An angular momentum management method based on a vector electric thruster

Abstract

The present invention discloses a method for angular momentum management based on a vector electric thruster. First, a linearized dynamic model for angular momentum management of the vector electric thruster is established according to the geometric structure, installation position, installation matrix and working combination of the vector electric thruster. Then, the control torque error term is estimated in real time through closed-loop feedback and compensated during the calculation of the angular momentum to be managed, and the rotation angle command of the vector electric thruster is calculated through hysteresis control and pseudo-inverse distribution algorithm. Finally, a geometric reduction processing method for the vector electric thruster exceeding the misalignment mechanism limit threshold is given. By linearly simplifying the dynamic model, the present invention reduces the computational amount of the angular momentum management method, and improves the angular momentum management accuracy by considering the introduction of closed-loop estimation of the control torque error. Hysteresis control and pseudo-inverse distribution reduce the adjustment times and adjustment amplitude of the misalignment adjustment, and reduce the influence on the attitude and orbit control accuracy.

Description

Technical Field

[0001] The present invention relates to an angular momentum management method based on a vector electric thruster, which is mainly used on a satellite configured with a vector electric thruster for orbital maneuvering, for overall satellite angular momentum management and thrust eccentricity elimination. Background Art

[0002] Vector electric thrusters are a development trend of communication satellites and deep space probes in recent years, generally composed of a vector adjustment mechanism and an electric thruster. Therefore, they have the advantages of an electric thruster, such as significantly reducing fuel consumption during space missions and increasing the lifespan of spacecraft. At the same time, they also have the advantages of flexible thrust direction, adapting to various working conditions (as shown in Figure 1), and high thrust efficiency. For a satellite configured with vector electric thrusters, the typical installation configuration of the vector electric thrusters is that four vector electric thrusters (N1N2S1S2) are symmetrically installed in pairs on the four sides of the back floor of the satellite. By adjusting the misalignment mechanism, various working conditions can be adapted.

[0003] Figure 1(a) shows the initial zero position, Figure 1(b) shows the working position of the vector thruster under the working condition of the orbit transfer section, where the resultant force efficiency is the highest; Figure 1(c) shows the working position of the vector thruster under the working condition of the position holding section. In this kind of thruster layout, electric propulsion angular momentum unloading needs to be carried out simultaneously with orbit keeping control ignition. By adjusting the vector adjustment mechanism of the electric thruster, the thrust direction is slightly deviated from the center of mass to generate a moment of momentum, so as to achieve overall satellite angular momentum management.

[0004] The existing angular momentum management methods for vector electric thrusters have the following deficiencies: ① Ignoring factors such as the installation error, control accuracy, thrust deviation of the thruster itself, and spacecraft center of mass drift of the vector adjustment mechanism, and performing 'open-loop control' on the vector electric thruster, resulting in low control accuracy of the vector electric thruster, and further causing large attitude and orbit control errors; ② The interference torque generated by the vector electric thruster itself cannot be eliminated, resulting in frequent misalignment adjustments, unable to meet the life constraints of the misalignment mechanism, and affecting the attitude and orbit control accuracy; ③ For combinations of vector thrusters with various configurations, there is currently no general command allocation algorithm. Therefore, it is necessary to redesign the angular momentum management method for vector electric propulsion orbital maneuvering to meet the attitude and orbit control requirements of all-electric propulsion satellites. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: to overcome the deficiencies of the prior art and provide a method for angular momentum management of a vector electric thruster, which is applicable to satellites with vector electric thrusters of various layouts. During the orbit transfer or position-keeping orbit phase, a control torque is generated by adjusting the vector adjustment mechanism of the vector electric thruster to achieve on-board angular momentum management. First, based on the geometric structure, installation position, installation matrix, and working combination of the vector electric thruster (to adapt to various working conditions), a linearized dynamic model for angular momentum management of the vector electric thruster is established; then, the control torque error term is estimated in real time through closed-loop feedback and compensated during the calculation of the angular momentum to be managed, and the rotation angle command of the vector electric thruster is calculated through the hysteresis control and pseudo-inverse distribution algorithm; finally, a proportional reduction processing method is given when the vector electric thruster exceeds the misalignment mechanism limit threshold. By linearly simplifying the dynamic model, the present invention reduces the computational complexity of the angular momentum management method and improves the angular momentum management accuracy by considering the introduction of closed-loop estimation, providing an effective and general method for realizing on-orbit angular momentum management of electric thrusters.

