Flexible space structure attitude vibration integrated control method, device and storage medium

Abstract

The present invention provides a method, device and storage medium for integrated control of the attitude and vibration of a flexible space structure. The method comprises: establishing a dynamic model of the flexible space structure according to the Euler-Lagrange equations; calculating the target modal frequency of the structure according to the dynamic model; designing a robust frequency-limited controller in a first control closed loop according to the target modal frequency to achieve effective suppression of the structural vibration mode; designing a PD controller in a second control closed loop according to the desired attitude control target to achieve precise control of the structural attitude; finally, the two control closed loops act simultaneously to achieve integrated attitude and vibration control of the flexible space structure.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and in particular to a method, a device and a storage medium for integrated control of attitude vibration of a flexible space structure. Background Art

[0002] Large space structures are the main form of support for future advanced space applications. However, the growth of space structure scale and the limitation of rocket launch weight will inevitably lead to the flexibility of the structure that cannot be ignored. Flexible space structures will experience strong vibrations when they are in attitude maneuvers or are subjected to space disturbance torques. Due to the mutual coupling of attitude and vibration, structural vibration will greatly weaken the accuracy of attitude control. In the worst case, it will also cause the attitude control system to become unstable, ultimately causing the failure of the space mission. For the attitude and vibration control problems of flexible space structures, many control schemes that have been proposed cannot effectively take into account the requirements of both attitude and vibration control at the same time, and cannot achieve integrated control of attitude and vibration. Summary of the invention

[0003] Purpose of the invention: In order to solve the problem in the prior art that it is impossible to take into account both the attitude control and vibration control of flexible space structures, the present invention provides a method, device and storage medium for integrated control of the attitude and vibration of flexible space structures, which can effectively control the attitude and vibration of flexible space structures at the same time.

[0004] The method comprises the following steps:

[0005] Step 1, defining structural parameters for the flexible space structure;

[0006] Step 2, calculating and obtaining the kinetic equation;

[0007] Step 3, calculate the state equation;

[0008] Step 4, calculating and obtaining the measurement output equation;

[0009] Step 5, calculate and obtain the control output equation;

[0010] Step 6, calculating and obtaining the optimized output equation;

[0011] Step 7, establishing a robust frequency limiting controller in the first control closed loop;

[0012] Step 8, establish optimization indicators;

[0013] Step 9, solving the optimization problem according to the optimization index;

[0014] Step 10, establishing a PD controller in a second control closed loop based on a frequency domain correction method;

[0015] Step 11, loading the controllers designed in step 7 and step 10 into the first control closed loop and the second control closed loop respectively, and running them together to realize integrated attitude vibration control.

[0016] Step 1 includes: defining the following structural parameters: φ represents the attitude rotation angle of the spacecraft, λ represents the structural radius of the spacecraft, J0 represents the moment of inertia of the spacecraft, β represents the cross-sectional inertia moment of the flexible structure, η represents the mass density per unit length of the flexible structure, ρ represents the length of the flexible structure, m represents the tip mass that may be attached to the flexible structure, ε1 represents the damping coefficient of the flexible structure, ε2 represents the elastic modulus of the flexible structure, γ represents the deformation amount of the tip of the flexible structure, θ represents the attitude rotation angle of the entire space structure, α=[α1 α2 … α n ] T represents the generalized modal coordinate vector of the flexible structure, α n represents the nth order vibration mode, n represents the number of modes, ξ i (·) represents the i-th mode vibration function, i = 1, 2, … n; O1-X1Y1 is the coordinate system fixed on the spacecraft, where O1 is the origin of the coordinate system, O1X1 is the horizontal axis of the coordinate system, and O1Y1 is the vertical axis of the coordinate system; O2-X2Y2 is the coordinate system fixed on the flexible structure, where O2 is the origin of the coordinate system, O2X2 is the horizontal axis of the coordinate system, and O2Y2 is the vertical axis of the coordinate system.

