CN107808025A - A kind of spacecraft structure thermal-induced deformation suppressing method and system - Google Patents

A kind of spacecraft structure thermal-induced deformation suppressing method and system Download PDF

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CN107808025A
CN107808025A CN201710800936.6A CN201710800936A CN107808025A CN 107808025 A CN107808025 A CN 107808025A CN 201710800936 A CN201710800936 A CN 201710800936A CN 107808025 A CN107808025 A CN 107808025A
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左博
范立佳
杨松
郭高峰
罗继强
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Beijing Institute of Spacecraft System Engineering
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Abstract

The invention discloses a kind of spacecraft structure thermal-induced deformation suppressing method and system, wherein, methods described, including：Thermal deformation analysis are carried out to the structural finite element model of spacecraft, displacement structure and Space Heat Flux load is tried to achieve and controls the functional relation between hot-fluid；According to given temperature field and thermal deformation suppressing requirement, by the functional relation between displacement structure and Space Heat Flux load and control hot-fluid, control hot-fluid is tried to achieve；Apply the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft structure thermal-induced deformation.It can be seen that the present invention can make use of existing temperature control device on aircraft, by the thermal deformation for changing the Temperature Distribution of structure itself to offset unfavorable, there is the advantages of control is simple, reliability is high, is easy to be engineered.

Description

A kind of spacecraft structure thermal-induced deformation suppressing method and system
Technical field
The invention belongs to spacecraft technology field, more particularly to a kind of spacecraft structure thermal-induced deformation suppressing method and it is System.
Background technology
For spacecraft structure thermal-induced deformation problem, at present, the suppressor mode of domestic and international generally use is：In body structure surface Or internal installation piezoelectric actuator, by piezoelectric actuator come the deformation of active control structure.
However, although the active control mode of piezoelectric actuator has the advantages of response is fast, control accuracy is high, together When there is also high energy consumption, interface easily to fail, the shortcomings such as reliability is low, disadvantages mentioned above hampers piezoelectric actuator to a certain extent Application on the high spacecraft structure of reliability requirement.
The content of the invention
The technology of the present invention solves problem：A kind of overcome the deficiencies in the prior art, there is provided spacecraft structure thermal-induced deformation suppression Method and system processed, by the thermal deformation for changing the Temperature Distribution of structure itself to offset unfavorable, there is simple in construction, reliability Height, it is easy to the advantages of engineering.
In order to solve the above-mentioned technical problem, the invention discloses a kind of spacecraft structure thermal-induced deformation suppressing method, including：
Thermal deformation analysis are carried out to the structural finite element model of spacecraft, try to achieve displacement structure and Space Heat Flux load and control Functional relation between heating stream；
According to given temperature field and thermal deformation suppressing requirement, by displacement structure and Space Heat Flux load and control hot-fluid it Between functional relation, try to achieve control hot-fluid；
Apply the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft knot Structure thermal-induced deformation.
It is described to apply the control heat on thin-walled bar surface in above-mentioned spacecraft structure thermal-induced deformation suppressing method Stream, change the Temperature Distribution of thin-walled bar, suppress spacecraft structure thermal-induced deformation, including：
Controlled heat piece is arranged on thin-walled bar surface；
Control the controlled heat piece to produce the local heat flux consistent with the control hot-fluid, change the temperature of thin-walled bar Distribution, suppress spacecraft structure thermal-induced deformation.
It is described to be wanted according to given temperature field and thermal deformation suppressing in above-mentioned spacecraft structure thermal-induced deformation suppressing method Ask, by the functional relation between displacement structure and Space Heat Flux load and control hot-fluid, try to achieve control hot-fluid, including：
According to given temperature field and thermal deformation suppressing requirement, the sensitivity to displacement field is analyzed, and obtains current displacement And deviation and the sensitivity of displacement of targets；
According to the current displacement and deviation and the sensitivity of displacement of targets, using Gauss-Newton algorithm to the structure Functional relation between displacement and Space Heat Flux load and control hot-fluid carries out optimization, obtains the control hot-fluid.