[0006] The technical solution of the present invention is as follows: A method for angular momentum management based on a vector electric thruster, and the specific steps are as follows:

[0007] Step (1): Obtain the rotation angle change-torque conversion matrix when a single vector electric thruster works;

[0008] Step (2): Obtain the rotation angle change-torque conversion matrix when vector electric thrusters work in combination;

[0009] Step (3): Calculate the angular momentum to be managed for the entire satellite according to the rotation angle change-torque conversion matrix obtained in step (2);

[0010] Step (4): Calculate the management torque for the entire satellite by using the hysteresis control algorithm according to the angular momentum to be managed for the entire satellite obtained in step (3);

[0011] Step (5): Calculate the change in the rotation angle position of the vector electric thruster by using pseudo-inverse command distribution according to the rotation angle change-torque conversion matrix obtained in step (2) and the management torque for the entire satellite obtained in step (4);

[0012] Step (6): Perform a limit processing on the change in the rotation angle position of the vector electric thruster obtained in step (5).

[0013] Further, in step (1), the method for obtaining the rotation angle-torque conversion matrix when a single vector electric thruster works is as follows:

[0014] The torque calculation formula generated by the i-th vector electric thruster is as follows:

[0015] T i =(R btpm rtpmy +R btpm R tpmy r yx +R btpm R tpmy R yx r x +r tpm )×R btpm R tpmy R yx F x

[0016] Among them, R btpm is the conversion matrix for vector adjustment to this system, R tpmy is the conversion matrix from the vector adjustment y-axis to the vector adjustment, R yx is the conversion matrix from the vector adjustment x-axis to the vector adjustment y-axis, r tpmy is the vector from the installation point to the origin of the y-axis coordinate system in the vector adjustment installation coordinate system, r yx is the vector from the origin of the y-axis coordinate system to the origin of the x-axis coordinate system in the y-axis coordinate system, r x is the vector from the origin of the x-axis coordinate system to the thrust application point of the thruster in the x-axis coordinate system, r tpmi is the vector from the center of mass to the i-th vector adjustment installation point in this system, F x is the thrust direction vector of the X-axis coordinate system,

[0017]

[0018]

[0019] Among them: β is the rotation angle of the Y-axis, α is the rotation angle of the X-axis, f is the nominal thrust modulus, h is the specific value of r tpmy 's specific value, l, m, n are the specific values of r tpmi 's specific value;

[0020] Further sorting gives the torque generated by the i-th vector electric thruster as:

[0021]

[0022] The theoretical torque is Taylor-expanded at the nominal rotation angle position (α i0 , β i0 ) to get:

[0023]

[0024] T err = T i (α i0 , β i0 ) + o(T i (Δα, Δβ))”

[0025] Among them, αi0 , β i0 is the nominal rotation angle of the i-th vector adjustment mechanism, and Δα i , Δβ i is the rotation angle offset of the i-th vector adjustment mechanism;

[0026] That is, the rotation angle change - torque transfer matrix is

[0027]

[0028] Furthermore, in the step (2), the method for obtaining the rotation angle change - torque conversion matrix during the combined operation of the vector electric thrusters is as follows:

[0029] For a spacecraft with m vector electric thrusters operating in combination, the Taylor expansion of the actual torque generated is:

[0030]

[0031]

[0032] where T err includes the control torque error terms caused by the installation error of the vector adjustment mechanism, control accuracy, thrust deviation of the thruster itself, and spacecraft centroid drift factors. Then, the rotation angle change - torque conversion matrix during the combined operation of the vector electric thrusters is: R = [r1…r i …r m .