[0017] Step 2 includes: the kinetic equation is as follows:

[0018] in, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, represents the coefficient matrix; σ is a newly introduced n+1-dimensional state vector, and are the first and second order derivatives of σ respectively; u represents the control input generated by the robust frequency limiting controller in the first control loop, v represents the control input generated by the PD controller in the second control loop, σ T =[φ α T ],and

[0019]

[0020]

[0021] Among them, x represents the spatial variable of the flexible structure along the O2X2 axis, and dx represents the differential of x.

[0022] Step 3 includes: setting the vector The following state equation is obtained from the kinetic equation in step 2:

[0023]

[0024] in, is a newly defined state vector, and σ, yes The first-order derivative of , A is the state matrix, B is the input matrix,

[0025] Step 4 includes: selecting the variable φ, γ, As the variable that can be actually measured, the following measurement output equation is obtained:

[0026]

[0027] Where z is the measurement vector and F is the measurement matrix, as shown below:

[0028]

[0029] Step 5 includes: selecting the attitude angle θ of the entire space structure as the control variable, and obtaining the following control output equation:

[0030]

[0031] Among them, y1 is the control output vector, F1 is the control output matrix, 0 1×(n+1) Represents a matrix whose elements are all 0, the number of rows in the matrix is ​​1, and the number of columns is n+1.

[0032] Step 6 includes: selecting the deformation variable γ of the tip of the flexible structure as the optimization variable, and obtaining the following optimization output equation:

[0033]

[0034] Where y2 is the optimized output vector, F2 is the optimized output matrix, F2=[0 ξ1(ρ) … ξ n (ρ) 0 1×(n+1) ].

[0035] Step 7 includes: designing the robust frequency limiting controller in the first control closed loop as:

[0036]

[0037] in, is the intermediate variable of the controller, yes The first derivative of is the intermediate variable of the controller related to the time lag τ, τ represents the estimated value of the control time lag caused by the measurement, A k , A τ , B k , C k is the parameter matrix to be designed in the controller;

[0038] Step 8 includes: calculating n vibration modal frequencies of the flexible space structure according to the dynamic model And meet Determine the modal frequency range for which design is required in, and All from Select from and satisfy Establish the target frequency interval [χ1, χ2], where χ1 is selected as the modal frequency The rounded-down value of , χ2 is selected as the modal frequency The rounded-up value of is designed as follows:

[0039]

[0040] Wherein, j represents the frequency domain operator, ω represents the frequency, and δ represents the gain value to be optimized.

[0041] The present invention also provides a flexible space structure attitude vibration integrated control device, comprising:

[0042] A structural parameter definition module is used to define structural parameters for the flexible space structure;

[0043] A calculation module is used to calculate the dynamic equation, the state equation, the measurement output equation, the control output equation, and the optimization output equation;

[0044] A first controller establishing module, used for establishing a robust frequency limiting controller in a first control closed loop;

[0045] An optimization index establishment module is used to establish optimization indexes;

[0046] A solution module is used to solve the optimization problem according to the optimization index;

[0047] A second controller establishing module, used for establishing a PD controller in a second control closed loop based on a frequency domain correction method;

[0048] The operation control module is used to load the robust frequency limiting controller in the first control closed loop and the PD controller in the second control closed loop into the first control closed loop and the second control closed loop respectively, and jointly operate them to realize integrated attitude vibration control.

[0049] The present invention also provides a storage medium, characterized in that a computer program or instruction is stored therein, and when the computer program or instruction is executed, a method for integrated control of the attitude and vibration of a flexible space structure is implemented.

