 2 ,...,r m ] T Represents the on-off state of m RCS thrusters, r i Only 0 or 1 can be taken.
In one example, the spacecraft control allocation problem is described as a quadratic programming problem according to the moment instruction, RCS optimal allocation is realized through an exhaustion method, and finally the on-off state of each RCS thruster is obtained.
Aiming at the quadratic programming problem, the RCS allocation optimization problem is solved by an exhaustion method, and the specific steps are as follows:
firstly, calculating values of the proposed quadratic programming function in all states of the RCS system, then comparing the values of the function values in different states, and finally selecting the RCS system in the state with the minimum function value as an optimal allocation result. And obtaining the state of each RCS thruster according to the optimized distribution result.
The RCS system of the spacecraft comprises a plurality of thrusters, triaxial moment instructions output by a designed supercoiled sliding mode controller are required to be reasonably distributed to each thruster, and the RCS control distribution problem is described as a quadratic programming problem.
In order to further save the calculation time of the exhaustion method, the quadratic programming function can be written as:
L 2 ＝αR T Q 2 R；
wherein ,L0 、L 1 and L2 Representing the amount of advance calculation.
In other embodiments of the present invention, the specific calculation process of the embodiments of the present invention is illustrated by simulation by Matlab/Simulink.
The simulation parameters were set as follows:
the parameters of the spacecraft are as follows: inertia matrixDisturbance moment D= [500+100sin (pi t/125) 700+100cos (pi t/125) 400+100sin (pi t/125)] T RCS number num=16.
The predetermined performance parameters are:δ＝[1 1 1] T ，T fv ＝10，c Vρ0 ＝1，c Vρr ＝-0.02，ρ fV∞ ＝0.01。
consistent convergence observerThe parameters are as follows: t (T) A ＝I 1×3 ，L A ＝5I 3 ，α A ＝0.01，k A1j ＝3，k A2j ＝4.16，k A3j ＝3.06，k A4j ＝1.1。
The parameters of the supercoiled sliding mode controller are as follows: c=0.04I 3 ，K 1 ＝1.5I 3 ，K 2 ＝1.1I 3 ，L 0 ＝0.1I 3 ，δ＝0.005。
The RCS control allocation parameters are: q (Q) 1 ＝I 3 ，Q 2 ＝I 16 ，σ＝0.1。
Simulation results for the non-control allocation are shown in fig. 3, fig. 4, fig. 5, fig. 6, fig. 7 and fig. 8.
From fig. 3, fig. 4 and fig. 5, it can be seen that, without considering control allocation (i.e. the actual torque value is equal to the command torque value), the designed supercoiled sliding mode controller can stably make the attitude angle of the spacecraft track the given command value, the convergence time is less than the set time, and the tracking error is always within the set performance boundary.
As can be seen from fig. 6, 7 and 8, the actual torque value is equal to the command torque value without control allocation, so that the two curves overlap, and the amplitude of the curve buffeting is small, which is about 5n·m.
Simulation results under control distribution are shown in fig. 9, fig. 10, fig. 11, fig. 12, fig. 13, and fig. 14.
From fig. 9, 10 and 11, it can be seen that, under the condition of considering control allocation, the designed supercoiled sliding mode controller can still stably make the attitude angle of the spacecraft track the given command value, the convergence time is smaller than the set time, and the tracking error is always within the set performance boundary.
As can be seen from fig. 12, 13 and 14, because the torque that the attitude control engine can provide is not a continuous quantity but a discrete quantity in consideration of the control distribution, the torque value that is actually provided cannot be completely equal to the command torque value, and the torque will also cause a buffeting phenomenon due to this, as can be seen from comparison between fig. 6, 7 and 8, the buffeting phenomenon is generated due to the control distribution, and the buffeting of the controller itself is small.
In summary, in the embodiment of the invention, a finite time performance function is constructed, and an error conversion state space equation is constructed according to the finite time performance function and an external disturbance moment estimated value borne by the spacecraft; the control method of the preset performance can finally meet some set control performance indexes by converting the original tracking error into the unconstrained error, and can realize accurate tracking control of the spacecraft in the limited time. Constructing a supercoiled sliding mode controller according to the error conversion state space equation; the supercoiled sliding mode control can effectively cope with larger interference and does not bring serious buffeting phenomenon, and can simultaneously realize the control allocation optimization with minimum instruction error and comprehensive optimal energy consumption.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and implementations of the embodiments of the present invention have been described herein with reference to specific examples, the description of the above examples being only for the purpose of aiding in the understanding of the methods of the embodiments of the present invention and the core ideas thereof; also, it is within the spirit of the embodiments of the present invention for those skilled in the art to vary from one implementation to another and from application to another. In view of the foregoing, this description should not be construed as limiting the embodiments of the invention.
Claims (7)
1. The spacecraft attitude control and RCS optimal allocation method is characterized by operating based on preset performances of a spacecraft and comprising the following steps of:
acquiring spacecraft parameters and spacecraft attitude control moment instructions; the spacecraft parameters at least comprise an inertia matrix;
constructing a spacecraft attitude dynamics model according to the spacecraft parameters;
constructing a state space equation according to the spacecraft attitude dynamics model; designing an interference observer according to the state space equation, and observing to obtain an estimated value of external interference moment borne by the spacecraft;
constructing a finite time performance function according to the required control performance index; constructing an error conversion state space equation according to the finite time performance function and an external disturbance moment estimated value borne by the spacecraft;
constructing a supercoiled sliding mode controller according to the error conversion state space equation;
constructing a saturation function according to the sliding mode surface; constructing a spacecraft attitude dynamics model after buffeting is restrained according to the supercoiled sliding mode controller and the saturation function;
obtaining an RCS optimal allocation result according to the spacecraft attitude control moment command and the buffeting-inhibited spacecraft attitude dynamics model; the RCS optimal allocation result comprises the on-off state of any RCS thruster.