[0033] Furthermore, in the step (3), the method for obtaining the overall satellite angular momentum to be managed is as follows:

[0034] For a satellite with n reaction wheels, the overall satellite angular momentum at time k is calculated as follows:

[0035] H k = I s ω bi + C W [h1 h2…h n T

[0036] h i = r i * 2πI i / 60; i = 1, 2, …n

[0037] where ω bi is the satellite attitude angular velocity, I i is the moment of inertia of the i-th flywheel, h i is the angular momentum of the i-th flywheel, I s is the overall satellite moment of inertia, r i ​is the rotational speed of the i-th flywheel, with the unit of rpm, C W is the flywheel installation matrix;

[0038] Based on the overall satellite angular momentum H k-1 at the (k - 1)th moment and the overall satellite angular momentum H k at the current moment, the overall satellite needs to manage the angular momentum:

[0039]

[0040] where, [Δα1 Δβ1…Δα m Δβ m k-1 T is the offset of the vector adjustment mechanism rotation angle relative to the nominal rotation angle at the (k - 1)th moment, R is the transfer matrix of the rotation angle deviation and torque at the nominal position of the vector thruster, and this item is determined by the specific vector thruster configuration, thrust magnitude, and overall satellite centroid position factors.

[0041] Furthermore, in the step (4), the overall satellite management torque calculated using the hysteresis control algorithm is obtained, and the specific method is as follows:

[0042] Given the controller parameters: open line H o , closed line H c and the vector adjustment mechanism control period t C , the switch state of the vector adjustment mechanism is IsGo, and the hysteresis control is used to calculate the vector adjustment mechanism control command, where the feedback signal is composed of the magnitude of the overall satellite angular momentum to be managed |H|;

[0043] Let the vector adjustment mechanism control command be T, and the control law is as follows:

[0044] Condition <![CDATA[|H|≥H c > <![CDATA[IsGo = 1H o >|H| ≥ H c > <![CDATA[IsGo = 0H o >|H|≥H c > <![CDATA[|H| < H o > Control <![CDATA[T = Ht C > <![CDATA[T = Ht C > T＝0 T＝0 Record IsGo = 1 IsGo = 1 IsGo = 0 IsGo = 0

[0045] Furthermore, in the step (5), the calculation of the change in the angular position of the vector electric thruster is as follows:

[0046] For a spacecraft equipped with m vector thrusters, by changing the angular positions of the x-axis and y-axis of its vector adjustment mechanism, the management torque command T calculated in the previous step can be achieved. These changes in angular positions are the vector thruster control allocation commands T wc ; if T is 0, then maintain the T of the previous cycle wc , otherwise T wc =-R - T; R - is the pseudo-inverse of the matrix R, R - =R T (RR T ) -1 .

[0047] ​Further, in step (6), a limiting process is performed on the change amount of the corner position of the vector electric thruster. The specific method is as follows:

[0048] Limit the maximum value of the corner position T of the vector electric thruster wc within ±η max :

[0049] Calculate the proportionality coefficient:

[0050] Calculate the change amount of the limited vector rotation angle position, that is: T wc = T wc ·T wcmax / T wci(max) where T wc(max) is the element with the largest modulus in T wc .

[0051] The beneficial effects of the present invention compared with the prior art are as follows:

[0052] (1) The method of the present invention aims at the control torque error terms caused by the installation error of the vector adjustment mechanism, control accuracy, thrust deviation of the thruster itself, and spacecraft centroid drift, estimates them in real time and performs closed-loop compensation, improves the management accuracy of the angular momentum management algorithm, and avoids problems such as frequent control of the vector thruster, serious attitude coupling, and low orbit control accuracy.

[0053] (2) The pseudo-inverse command distribution form of the present invention makes: when the rows of R are full rank, that is, the control dimension of the vector thruster is greater than 3, the corner position obtained by the pseudo-inverse takes the minimum norm, that is, the deviation degree of the thrust direction from the nominal position is the smallest, ensuring the orbit control accuracy; when the rows of R are not full rank, the corner position obtained by the pseudo-inverse is the least squares estimate of this equation.

[0054] (3) This method fully considers the constraints brought by the service life of the vector adjustment mechanism of the electric thruster, reduces the rotation frequency of the vector adjustment mechanism, extends the service life of the adjustment mechanism, and considers the problem of limited rotation angle of the vector adjustment mechanism, and identifies the overload of angular momentum unloading. Description of the Drawings

[0055] Figures 1(a), 1(b), and 1(c) are schematic diagrams of different working conditions of a typical vector electric thruster layout;

[0056] Figure 2 is the whole satellite angular momentum curve using the traditional angular momentum management algorithm;

[0057] Figure 3 is the whole satellite angular momentum curve using the angular momentum management algorithm of the present invention;

[0058] Figure 4Flowchart of the angular momentum management method based on a vector electric thruster. Detailed implementation manners

[0059] The following further describes in detail the specific implementation manners of the present invention with reference to the accompanying drawings.