[0050] Beneficial effects: This method is based on the dual closed-loop design concept, which realizes the decomposition of the attitude control task and the vibration suppression task of the flexible space structure. It is simple and intuitive, and convenient for engineering practice. The robust frequency-limited controller in the first control closed loop can effectively suppress the vibration mode of the flexible space structure, and the PD controller in the second control closed loop can control the flexible space structure to perform rapid attitude maneuvers. The two control closed loops act simultaneously, which can realize the effective control of the attitude and vibration of the flexible space structure at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0052] Figure 1 It is a schematic diagram of a flexible space structure.

[0053] Figure 2 It is a control structure block diagram.

[0054] Figure 3 It is a schematic diagram of the response curves of the attitude angle θ, the flexible structural variable γ, the first-order vibration mode α1, and the second-order vibration mode α2. DETAILED DESCRIPTION

[0055] The present invention provides a method for integrating attitude and vibration control of a flexible space structure, wherein the flexible space structure is Figure 1 As shown, the spacecraft is attached with a flexible structure which can be abstracted as a beam. The present invention focuses on the dynamics and control problems of the flexible space structure in the plane, and realizes the integrated control of the attitude-vibration of the space structure during the attitude redirection process. The specific invention steps include:

[0056] Step 1, for Figure 1 The flexible space structure shown in the figure defines the following structural parameters: φ represents the attitude rotation angle of the spacecraft, λ represents the structural radius of the spacecraft, J0 represents the moment of inertia of the spacecraft, β represents the cross-sectional inertia moment of the flexible structure, η represents the mass density per unit length of the flexible structure, ρ represents the length of the flexible structure, m represents the tip mass that may be attached to the flexible structure, ε1 represents the damping coefficient of the flexible structure, ε2 represents the elastic modulus of the flexible structure, γ represents the deformation of the tip of the flexible structure, θ represents the attitude rotation angle of the entire space structure, α=[α1 α2 … α n ] T represents the generalized modal coordinate vector of the flexible structure, α nrepresents the nth order vibration mode, n represents the number of modes, ξ i (·) represents the i-th mode vibration function, i = 1, 2, ... n. Symbol [·] s represents the sum of the matrix in the brackets and its own transpose, T It represents the transpose of the matrix “·”, and the symbol “*” in the matrix represents symmetric elements. Figure 1 In the figure, O1-X1Y1 is a coordinate system fixed on the spacecraft, wherein O1 is the origin of the coordinate system, O1X1 is the horizontal axis of the coordinate system, and O1Y1 is the vertical axis of the coordinate system; O2-X2Y2 is a coordinate system fixed on the flexible structure, wherein O2 is the origin of the coordinate system, O2X2 is the horizontal axis of the coordinate system, and O2Y2 is the vertical axis of the coordinate system.

[0057] Step 2: According to the Euler-Lagrange equation, ignoring the high-order nonlinear coupling terms, we get Figure 1 The structure shown is:

[0058]

[0059] in, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, represents the coefficient matrix; σ is a newly introduced n+1-dimensional state vector, and are the first and second order derivatives of σ respectively. u represents the control input generated by the robust frequency limiting controller in the first control loop, v represents the control input generated by the PD (PD is the abbreviation of the two English words proportional derivative, translated into Chinese as proportional differential) controller in the second control loop, σ T =[φα T ],and

[0060]

[0061]

[0062] Among them, x represents the spatial variable of the flexible structure along the O2X2 axis, and dx represents the differential of x;

[0063] Step 3: Set the vector The state equation is obtained from the kinetic equation in step 2:

[0064]

[0065] in, is a newly defined state vector, and σ, yes The first-order derivative of , A is the state matrix, B is the input matrix,

[0066] Step 4, select variable φ, γ, As the variable that can be actually measured, the following measurement output equation is obtained:

[0067]

[0068] Where z is the measurement vector and F is the measurement matrix, as shown below:

[0069]

[0070] Step 5, select the attitude angle θ of the entire space structure as the control variable, and obtain the following control output equation:

[0071]

[0072] Among them, y1 is the control output vector, F1 is the control output matrix, 0 1×(n+1) Represents a matrix whose elements are all 0, the number of rows in the matrix is ​​1, and the number of columns is n+1;

[0073] Step 6, select the deformation variable γ of the tip of the flexible structure as the optimization variable, and obtain the following optimization output equation:

[0074]

[0075] Where y2 is the optimized output vector, F2 is the optimized output matrix, F2=[0 ξ1(ρ) … ξ n (ρ) 0 1×(n+1) ].