In above-mentioned spacecraft structure thermal-induced deformation suppressing method,
Displacement structure corresponding to determining the control hot-fluid, judges whether control deviation meets that thermal deformation suppressing is wanted The control accuracy asked；
If control deviation is unsatisfactory for the required control accuracy of thermal deformation suppressing requirement, control heat is recalculated in return Stream, until control deviation meets the required control accuracy of thermal deformation suppressing requirement.
In above-mentioned spacecraft structure thermal-induced deformation suppressing method, displacement structure and Space Heat Flux are determined as follows Functional relation between load and control hot-fluid：
Using Fourier unit, spacecraft frame structure is tried to achieve in Space Heat Flux load QsAnd control hot-fluid Q (t)c(t) make With lower caused temperature-responsive：
Wherein, formula (1) and (2) are respectively the mean temperature of Fourier unit and the transient heat conduction of perturbation temperature composition Finite element equation；T0Represent mean temperature；TmRepresent perturbation temperature；C represents heat capacity matrix；K0And KmRespectively Represent mean temperature equation and the heat transfer matrix to perturb corresponding to temperature equation；R(T0) radiation matrix is represented, with mean temperature Cube it is directly proportional；WithThe Space Heat Flux load vectors of mean temperature equation and the temperature equation that perturbs are represented respectively； WithThe control hot-fluid load vectors of mean temperature equation and the temperature equation that perturbs are represented respectively；
According to the static(al) finite element equation of structure, displacement structure u (t) is tried to achieve：
Ku (t)=F (T (t)) (3)
Wherein, K is the stiffness matrix of structure；F (T) represents structure equivalent temperature load；T (t)=[[T0(t)]T [Tm (t)]T]；
Determine displacement structure and Space Heat Flux load and control the functional relation between hot-fluid：
U (t)=F [Qs(t),Qc(t),t]。
It is described according to the inclined of the current displacement and displacement of targets in above-mentioned spacecraft structure thermal-induced deformation suppressing method Difference and sensitivity, using Gauss-Newton algorithm to the function between the displacement structure and Space Heat Flux load and control hot-fluid Relation carries out optimization, obtains the control hot-fluid, including：
By the functional relation between the displacement structure and Space Heat Flux load and control hot-fluid, discrete time system is converted into The NONLINEAR OPTIMAL CONTROL of system, obtains object function；
Optimization is carried out to the object function using Gauss-Newton algorithm：
Order：Gauss-Newton algorithm kth step iterative relation be：
Then, object function existsPoint Taylor expansion be：
Wherein,It is to QcGradient operator；
Wherein, Jacobian matrix
Order：
Then,
Formula (5) and (6) are substituted into formula (7), and the Derivative Terms for ignoring V can obtain：
According to formula (4) and (8), the Iteration of Gauss-Newton algorithm can be obtained：
WhenWithWhen meeting, iteration convergence is determined, is tried to achieve The control hot-fluid：
Wherein, c is control variable number.
In above-mentioned spacecraft structure thermal-induced deformation suppressing method, Jacobian matrix is determined as follows：
Order control hot-fluid QcK-th of element be control variable dk, to formula (1) (2) and (3) on dkLocal derviation is sought, can ：
Wherein,Represent to controlling variable dkPartial derivative；WithRepresent respectively to mean temperature vector T0With take the photograph Dynamic temperature vector TmPartial derivative；
Formula (9), (10) and (11), which is arranged, to be obtained：
Wherein, Q0And QmRespectively：
Using Wilson- θ methods, with the mean temperature sensitivity of tWith perturbation temperature controlRepresent t+ Δs t When mean temperature sensitivityWith perturbation temperature controlObtain：
Formula (15) and the solving result of (16) are substituted into formula (14), solution obtains Jacobian matrix
Accordingly, the invention also discloses a kind of spacecraft structure thermal-induced deformation suppression system, including：
First resolves module, for carrying out thermal deformation analysis to the structural finite element model of spacecraft, tries to achieve displacement structure With the functional relation between Space Heat Flux load and control hot-fluid；
Second resolves module, for according to given temperature field and thermal deformation suppressing requirement, passing through displacement structure and Space Thermal Functional relation between stream loading and control hot-fluid, tries to achieve control hot-fluid；
Control module, for applying the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, Suppress spacecraft structure thermal-induced deformation.