[0060] Considering the commonly used configurations of current vector thrusters, a four-diagonal vector thruster configuration is adopted. In the orbit transfer section, to balance the propulsion efficiency and energy constraints, two thrusters on the diagonal work in pairs, and the nominal thrust points in the direction parallel to the z-axis. In the station-keeping section, each thruster works in a time-sharing and segmented manner.

[0061] As Figure 4 shown, an angular momentum management method based on a vector electric thruster is applicable to satellites with various layouts of vector electric thrusters. Taking the conical electric thruster layout as an example, four vector electric thrusters are symmetrically and diagonally installed on the four sides of the back floor of the satellite in pairs. Two electric thrusters on each diagonal form a pair, and there are a total of two pairs of electric thrusters. This method is calculated at the starting moment of a variation period of the vector adjustment mechanism of an electric thruster. The steps are as follows:

[0062] Step (1): Obtain the rotation angle change - torque conversion matrix when a single vector electric thruster works.

[0063] Step (2): Obtain the rotation angle change - torque conversion matrix when vector electric thrusters work in combination.

[0064] Step (3): Calculate the angular momentum to be managed for the entire satellite according to the rotation angle change - torque conversion matrix obtained in step (2).

[0065] Step (4): Calculate the management torque for the entire satellite by using the hysteresis control algorithm according to the angular momentum to be managed for the entire satellite obtained in step (3).

[0066] Step (5): Calculate the change amount of the rotation angle position of the vector electric thruster by using the pseudo-inverse command distribution according to the rotation angle change - torque conversion matrix obtained in step (2) and the management torque for the entire satellite obtained in step (4).

[0067] Step (6): Perform amplitude limiting processing on the change amount of the rotation angle position of the vector electric thruster obtained in step (5).

[0068] In step (1), the method for obtaining the rotation angle - torque conversion matrix when a single vector electric thruster works in combination is as follows:

[0069] The definitions, symbols, and numerical values of the required variables are shown in the following table:

[0070]

[0071]

[0072]

[0073] That is, the angle change amount - torque transfer matrix of each vector electric thruster is as follows:

[0074]

[0075] In step (2), the angle - torque conversion matrix is obtained when the vector electric thrusters work in combination. Define the diagonal electric thruster pair (the 1st and the 3rd vector electric thrusters work) during the orbit transfer phase. Therefore, the angle - torque conversion matrix when the electric thruster pair works is:

[0076]

[0077] In step (3), the total angular momentum that needs to be managed for the entire satellite is calculated as follows: For a satellite carrying 4 skewed - mounted flywheels, the definitions, symbols, and numerical values of the variables required to calculate the total angular momentum that needs to be managed for the entire satellite are shown in the following table:

[0078]

[0079]

[0080] Calculation of the flywheel angular momentum at time k: h1 = h2 = h3 = h4 = 1000 * 2π * 0.10823 / 60 = 11.328.

[0081] Calculation of the total satellite angular momentum at time k: H k = [2.3024 0.2632 2.38] T .

[0082] According to the total satellite angular momentum H k-1 at time k - 1 and the total satellite angular momentum H k at the current time, then the total angular momentum that needs to be managed for the entire satellite:

[0083]

[0084] In step (4), the total satellite management torque using hysteresis control is obtained as follows: The definitions, symbols, and numerical values of the variables required to calculate the total angular momentum that needs to be managed for the entire satellite are shown in the following table:

[0085]

[0086] The control command of the vector adjustment mechanism is calculated using hysteresis control, where the feedback signal is composed of the modulus |H| of the total angular momentum that needs to be managed for the entire satellite.