[0076] Step 7: Based on the dynamic output feedback method, the robust frequency limiting controller in the first control closed loop is designed as:

[0077]

[0078] in, is the intermediate variable of the controller, yes The first derivative of is the intermediate variable of the controller related to the time lag τ, τ represents the estimated value of the control time lag caused by factors such as measurement, A k , A τ , B k , C k is the parameter matrix to be designed in the controller.

[0079] Step 8: Calculate the n vibration modal frequencies of the flexible space structure according to the dynamic model And meet Secondly, determine the modal frequency range that needs to be designed in, and All from Select from and satisfy Then, establish the target frequency interval [χ1, χ2], where χ1 is selected as the modal frequency The rounded-down value of , χ2 is selected as the modal frequency The value rounded up. Design the following optimization indicators:

[0080]

[0081] Wherein, j represents the frequency domain operator, ω represents the frequency, and δ represents the gain value to be optimized.

[0082] Step 9, according to the optimization index, solve the following optimization problem:

[0083] minδ

[0084] st

[0085]

[0086] symmetric matrices G>0,H>0,L>0,R>0,S>0,X>0,Z>0,W

[0087] general matrices

[0088] scalarsδ>0,τ>0,μ1>0,μ2>0,μ3>0,χ1>0,χ2>0

[0089] Among them, st is the international standard mathematical term for optimization problems, which is the abbreviation of the two words subject to, meaning "subject to"; min is the international standard mathematical term, meaning "find the minimum value"; symmetric matrices means "symmetric matrix"; general matrices means "general matrix"; scalars means "scalar". Ω 11 =τ 2 XZ-[μ2P] s , By solving the optimization problem, the parameter matrix of the robust frequency-limited controller is obtained as follows:

[0090]

[0091]

[0092]

[0093]

[0094] Step 10: Based on the frequency domain correction method, the PD controller in the second control closed loop is designed as follows:

[0095] C(s)=ψ1+ψ2s

[0096] The controller of the present invention is designed using a transfer function representation method, where C(s) is the transfer function of the controller, i.e., the PD controller represented in the frequency domain after Laplace transform, where s represents the Laplace transform operator; parameters ψ1 and ψ2 are the proportional and differential gains of the controller, respectively. In the frequency correction design, the desired shear angle frequency is ω c , the desired amplitude margin is θ, if the PD controller needs to be at the shear angle frequency ω c Provide a margin of merit and phase margin κ, the parameter design of the PD controller is and

[0097] Step 11: Load the controllers designed in Step 7 and Step 10 into Figure 2 The first control closed loop and the second control closed loop shown in the figure can be operated jointly to realize attitude-vibration integrated control.

[0098] The present invention also provides a flexible space structure attitude vibration integrated control device, comprising:

[0099] A structural parameter definition module is used to define structural parameters for the flexible space structure;

[0100] A calculation module is used to calculate the dynamic equation, the state equation, the measurement output equation, the control output equation, and the optimization output equation;

[0101] A first controller establishing module, used for establishing a robust frequency limiting controller in a first control closed loop;

[0102] An optimization index establishment module is used to establish optimization indexes;

[0103] A solution module is used to solve the optimization problem according to the optimization index;

[0104] A second controller establishing module, used for establishing a PD controller in a second control closed loop based on a frequency domain correction method;

[0105] The operation control module is used to load the robust frequency limiting controller in the first control closed loop and the PD controller in the second control closed loop into the first control closed loop and the second control closed loop respectively, and jointly operate them to realize integrated attitude vibration control.