The present invention has advantages below：
The invention discloses a kind of spacecraft structure thermal-induced deformation suppressing method, the structural finite element model of spacecraft is entered Row thermal deformation analysis, try to achieve displacement structure and Space Heat Flux load and control the functional relation between hot-fluid；According to given temperature Field and thermal deformation suppressing requirement, by the functional relation between displacement structure and Space Heat Flux load and control hot-fluid, try to achieve control Heating stream；Apply the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft structure Thermal-induced deformation.It can be seen that the present invention can make use of existing temperature control device on aircraft, by the temperature point for changing structure itself Cloth has to offset unfavorable thermal deformation and controls simple, reliability height, is easy to the advantages of engineering.
Brief description of the drawings
Fig. 1 is a kind of step flow chart of spacecraft structure thermal-induced deformation suppressing method in the embodiment of the present invention；
Fig. 2 is a kind of numbering schematic diagram of the temperature control point of the bottom plate in certain satellite service cabin in the embodiment of the present invention.
Embodiment
It is public to the present invention below in conjunction with accompanying drawing to make the object, technical solutions and advantages of the present invention clearer Embodiment is described in further detail.
The invention discloses a kind of spacecraft structure thermal-induced deformation suppressing method, by the Temperature Distribution for changing structure itself To offset unfavorable thermal deformation.
Reference picture 1, show a kind of step flow of spacecraft structure thermal-induced deformation suppressing method in the embodiment of the present invention Figure.In the present embodiment, the spacecraft structure thermal-induced deformation suppressing method, including：
Step 101, thermal deformation analysis are carried out to the structural finite element model of spacecraft, tries to achieve displacement structure and Space Heat Flux Functional relation between load and control hot-fluid.
In the preferred embodiment of the present invention, can determine as follows displacement structure and Space Heat Flux load and Control the functional relation between hot-fluid：
Step S11, using Fourier unit, spacecraft frame structure is tried to achieve in Space Heat Flux load Qs(t) and control is hot Flow Qc(t) the lower caused temperature-responsive of effect：
Wherein, formula (1) and (2) are respectively the mean temperature of Fourier unit and the transient heat conduction of perturbation temperature composition Finite element equation, namely mean temperature field equation and perturbation temperature field equation；T0Represent mean temperature；TmTable Show perturbation temperature；C represents heat capacity matrix；K0And KmMean temperature equation and the heat biography to perturb corresponding to temperature equation are represented respectively Lead matrix；R(T0) radiation matrix is represented, it is directly proportional to the cube of mean temperature；WithMean temperature equation is represented respectively With the Space Heat Flux load vectors of perturbation temperature equation；WithMean temperature equation and the temperature equation that perturbs are represented respectively Control hot-fluid load vectors；T represents action time.In the present embodiment, formula (1) and (2) are ODE, can be used The discrete solution in time-domain of Wilson- θ methods.Because formula (1) is nonlinear, therefore also need to use in each time step Newton-Raphson iteratives.After trying to achieve mean temperature, formula (2) be it is linear, can direct solution.Due to mean temperature Field equation and perturbation temperature field equation are decoupled, and therefore, solution efficiency can be greatly improved using Fourier unit.
Step S12, according to the static(al) finite element equation of structure, try to achieve displacement structure u (t)：
Ku (t)=F (T (t)) (3)
In the present embodiment, the influence of inertia force is not considered, displacement structure u can be tried to achieve by the static(al) finite element equation of structure (t).Wherein, K is the stiffness matrix of structure；F (T) represents structure equivalent temperature load；T (t)=[[T0(t)]T [Tm(t)]T]。
Step S13, determine displacement structure and Space Heat Flux load and control the functional relation between hot-fluid：
U (t)=F [Qs(t),Qc(t),t]。
Step 102, according to given temperature field and thermal deformation suppressing requirement, displacement structure and Space Heat Flux load and control are passed through Functional relation between heating stream, tries to achieve control hot-fluid.
In the present embodiment, can be according to given temperature field and thermal deformation suppressing requirement, the sensitivity to displacement field is carried out Analysis, obtains deviation and the sensitivity of current displacement and displacement of targets；According to the deviation of the current displacement and displacement of targets and Sensitivity, using Gauss-Newton algorithm to the functional relation between the displacement structure and Space Heat Flux load and control hot-fluid Optimization is carried out, obtains the control hot-fluid.