2. The spacecraft attitude control and RCS optimal allocation method according to claim 1, wherein constructing a spacecraft attitude dynamics model according to the spacecraft parameters specifically comprises:
wherein , indicating the roll under the inertia system,psi represents pitch in inertial frame, gamma represents yaw angle in inertial frame, and θ∈r 3×1 Representing spacecraft attitude angle, < >>Represents the first derivative of θ, ++>Represents the first derivative of ω, ω εR 3 ×1 The attitude angular speed of the spacecraft is represented, and M is the triaxial moment born by the spacecraft;
according to the spacecraft attitude dynamics model, a state space equation is constructed, and the method specifically comprises the following steps:
A＝-J -1 ω×J；
B＝J -1 ；
wherein ,x1 ＝θ，x 2 =ω, a and B represent the sign of the equation,represents x 2 First derivative of>Represents x 2 U e R 3×1 Representing control moment D.epsilon.R 3×1 And representing the estimated value of the external disturbance moment borne by the spacecraft.
3. The spacecraft attitude control and RCS optimal allocation method according to claim 2, wherein the disturbance observer is designed according to the state space equation, and the estimated value of the external disturbance moment to which the spacecraft is subjected is observed, and specifically comprises:
wherein ,LA ＝diag(L A1 L A2 L A3 )＞0；k Ai ＝diag(k Ai1 k Ai2 k Ai3 )，i＝1,...,4；κ Ai ，α A Are all expected parameters;x 1d representing the spacecraft attitude control moment command x 1 Instruction value of (2); x is x 2d Representing the spacecraft attitude control moment command x 2 Instruction value of (2); function sig r (x)＝|x| r ·sgn(x)；
Parameter σ=diag (σ) 1 σ 2 σ 3 ) The definition is as follows:
wherein ,TAj Is a direct switching time parameter.
4. The spacecraft attitude control and RCS optimal allocation method of claim 1, wherein constructing a finite time performance function according to a desired control performance index comprises:
ρ fV (t)＝a V3 t 4 +a V2 t 3 +a V1 t 2 +c Vρr t+c Vρ0 ；
wherein ,aV3 、a V2 And a V1 The expressions of (2) are respectively:
wherein parameter c Vρ0 、c Vρr 、ρ fV∞ And T is fV Are all expected parameters, and t represents time; c Vρ0 Is positive, represents an initial margin of error, c Vρr Representing the initial change direction of the performance function ρ fV∞ Characterization function ρ fV Steady state convergence value of (T), T fV Representation ρ fV (t) convergence to a steady state value ρ fV∞ Is set for a predetermined time period.
5. The spacecraft attitude control and RCS optimal allocation method according to claim 2, wherein the constructing an error-conversion state space equation according to the finite time performance function and the estimated external disturbance moment value of the spacecraft specifically comprises:
where xi represents the conversion error,representing the first derivative of xi +.> Representation->Q and P represent the sign of the equation, +.>The upper limit coefficient of the finite time performance function error is obtained, and delta is obtained as the lower limit coefficient of the finite time performance function error;
according to the error conversion state space equation, constructing a supercoiled sliding mode controller, which specifically comprises the following steps:
wherein ,x′1 ＝ξ，Represents x' 1 First derivative of> Represents x' 2 First derivative of>Representing a diagonal matrix of vectors Q +.>Represents x 1d Is a second derivative of (c).
6. The spacecraft attitude control and RCS optimal allocation method according to claim 5, wherein,
the sliding mode surface s in the supercoiled sliding mode controller is as follows:
s＝Cx′ 1 +x' 2 ；
super-spiral approach lawThe method comprises the following steps:
wherein ,is the first derivative of s, C is the predicted parameter, x' 1 、x′ 2 And v is the equation sign; k (K) 1 ，K 2 For the controller gain, +>Is the first derivative of v; u (u) d Representing control output instruction, ++>Representing the total disturbance observed by the disturbance observer;
constructing a saturation function according to the sliding mode surface, wherein the method specifically comprises the following steps of:
wherein delta is a preset parameter.
7. The spacecraft attitude control and RCS optimal allocation method according to claim 6, wherein,
obtaining an RCS (radar cross section) optimal allocation result according to the spacecraft attitude control moment command and the spacecraft attitude dynamics model after buffeting inhibition, wherein the RCS optimal allocation result comprises the following steps of:
M RCS ＝F I R；
wherein ,MRCS Indicating the moment provided by RCS, M d Representing the spacecraft attitude control moment command, wherein alpha is a weight coefficient, Q 1 ∈R 3×3 and Q2 ∈R m×m Setting a matrix for a preset; f (F) I Coefficient matrix representing torque provided by RCS, R= [ R ] 1 ,r 2 ,...,r m ] T Represents the on-off state of m RCS thrusters, r i Only 0 or 1 can be taken.
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| CN117724337A (en) * | 2023-12-18 | 2024-03-19 | 大连理工大学 | Aeroengine surge active control system based on second-order sliding mode control |
| CN117826617A (en) * | 2024-03-04 | 2024-04-05 | 西北工业大学 | Intelligent network model-based sliding mode control method and device for preset performance of aircraft |
| CN117826617B (en) * | 2024-03-04 | 2024-05-10 | 西北工业大学 | Intelligent network model-based sliding mode control method and device for preset performance of aircraft |
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