[0087] Calculate the modulus of the total angular momentum that needs to be managed for the entire satellite:

[0088] Let the control command of the vector adjustment mechanism be T, and the control law is as follows:

[0089] Condition <![CDATA[|H|≥H c > <![CDATA[IsGo=1H o >|H|≥H c > <![CDATA[IsGo=0H o >|H|≥H c > <![CDATA[|H| < H o <!-- 7 -->]]> Control <![CDATA[T = Ht c > <![CDATA[T = Ht c > T＝0 T＝0 Record IsGo = 1 IsGo = 1 IsGo = 0 IsGo = 0

[0090] The control torque T of the vector adjustment mechanism = H / t c = [-0.0030 -0.0053 -0.0029] T .

[0091] In the step (5), to obtain the change amount of the angular position of the vector electric thruster, the specific method is as follows: For a spacecraft equipped with m vector thrusters, by changing the angular positions of its vector adjustment mechanism on the x-axis and y-axis, the management torque command T calculated in the previous step can be achieved, and these change amounts of the angular positions are the control distribution commands T of the vector thrusters wc . If T is 0, then maintain the T of the previous cycle wc , otherwise T wc = -R - T. R - is the pseudo-inverse of the matrix R:

[0092]

[0093] T wc = -R - T = [0.0067 -0.0235 -0.0056 -0.0061] T .

[0094] In the step (6), to perform the limiting process on the angular position of the vector electric thruster, the specific method is as follows: Define the maximum limiting value η of the angular position of the vector electric thruster max = 0.02.

[0095] Proportional coefficient: T wcmax = -η max = -0.02, T wc(max) = -0.0235.

[0096] Calculate the angular control command of each direction of the vector adjustment mechanism after limiting, that is:

[0097] T wc = η max / T wcmax *T wc = [0.0057 -0.0200 -0.0048 -0.0052] T

[0098] Figure 2 And Figure 3 is the control effect using the traditional method, Figure 4To utilize the management method in the present invention. The traditional angular momentum management algorithm cannot compensate for the control torque error term, resulting in low control accuracy. Especially for the long bias error term of the control torque, a constant deviation appears in the angular momentum curve; while for the algorithm of the present invention, due to the addition of a compensation term, the angular momentum curve gradually converges smoothly to near zero value, with high control accuracy.

[0099] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. An angular momentum management method based on a vector electric thruster, characterized in that: The specific steps are as follows: Step (1): Obtain the rotation angle change - torque conversion matrix when a single - vector electric thruster works; Step (2): Obtain the rotation angle change - torque conversion matrix when vector electric thrusters work in combination; Step (3): Calculate the angular momentum that needs to be managed for the entire satellite according to the rotation angle change - torque conversion matrix obtained in Step (2); Step (4): Calculate the management torque for the entire satellite using the hysteresis control algorithm according to the angular momentum that needs to be managed for the entire satellite obtained in Step (3); Step (5): Calculate the change in the rotation angle position of the vector electric thruster using pseudo - inverse command allocation according to the rotation angle change - torque conversion matrix obtained in Step (2) and the management torque for the entire satellite obtained in Step (4); Step (6): Perform a limiting process on the change in the rotation angle position of the vector electric thruster obtained in Step (5); In Step (1), the method for obtaining the rotation angle - torque conversion matrix when a single - vector electric thruster works is as follows: The torque calculation formula generated by the i - th vector electric thruster is as follows: T i = (R btpm r tpmy + R btpm R tpmy r yx + R btpm R tpmy R yx r x + r tpm ) × R btpm R tpmy R yx F x Among them, R btpm is the conversion matrix for aligning to the system, R tpmy is the conversion matrix for aligning the y-axis to the alignment, R yx is the conversion matrix for aligning the x-axis to the y-axis of the alignment, r tpmy is the vector from the installation point to the origin of the y-axis coordinate system in the alignment installation coordinate system, r yx is the vector from the origin of the y-axis coordinate system to the origin of the x-axis coordinate system in the y-axis coordinate system, r x is the vector from the origin of the x-axis coordinate system to the thrust application point of the thruster in the x-axis coordinate system, r tpm is the vector from the center of mass to the i-th alignment installation point in the system, F x is the thrust direction vector of the X-axis coordinate system, Where: β is the rotation angle of the Y axis, α is the rotation angle of the X axis, f is the nominal thrust modulus, h is the specific value of r tpmy ; l, m, n are the specific values of r tpm ; After further arrangement, the torque generated by the i - th vector electric thruster is: The theoretical torque is Taylor-expanded at the nominal rotation angle position (α i0 , β i0 ) as follows: T err = T i (α i0 ,β i0 ) + o(T i (Δα, Δβ)) Among them, Terr includes the control torque error terms caused by the installation error of the vector adjustment mechanism, control accuracy, the thrust deviation of the thruster itself, and the centroid drift factor of the spacecraft; α i0 , β i0 is the nominal rotation angle of the i-th vector adjustment mechanism; Δα i , Δβ i is the rotation angle offset of the i-th vector adjustment mechanism; That is, the rotation angle change - torque transfer matrix is 2. The angular momentum management method based on a vector electric thruster according to claim 1, characterized in that: In Step (2), the method for obtaining the rotation angle change - torque conversion matrix when vector electric thrusters work in combination is as follows: For a spacecraft with m vector electric thrusters working in combination, the Taylor expansion of the true torque it generates is: Among them, T err includes the control torque error terms caused by the installation error of the vector adjustment mechanism, control accuracy, the thrust deviation of the thruster itself, and the center-of-mass drift factor of the spacecraft. Then, when the vector electric thrusters work in combination, the angle change-moment conversion matrix: R = [r1…r i …r m .