In the present embodiment, it may be determined that displacement structure corresponding to the control hot-fluid, judge whether control deviation meets The required control accuracy of thermal deformation suppressing requirement；Wherein, if control deviation is unsatisfactory for the required control of thermal deformation suppressing requirement Precision processed, then return and recalculate control hot-fluid, until control deviation meets the required control accuracy of thermal deformation suppressing requirement.
In the preferred embodiment of the present invention, the deviation according to the current displacement and displacement of targets and sensitive Degree, the functional relation between the displacement structure and Space Heat Flux load and control hot-fluid is carried out using Gauss-Newton algorithm Optimization, the control hot-fluid is obtained, can specifically be included：
Step S21, by the displacement structure and Space Heat Flux load and control hot-fluid between functional relation, be converted into from The NONLINEAR OPTIMAL CONTROL of time system is dissipated, obtains object function.
In the present embodiment, for u (t)=F [Qs(t),Qc(t), t], using the control energy of minimum, by controlling heat Flow Qc(t) displacement structure u (t) elapsed time sections (t is made0,tf) after in tfMoment and displacement of targets ud(t) deviation is minimum, can With the optimal control problem being expressed as：
State equation
Object function W：
For given state equationSeeking one allows to control hot-fluidMake object function W minimalizations,As required optimum control.
Preferably, due to the presence of radiation heat transfer, above-mentioned optimal control problem is a nonlinear Control problem, by the time Section (t0,tf) it is divided into n section：(t0,t1), (t1,t2) ... (tr-1,tr), (tn-1,tn=tf), wherein (r=1,2 ..., n).In this manner it is possible to this nonlinear control system is done into following simplification：
(1) u (t) is simply in limited individual time point trMeet u (tr)=udr, trThe displacement of targets at time point, tr∈(0,t)。
(2)Qc(t) in (tr-1,tr) linear change in the period, remember Qcr=Qc(tr), trThe control hot-fluid at time point.
Then, the nonlinear Control problem of above-mentioned continuous time system can be converted into the non-linear optimal of discrete-time system Control problem：
Dynamical equation：u(tr)=F ' [u (tr-1),Qs(tr-1),Qc(tr-1),tr-1], (r=1,2 ..., n)
Object function：
If：
U=[u (t1)T u(t2)T … u(tn)T]T
Then, object function is represented by：
Wherein：
V=ud-u
Then, seeking one allows to control hot-fluidMake object function W*Minimalization,As required discrete time system The optimum control of system.
Step S22, optimization is carried out to the object function using Gauss-Newton algorithm.
In the present embodiment, Gauss-Newton algorithm is an iterative process, with Gauss-Newton algorithm to the target letter The process that number carries out optimization can be as follows：
Order：Gauss-Newton algorithm kth step iterative relation be：
Then, object function W* Point Taylor expansion be：
Wherein, k is variable,It is QcGradient operator；
Wherein, Jacobian matrix
Order：
Then,
Formula (5) and (6) are substituted into formula (7), and the Derivative Terms for ignoring V can obtain：
According to formula (4) and (8), the Iteration of Gauss-Newton algorithm can be obtained：
WhenWithWhen meeting, iteration convergence is determined, is tried to achieve The control hot-fluid：
Wherein, c is control variable number.
In the preferred embodiment of the present invention, Jacobian matrix can be determined as follows：
Order, control hot-fluid QcK-th of element be control variable dk, to formula (1) (2) and (3) on dkLocal derviation is sought, can ：
Wherein,Represent to controlling variable dkPartial derivative；WithRepresent respectively to mean temperature vector T0With take the photograph Dynamic temperature vector TmPartial derivative；
Formula (9), (10) and (11), which is arranged, to be obtained：
Wherein, Q0And QmRespectively：
In the present embodiment, can be first under unit meaning in order to solve the partial derivative of coefficient matrix and load vectors Corresponding sensitivity expression formula is explicitly provided by unit coefficient matrix and load vectors, global coordinate is then obtained by a group collection Partial derivative under system.After being solved to formula (1) and (2), formula (12) and (13) are Differential Equation with Constant Coefficients.Thus may be used With using Wilson- θ methods that it is discrete in time-domain, with the mean temperature sensitivity of tWith perturbation temperature controlRepresent mean temperature sensitivity during t+ Δ tWith perturbation temperature controlObtain：
Wherein, θ is intermediate variable.Formula (15) and the solving result of (16) are substituted into formula (14), solution obtain it is refined can Compare matrix
Step 103, apply the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress Spacecraft structure thermal-induced deformation.