[0106] As described above, the apparatus according to the embodiment of the present application can be implemented in various terminal devices, such as a server of a distributed computing system. In one example, the apparatus according to the embodiment of the present application can be integrated into the terminal device as a software module and / or a hardware module. For example, the apparatus can be a software module in the operating system of the terminal device, or can be an application developed for the terminal device; of course, the apparatus can also be one of the many hardware modules of the terminal device.

[0107] Alternatively, in another example, the apparatus and the terminal device may also be separate terminal devices, and the apparatus may be connected to the terminal device via a wired and / or wireless network, and transmit the interactive information in accordance with an agreed data format.

[0108] The present invention also provides a storage medium, characterized in that a computer program or instruction is stored therein, and when the computer program or instruction is executed, a method for integrated control of the attitude and vibration of a flexible space structure is implemented.

[0109] Simulation verification: The present invention verifies the effectiveness of the proposed fuzzy control method through the following example. The parameters of the flexible space structure are set as follows: J0 = 11 kgm 2 , λ=0.5m, ρ=2m, m=1kg, η=1.66kg / m, β=1.5×10 -4 m 4 , ε1=2.966×10 5 N / m,ε2=6.895×10 10 N / m. Only the first two vibration modes of the flexible structure are considered, and the modal frequencies are and Then the target frequencies are selected as χ1 = 2 rad / s and χ2 = 12 rad / s. The optimization problem related parameters are set as τ = 100 ms, μ1 = μ2 = μ3 = 1. In addition, the expected attitude maneuvering angle of the flexible space structure is set to θ = 60°, and the expected cut-off angle frequency is ω c =0.25rad / s, the amplitude margin that the PD controller needs to provide at the cut-off frequency is The phase margin is κ=1.0438rad. According to the above design parameters, the robust frequency limiting controller and the PD controller can be obtained by the design method proposed by the present invention, and they are loaded into the following Figure 2The first control closed loop and the second control closed loop shown in the figure are operated together, and the result is Figure 3 The system response curve shown is Figure 3 In the figure, the horizontal axis is time, and the unit s represents seconds; the meanings of the vertical axes θ, γ, α1, and α2 have been explained in step 1, the circle represents degrees, and mm represents millimeters. It can be seen from the figure that under the joint action of the designed controller, the attitude angle of the flexible structure can be quickly redirected to the desired 60°, and during the attitude maneuver, the vibration of the flexible structure can also be quickly and effectively suppressed, realizing the integrated control of attitude and vibration.