3. A method for angular momentum management based on a vector electric thruster according to claim 1, characterized in that: In Step (3), the method for obtaining the angular momentum that needs to be managed for the entire satellite is as follows: For a satellite with n reaction wheels, the angular momentum of the entire satellite at the k - th moment is calculated as follows: H k = I s ω bi + C W [h1 h2 … h n T ​ h i = r i * 2πI i / 60; i = 1, 2, … n where, ω bi is the satellite attitude angular velocity, I i is the moment of inertia of the i-th flywheel, h i is the angular momentum of the i-th flywheel, I s is the moment of inertia of the entire satellite, r i is the rotational speed of the i-th flywheel, with the unit of rpm, C W is the flywheel installation matrix; According to the overall satellite angular momentum H at time k-1 k-1 and the overall satellite angular momentum H at the current time k , the overall satellite needs to manage the angular momentum: Among them, [Δα1Δβ1…Δα m Δβ m k-1 T is the offset of the rotation angle of the vector adjustment mechanism at the k-1 moment relative to the nominal rotation angle, and R is the transfer matrix of the rotation angle deviation and torque of the vector thruster at the nominal position. This item is determined by the specific vector thruster configuration, the magnitude of the thrust, and the position of the overall satellite centroid.​ 4. A method for angular momentum management based on a vector electric thruster according to claim 1, characterized in that: In Step (4), the method for obtaining the management torque for the entire satellite using the hysteresis control algorithm is as follows: Given controller parameters: open line H o , closed line H c and the control period t of the vector adjustment mechanism C , the switch state of the vector adjustment mechanism is IsGo, and the control command of the vector adjustment mechanism is calculated by hysteresis control, where the feedback signal is composed of the magnitude of the angular momentum |H| that needs to be managed by the entire satellite; Let the control command of the vector adjustment mechanism be T, and the control law is as follows: 。 5. A method for angular momentum management based on a vector electric thruster according to claim 2, characterized in that: In Step (5), the method for calculating the change in the rotation angle position of the vector electric thruster is as follows: A spacecraft equipped with m vector thrusters can achieve the management torque command T obtained from the previous calculation by changing the angular positions of its vector adjustment mechanism on the x-axis and y-axis. These changes in angular positions are the vector thruster control allocation commands T wc ; if T is 0, then maintain the T of the previous cycle wc , otherwise T wc =-R - T; R - is the pseudo-inverse of the matrix R, and R - =R T (RR T ) -1 .

6. A method for angular momentum management based on a vector electric thruster according to claim 1, characterized in that: In Step (6), the method for performing a limiting process on the change in the rotation angle position of the vector electric thruster is as follows: Limit the maximum value of the vector electric thruster rotation angle position T wc within ±η max as follows: Calculate the proportionality coefficient: Calculate the change in the vector rotation angle after clipping, i.e.: T wc = T wc ·T wcmax / T wci(max) , where T wci(max) is the element with the largest modulus in T wc .

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