In the present embodiment, controlled heat piece can be arranged on thin-walled bar surface；The controlled heat piece is controlled to produce The raw local heat flux consistent with the control hot-fluid, changes the Temperature Distribution of thin-walled bar, suppresses spacecraft structure thermal-induced deformation. Present invention utilizes existing temperature control device on aircraft, has the advantages of control is simple, reliability is high, is easy to be engineered.
Based on above-described embodiment, the spacecraft structure thermal-induced deformation suppressing method is said with reference to an instantiation It is bright.Reference picture 2, show a kind of numbering signal of temperature control point of the bottom plate in certain satellite service cabin in the embodiment of the present invention Figure.In the present embodiment, for certain satellite service cabin-Y+X bottom plates normal vector under worst hot case, normal vector maximum angle has 30 jiaos Second to service module-Y+X bottom plate normal vector variable angles, it is necessary to suppress.29 chosen in service module-Y+X base plate vicinities Temperature control point is (as shown in Figure 2) to be used as candidate's temperature control point set, using spacecraft structure thermal-induced deformation suppressing method of the present invention, Z-direction displacement to service module-Y+X bottom plates suppresses.
Preferably, have chosen two moment of 600s and 1200s is controlled.As a result as shown in table 1, vector angle is by 28.4 Rad (angle maximum point) control has reached control effect to 5.9 rads (angle maximum points)：
Time Angle (rad) is not controlled Angle (rad) after control
600s 13.8 4.4
1200s 28.4 5.9
Table 1, service module-Y+X bottom plate normal vector angle control result tables
On the basis of above method embodiment, the invention also discloses a kind of spacecraft structure thermal-induced deformation to suppress system System, including：First resolves module, for carrying out thermal deformation analysis to the structural finite element model of spacecraft, tries to achieve displacement structure With the functional relation between Space Heat Flux load and control hot-fluid；Second resolves module, for being become according to given temperature field and heat Shape suppresses to require, by displacement structure and Space Heat Flux load and controls the functional relation between hot-fluid, try to achieve control hot-fluid；Control Molding block, for applying the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft Structure thermal-induced deformation.
For system embodiment, because it is corresponding with embodiment of the method, so description is fairly simple, correlation Place referring to embodiment of the method part explanation.
Each embodiment in this explanation is described by the way of progressive, what each embodiment stressed be and its The difference of his embodiment, between each embodiment identical similar part mutually referring to.
It is described above, it is only the optimal embodiment of the present invention, but protection scope of the present invention is not limited thereto, Any one skilled in the art the invention discloses technical scope in, the change or replacement that can readily occur in, It should all be included within the scope of the present invention.
The content not being described in detail in description of the invention belongs to the known technology of professional and technical personnel in the field.

Claims (8)

  1. A kind of 1. spacecraft structure thermal-induced deformation suppressing method, it is characterised in that including：
    Thermal deformation analysis are carried out to the structural finite element model of spacecraft, try to achieve displacement structure and Space Heat Flux load and control heat Functional relation between stream；
    According to given temperature field and thermal deformation suppressing requirement, by between displacement structure and Space Heat Flux load and control hot-fluid Functional relation, try to achieve control hot-fluid；
    Apply the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft structure heat Mutagens shape.
  2. 2. spacecraft structure thermal-induced deformation suppressing method according to claim 1, it is characterised in that described in thin-walled bar Apply the control hot-fluid on surface, change the Temperature Distribution of thin-walled bar, suppress spacecraft structure thermal-induced deformation, including：
    Controlled heat piece is arranged on thin-walled bar surface；
    Control the controlled heat piece to produce the local heat flux consistent with the control hot-fluid, change the temperature point of thin-walled bar Cloth, suppress spacecraft structure thermal-induced deformation.