[0110] The present invention provides a method, device and storage medium for integrated control of attitude vibration of a flexible space structure. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A flexible space structure attitude vibration integrated control method, characterized in that: The following steps are involved: Step 1, defining structural parameters for the flexible space structure; Step 2, calculating and obtaining the kinetic equation; Step 3, calculate the state equation; Step 4, calculating and obtaining the measurement output equation; Step 5, calculate and obtain the control output equation; Step 6, calculating and obtaining the optimized output equation; Step 7, establishing a robust frequency limiting controller in the first control closed loop; Step 8, establish optimization indicators; Step 9, solving the optimization problem according to the optimization index; Step 10, establishing a PD controller in a second control closed loop based on a frequency domain correction method; Step 11, loading the controllers designed in step 7 and step 10 into the first control closed loop and the second control closed loop respectively, and jointly operating them to realize the integrated control of attitude vibration; Step 1 includes: defining the following structural parameters: φ represents the attitude rotation angle of the spacecraft, λ represents the structural radius of the spacecraft, J0 represents the moment of inertia of the spacecraft, β represents the cross-sectional inertia moment of the flexible structure, η represents the mass density per unit length of the flexible structure, ρ represents the length of the flexible structure, m represents the tip mass that may be attached to the flexible structure, ε1 represents the damping coefficient of the flexible structure, ε2 represents the elastic modulus of the flexible structure, γ represents the deformation amount of the tip of the flexible structure, θ represents the attitude rotation angle of the entire space structure, α=[α1α2…α n ] T represents the generalized modal coordinate vector of the flexible structure, α n represents the nth order vibration mode, n represents the number of modes, ξ i (·) represents the i-th mode vibration function, i = 1, 2, ... n; O1-X1Y1 is the coordinate system fixed on the spacecraft, where O1 is the origin of the coordinate system, O1X1 is the horizontal axis of the coordinate system, and O1Y1 is the vertical axis of the coordinate system; O2-X2Y2 is the coordinate system fixed on the flexible structure, where O2 is the origin of the coordinate system, O2X2 is the horizontal axis of the coordinate system, and O2Y2 is the vertical axis of the coordinate system; Step 2 includes: the kinetic equation is as follows: in, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, represents the coefficient matrix; σ is a newly introduced n+1-dimensional state vector, and are the first and second order derivatives of σ respectively; u represents the control input generated by the robust frequency limiting controller in the first control loop, v represents the control input generated by the PD controller in the second control loop, σ T =[φα T ],and Among them, x represents the spatial variable of the flexible structure along the O2X2 axis, and dx represents the differential of x; Step 3 includes: setting the vector The following state equation is obtained from the kinetic equation in step 2: in, is a newly defined state vector, and σ, yes The first-order derivative of , A is the state matrix, B is the input matrix, Step 4 includes: Selecting variables As the variable that can be actually measured, the following measurement output equation is obtained: Where z is the measurement vector and F is the measurement matrix, as shown below: Step 5 includes: selecting the attitude angle θ of the entire space structure as the control variable, and obtaining the following control output equation: Among them, y1 is the control output vector, F1 is the control output matrix, 0 1×(n+1) Represents a matrix whose elements are all 0, the number of rows in the matrix is ​​1, and the number of columns is n+1; Step 6 includes: selecting the deformation variable γ of the tip of the flexible structure as the optimization variable, and obtaining the following optimization output equation: Where y2 is the optimized output vector, F2 is the optimized output matrix, F2=[0 ξ1(ρ) … ξ n (ρ) 0 1×(n+1) ].

2. The method according to claim 1, characterized in that Step 7 includes: designing the robust frequency limiting controller in the first control closed loop as: in, is the intermediate variable of the controller, yes The first derivative of is the intermediate variable of the controller related to the time lag τ, τ represents the estimated value of the control time lag caused by the measurement, A k , A τ , B k , C k is the parameter matrix to be designed in the controller; Step 8 includes: calculating n vibration modal frequencies of the flexible space structure according to the dynamic model And meet Determine the modal frequency range for which design is required in, and All from Select from and satisfy Establish the target frequency interval [χ1, χ2], where χ1 is selected as the modal frequency The rounded-down value of , χ2 is selected as the modal frequency The rounded-up value of is designed as follows: Wherein, j represents the frequency domain operator, ω represents the frequency, and δ represents the gain value to be optimized.

3. A flexible space structure attitude vibration integrated control device implemented based on the method according to any one of claims 1 to 2, characterized in that: include: A structural parameter definition module is used to define structural parameters for the flexible space structure; A calculation module is used to calculate the dynamic equation, the state equation, the measurement output equation, the control output equation, and the optimization output equation; A first controller establishing module, used for establishing a robust frequency limiting controller in a first control closed loop; An optimization index establishment module is used to establish optimization indexes; A solution module is used to solve the optimization problem according to the optimization index; A second controller establishing module, used for establishing a PD controller in a second control closed loop based on a frequency domain correction method; The operation control module is used to load the robust frequency limiting controller in the first control closed loop and the PD controller in the second control closed loop into the first control closed loop and the second control closed loop respectively, and jointly operate them to realize integrated attitude vibration control.

4. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is executed, the method according to any one of claims 1 to 2 is implemented.

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