  3. 3. spacecraft structure thermal-induced deformation suppressing method according to claim 1, it is characterised in that the basis is to constant temperature Field and thermal deformation suppressing requirement are spent, by the functional relation between displacement structure and Space Heat Flux load and control hot-fluid, is tried to achieve Hot-fluid is controlled, including：
    According to given temperature field and thermal deformation suppressing requirement, the sensitivity to displacement field is analyzed, and obtains current displacement and mesh The deviation of marker displacement and sensitivity；
    According to the current displacement and deviation and the sensitivity of displacement of targets, using Gauss-Newton algorithm to the displacement structure Functional relation between Space Heat Flux load and control hot-fluid carries out optimization, obtains the control hot-fluid.
  4. 4. the spacecraft structure thermal-induced deformation suppressing method according to claim 1 or 3, it is characterised in that
    Displacement structure corresponding to determining the control hot-fluid, judges whether control deviation meets that thermal deformation suppressing requirement is required Control accuracy；
    If control deviation is unsatisfactory for the required control accuracy of thermal deformation suppressing requirement, control hot-fluid is recalculated in return, directly Meet the required control accuracy of thermal deformation suppressing requirement to control deviation.
  5. 5. spacecraft structure thermal-induced deformation suppressing method according to claim 3, it is characterised in that true as follows Determine displacement structure and Space Heat Flux load and control the functional relation between hot-fluid：
    Using Fourier unit, spacecraft frame structure is tried to achieve in Space Heat Flux load QsAnd control hot-fluid Q (t)c(t) under acting on Caused temperature-responsive：
    <mrow> <mi>C</mi> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>0</mn> </msup> <mo>+</mo> <mo>&amp;lsqb;</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <mo>+</mo> <mfrac> <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> <mo>)</mo> </mrow> </mrow> <mn>4</mn> </mfrac> <mo>&amp;rsqb;</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>s</mi> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mn>...</mn> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>C</mi> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msup> <mo>+</mo> <mo>&amp;lsqb;</mo> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>+</mo> <mi>R</mi> <mrow> <mo>(</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msup> <mi>T</mi> <mi>m</mi> </msup> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>s</mi> <mi>m</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mi>m</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mn>...</mn> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, formula (1) and (2) are respectively that the transient heat conduction that the mean temperature of Fourier unit and perturbation temperature form is limited First equation；T0Represent mean temperature；TmRepresent perturbation temperature；C represents heat capacity matrix；K0And KmRepresent respectively Heat transfer matrix corresponding to mean temperature equation and perturbation temperature equation；R(T0) expression radiation matrix, three with mean temperature Power is directly proportional；WithThe Space Heat Flux load vectors of mean temperature equation and the temperature equation that perturbs are represented respectively；WithThe control hot-fluid load vectors of mean temperature equation and the temperature equation that perturbs are represented respectively；
    According to the static(al) finite element equation of structure, displacement structure u (t) is tried to achieve：
    Ku (t)=F (T (t)) ... (3)
    Wherein, K is the stiffness matrix of structure；F (T) represents structure equivalent temperature load；T (t)=[[T0(t)]T [Tm(t)]T]；
    Determine displacement structure and Space Heat Flux load and control the functional relation between hot-fluid：
    U (t)=F [Qs(t),Qc(t),t]。
  6. 6. spacecraft structure thermal-induced deformation suppressing method according to claim 5, it is characterised in that work as described in the basis The deviation and sensitivity of preceding displacement and displacement of targets, using Gauss-Newton algorithm to the displacement structure and Space Heat Flux load Functional relation between control hot-fluid carries out optimization, obtains the control hot-fluid, including：
    By the functional relation between the displacement structure and Space Heat Flux load and control hot-fluid, discrete-time system is converted into NONLINEAR OPTIMAL CONTROL, obtain object function；
    Optimization is carried out to the object function using Gauss-Newton algorithm：
    Order：Gauss-Newton algorithm kth step iterative relation be：
    <mrow> <msubsup> <mi>Q</mi> <mi>c</mi> <mi>k</mi> </msubsup> <mo>=</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>&amp;Delta;Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>,</mo> <mi>k</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mn>...</mn> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Then, object function existsPoint Taylor expansion be：
    <mrow> <msup> <mi>W</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mi>k</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;ap;</mo> <mi>q</mi> <mo>&amp;equiv;</mo> <msup> <mi>W</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> </msub> <msup> <mi>W</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>&amp;Delta;Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>dQ</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msubsup> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>2</mn> </msubsup> <msup> <mi>W</mi> <mo>*</mo> </msup> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>&amp;Delta;Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow>
    Wherein,It is to QcGradient operator；
    <mrow> <msub> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> </msub> <mi>W</mi> <mo>=</mo> <mn>2</mn> <msup> <mi>J</mi> <mi>T</mi> </msup> <mi>V</mi> <mo>+</mo> <mn>2</mn> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>...</mn> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>2</mn> </msubsup> <mi>W</mi> <mo>=</mo> <mn>2</mn> <msup> <mi>J</mi> <mi>T</mi> </msup> <mi>J</mi> <mo>+</mo> <mn>2</mn> <msup> <mi>V</mi> <mi>T</mi> </msup> <msubsup> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>2</mn> </msubsup> <mi>V</mi> <mo>+</mo> <mn>2</mn> <mi>I</mi> <mn>...</mn> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, Jacobian matrix
    Order：
    Then,
    <mrow> <msubsup> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>2</mn> </msubsup> <mi>W</mi> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>&amp;Delta;Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mo>-</mo> <msub> <mo>&amp;dtri;</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> </msub> <mi>W</mi> <mrow> <mo>(</mo> <msubsup> <mi>Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>...</mn> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Formula (5) and (6) are substituted into formula (7), and the Derivative Terms for ignoring V can obtain：
    <mrow> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mi>J</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mi>I</mi> <mo>&amp;rsqb;</mo> <msubsup> <mi>&amp;Delta;Q</mi> <mi>c</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msup> <mi>J</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mi>T</mi> </msup> <msup> <mi>V</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>Q</mi> <mi>c</mi> </msub> <mn>...</mn> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    According to formula (4) and (8), the Iteration of Gauss-Newton algorithm can be obtained：
    WhenWithWhen meeting, iteration convergence is determined, is tried to achieve described Control hot-fluid：
    <mrow> <mfrac> <mrow> <mo>|</mo> <mo>|</mo> <msup> <mi>u</mi> <mi>k</mi> </msup> <mo>-</mo> <msup> <mi>u</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>|</mo> <mo>|</mo> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msup> <mi>u</mi> <mi>k</mi> </msup> <mo>|</mo> <mo>|</mo> </mrow> </mfrac> <mo>&lt;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow>
    <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mo>{</mo> <mrow> <mo>|</mo> <mfrac> <mrow> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> <mi>k</mi> </msubsup> <mo>-</mo> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> <mrow> <mi>k</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mi>i</mi> </mrow> <mi>k</mi> </msubsup> </mfrac> <mo>|</mo> </mrow> <mo>}</mo> <mo>&lt;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>c</mi> </mrow>
    Wherein, c is control variable number.
  7. 7. spacecraft structure thermal-induced deformation suppressing method according to claim 6, it is characterised in that true as follows Determine Jacobian matrix：
    Order control hot-fluid QcK-th of element be control variable dk, to formula (1) (2) and (3) on dkLocal derviation is sought, can be obtained：
    <mrow> <msub> <mi>C</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>0</mn> </msup> <mo>+</mo> <mi>C</mi> <msubsup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <msubsup> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <msub> <mi>R</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <msup> <mi>T</mi> <mn>0</mn> </msup> <mo>+</mo> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <mo>+</mo> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> <mi>R</mi> <mo>)</mo> </mrow> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msubsup> <mi>Q</mi> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mn>...</mn> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>C</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msup> <mo>+</mo> <mi>C</mi> <msubsup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <msubsup> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <msub> <mi>R</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <msup> <mi>T</mi> <mi>m</mi> </msup> <mo>+</mo> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>=</mo> <msubsup> <mi>Q</mi> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mn>...</mn> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>Ku</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <mi>u</mi> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mi>m</mi> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mn>...</mn> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent to controlling variable dkPartial derivative；WithRepresent respectively to mean temperature vector T0With perturbation temperature Spend vector TmPartial derivative；
    Formula (9), (10) and (11), which is arranged, to be obtained：
    <mrow> <mi>C</mi> <msubsup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> <msup> <mi>Q</mi> <mn>0</mn> </msup> <mn>...</mn> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>C</mi> <msubsup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>+</mo> <mi>R</mi> <mo>)</mo> </mrow> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>=</mo> <msup> <mi>Q</mi> <mi>m</mi> </msup> <mn>...</mn> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>Ku</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>F</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msub> <mi>F</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mi>m</mi> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>-</mo> <msub> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <mi>u</mi> <mn>...</mn> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, Q0And QmRespectively：
    <mrow> <msup> <mi>Q</mi> <mn>0</mn> </msup> <mo>=</mo> <msubsup> <mi>Q</mi> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>0</mn> </msup> <mo>-</mo> <msubsup> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow>
    <mrow> <msup> <mi>Q</mi> <mi>m</mi> </msup> <mo>=</mo> <msubsup> <mi>Q</mi> <mrow> <mi>s</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <msubsup> <mi>Q</mi> <mrow> <mi>c</mi> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>-</mo> <msub> <mi>C</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> </msub> <msup> <mover> <mi>T</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>m</mi> </msup> <mo>-</mo> <mrow> <mo>(</mo> <msubsup> <mi>K</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <msub> <mi>R</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> </msub> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <msup> <mi>T</mi> <mi>m</mi> </msup> </mrow>
    Using Wilson- θ methods, with the mean temperature sensitivity of tWith perturbation temperature controlDuring expression t+ Δ t Mean temperature sensitivityWith perturbation temperature controlObtain：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <mi>C</mi> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <mo>+</mo> <msubsup> <mi>R</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </msup> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <mi>C</mi> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mn>0</mn> </msup> <mo>+</mo> <msubsup> <mi>R</mi> <mrow> <mo>,</mo> <msup> <mi>T</mi> <mn>0</mn> </msup> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>t</mi> </msup> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mn>0</mn> </msubsup> <mo>+</mo> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>t</mi> </msup> <msup> <mi>Q</mi> <mn>0</mn> </msup> <mo>+</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </msup> <msup> <mi>Q</mi> <mn>0</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mn>...</mn> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <mi>C</mi> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mo>+</mo> <mi>&amp;theta;</mi> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>+</mo> <msup> <mi>R</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </msup> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>=</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <mi>C</mi> <mrow> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msup> <mi>K</mi> <mi>m</mi> </msup> <mo>+</mo> <msup> <mi>R</mi> <mi>m</mi> </msup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>t</mi> </msup> <msubsup> <mi>T</mi> <mrow> <mo>,</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow> <mi>m</mi> </msubsup> <mo>+</mo> <mo>&amp;lsqb;</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>t</mi> </msup> <msup> <mi>Q</mi> <mi>m</mi> </msup> <mo>+</mo> <msup> <mi>&amp;theta;</mi> <mrow> <mi>t</mi> <mo>+</mo> <mi>&amp;Delta;</mi> <mi>t</mi> </mrow> </msup> <msup> <mi>Q</mi> <mi>m</mi> </msup> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> <mn>...</mn> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
    Formula (15) and the solving result of (16) are substituted into formula (14), solution obtains Jacobian matrix
  8. A kind of 8. spacecraft structure thermal-induced deformation suppression system, it is characterised in that including：
    First resolves module, for carrying out thermal deformation analysis to the structural finite element model of spacecraft, tries to achieve displacement structure and sky Between hot-fluid load and control hot-fluid between functional relation；
    Second resolves module, for according to given temperature field and thermal deformation suppressing requirement, being carried by displacement structure and Space Heat Flux Functional relation between lotus and control hot-fluid, tries to achieve control hot-fluid；
    Control module, for applying the control hot-fluid on thin-walled bar surface, change the Temperature Distribution of thin-walled bar, suppress Spacecraft structure thermal-induced deformation.
CN201710800936.6A 2017-09-07 2017-09-07 Method and system for inhibiting thermally induced deformation of spacecraft structure Active CN107808025B (en)

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