A design method for high-fidelity digital model of satellite reaction wheel

Abstract

A method for designing a high-fidelity digital model of a single satellite reaction wheel relates to a method for designing a satellite component model. A reaction wheel drive model consisting of a three-phase inverter bridge, a three-phase winding, and a reaction wheel body and a rotor sector detection model based on a Hall sensor are established, and a reaction wheel linear switching system model is built based on the above results. On the one hand, the present invention solves the problems of inaccurate results and imprecise modeling of existing methods, and has high fidelity with the actual satellite reaction wheel system. On the other hand, it has the characteristics of modularization and parameterization, and can adapt to reaction wheels of different models.

Description

Technical Field

[0001] The invention relates to a satellite component model design method, in particular to a satellite reaction wheel stand-alone high-fidelity digital model design method, belonging to the technical field of satellite stand-alone component modeling. Background Art

[0002] The satellite reaction wheel is a component used for satellite attitude control. Its main function is to change the satellite's attitude by using the principle of conservation of angular momentum, thereby maintaining the satellite's stable operation. Specifically, the satellite in space will be subject to interference torque caused by external factors such as the atmosphere and solar pressure. The interference torque generates angular momentum under the cumulative effect of time, which makes the satellite's attitude unstable. At this time, the reaction wheel needs to rotate so that the satellite also generates angular momentum of equal magnitude and opposite direction, so that the satellite's attitude remains unchanged. Therefore, the accuracy of the reaction wheel model is crucial for satellite attitude control. An accurate reaction wheel model can improve the accuracy and stability of satellite attitude control, thereby ensuring the normal operation of the satellite. However, the accuracy of the reaction wheel model depends on multiple factors, such as the mechanical structure of the reaction wheel, motor drive, control algorithm, etc. Therefore, in order to ensure the accuracy of the model, multi-faceted research and analysis is required.

[0003] According to the relevant literature published at home and abroad, the current research on reaction wheels is mainly focused on control algorithms and fault detection. There is a lack of research results on the reaction wheel model itself, which is often replaced by a simple linear DC motor model and engineering experience. Faced with the increasingly frequent demands for spacecraft attitude maneuvers and long-term transfer orbit conditions such as deep space exploration, this simplified model is not only unable to meet the mission requirements of high-precision attitude control of spacecraft, but also difficult to invert the inertia, circuit, bearing friction and other parameters of the reaction wheel, so as to monitor the status and life of the satellite.

[0004] Therefore, establishing a high-precision and highly detailed reaction wheel system model is of great significance both for onboard attitude control missions and for the construction of ground digital satellite platforms. Summary of the invention

[0005] In order to address the deficiencies in the background technology, the present invention provides a method for designing a high-fidelity digital model of a single satellite reaction wheel, which solves the problems of inaccurate results and imprecise modeling in existing methods, and has high fidelity with the actual satellite reaction wheel system.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for designing a high-fidelity digital model of a single satellite reaction wheel, comprising the following steps:

[0007] Step 1: Establish a reaction wheel drive model consisting of a three-phase inverter bridge-three-phase winding-reaction wheel body

[0008] The brushless DC motor consists of a three-phase inverter bridge and a three-phase winding. Its input includes the inverter bridge bus voltage V DC , sector signal σ s and the back EMF e=[e A e B e C ] T , whose output is electromagnetic power P m , the reaction wheel body is in the electromagnetic power P m Under the action of the self-inertia and bearing friction characteristics, the output speed ω and electrical angle θ e ;

[0009] In the brushless DC motor, each sector is divided into the freewheeling phase and the DC phase, and a model that uniformly describes the three-phase current i is established using linear transformation, as follows:

[0010] In the freewheeling stage, a linear transformation P1(k) is introduced, and its expression is as follows:

[0011] P1(k)=(E 1,3 E 1,2 ) k (1)

[0012] Among them, E i,j represents a third-order elementary matrix, that is, the matrix obtained by exchanging the i-th and j-th rows of the identity matrix;

[0013] Then, the linear transformation P1(k) is used for the back electromotive force e and combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the freewheeling stage of different sectors:

[0014]

[0015] Among them, R represents the phase resistance of the motor winding, L represents the phase inductance of the motor winding, and The intermediate variables representing the three-phase current i and the back electromotive force e in the freewheeling stage;

[0016] In the DC stage, a linear transformation P2(k) is introduced, and its recursive method is described as follows:

[0017] P2(k)=E(k)P2(k-1) (3)

[0018] When k = 1, P2(0) is a third-order unit matrix, and the value of E(k) is determined by the sector, expressed as:

[0019]

[0020] Then, the linear transformation P2(k) of the back electromotive force e is combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the DC phase of different sectors:

[0021]

[0022] in, i and e The intermediate variables representing the three-phase current i and the back electromotive force e in the DC phase;

[0023] After obtaining the three-phase current i, the electromagnetic power P output by the brushless DC motor is m It is expressed as:

[0024] P m =e T ·i (6)

[0025] The reaction wheel generates a rotation speed ω and an electrical angle θ e The process is expressed as:

[0026]

[0027] Where J represents the moment of inertia of the wheel, c v represents the viscous friction coefficient of the bearing, p represents the number of pole pairs of the motor, mod(a,b) represents the remainder of a and b, and Ω represents the square of the rotation speed;

[0028] Finally, according to the electrical angle θ e The expression of back electromotive force e is obtained:

[0029]

[0030] Where, Wave represents the unit back electromotive force, K e represents the back electromotive force coefficient, f(θ e ) represents the trapezoidal wave function, and its formula is as follows:

[0031]

[0032] In summary, formula (1) to formula (9) give the reaction wheel drive model consisting of three-phase inverter bridge-three-phase winding-reaction wheel body;

[0033] Step 2: Establish a rotor sector detection model based on Hall sensor

[0034] The Hall sensor detects the electrical angle θ e Generate the corresponding Hall signal H, the expression is as follows:

[0035]

[0036] Among them, h(θe ) represents the measurement equation of the single-phase Hall sensor, which is expressed as:

[0037]

[0038] Secondly, according to the Hall signal H, a sector signal σ is generated to control the on / off of each MOS tube of the three-phase inverter bridge. s , the expression is as follows:

[0039]

[0040] Finally, according to the sector signal σ s The value of is used to obtain the on / off status of each MOS tube;

[0041] Step 3: Establish the reaction wheel linear switching system model based on steps 1 and 2

[0042] The state space model of the reaction wheel obeys the two-layer switching law: the sector signal σ s The switching law of the known switching signal measured by the Hall sensor is ①; in each sector, the switching law constrained to the state-dependent switching law of formula (2) or formula (5) is determined according to the specific value of the three-phase current i;

[0043] Let the state vector x = [i A ,i B ,i C ,ω] T , input vector u=V DC , the output vector y = ω, when it is in the freewheeling stage in a certain sector, a linear transformation is introduced:

[0044]

[0045] Where diag[] represents a diagonal matrix consisting of the elements in brackets. According to formula (2), The state space representation of is:

[0046]

[0047] in, 1 k,j represents a k-row and j-column matrix with all elements set to 1;

[0048] when After dropping to 0, the circuit enters the DC stage and introduces linear transformation:

[0049]

[0050] at this time x The state space representation of is:

[0051]

[0052] In summary, first of all, according to the switching rule ①, and The value of is then determined according to the switching rule ② to determine whether the system adopts formula (14) or formula (16).

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] 1. Model each minimum functional unit of the reaction wheel to ensure the refinement of the model;

[0055] 2. The high fidelity of this model was proved by building a physical verification platform and conducting comparisons;

[0056] 3. A modular and parameterized reaction wheel model was established, which can adapt to different reaction wheels;

[0057] 4. Provides an interface for testing the controller and simulating faults for actual use, which is convenient for users. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of information flow between the reaction wheel drive model established by the present invention;

[0059] Figure 2 It is the equivalent circuit diagram of the brushless DC motor;

[0060] Figure 3 It is a comparison diagram of the speed curve of the reaction wheel model of the present invention and the speed curve of the real object;

[0061] Figure 4 It is a schematic diagram of the secondary development interface of the reaction wheel model of the present invention. DETAILED DESCRIPTION

[0062] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0063] like Figure 1-2 As shown, a method for designing a high-fidelity digital model of a single satellite reaction wheel comprises the following steps:

[0064] Step 1: Establish a reaction wheel drive model consisting of a three-phase inverter bridge-three-phase winding-reaction wheel body

[0065] Information flow integration of the drive part in the reaction wheel drive model Figure 1As shown in the dashed box, the brushless DC motor is first composed of a three-phase inverter bridge and a three-phase winding. Its input includes the inverter bridge bus voltage V DC , sector signal σ s and the back EMF e=[e A e B e C ] T , whose output is the electromagnetic power P that drives the reaction wheel m , and secondly, the reaction wheel body has an electromagnetic power P m Under the action of the self-inertia and bearing friction characteristics, the output speed ω and electrical angle θ e ;

[0066] Equivalent circuit of brushless DC motor Figure 2 As shown, the MOS tubes T1~T6 of each sector will have 2 on and 4 off, and after each sector change, due to the existence of the winding phase inductance, the three-phase current will maintain the characteristics of the previous sector in a short time, so it is difficult to directly analyze the three-phase current i=[i A i B i C ] T Therefore, this scheme divides each sector into the freewheeling phase and the DC phase, and uses linear transformation to establish a model that can uniformly describe the change law of the three-phase current in different sectors over time, as follows:

[0067] In the freewheeling stage, the expression of the linear transformation P1(k) is first given:

[0068] P1(k)=(E 1,3 E 1,2 ) k (1)

[0069] Among them, E i,j represents a third-order elementary matrix, that is, the matrix obtained by swapping the i-th and j-th rows of the identity matrix.

[0070] Then, the linear transformation P1(k) is used for the back electromotive force e and combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the freewheeling stage of different sectors:

[0071]

[0072] Among them, R represents the phase resistance of the motor winding, L represents the phase inductance of the motor winding, and It represents the intermediate variables of the three-phase current i and the back electromotive force e in the freewheeling stage.

[0073] Similarly, in the DC stage, a linear transformation P2(k) is introduced, which can be described recursively as follows:

[0074] P2(k)=E(k)P2(k-1) (3)

[0075] When k = 1, P2(0) is a third-order unit matrix, and the value of E(k) is determined by the sector, expressed as:

[0076]

[0077] Then, the linear transformation P2(k) of the back electromotive force e is combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the DC phase of different sectors:

[0078]

[0079] in, i and e It represents the intermediate variables of the three-phase current i and the back electromotive force e in the DC stage.

[0080] After obtaining the three-phase current i, the electromagnetic power P output by the brushless DC motor is m It is expressed as:

[0081] P m =e T ·i (6)

[0082] According to the electromagnetic effect and rigid body rotational dynamics, the reaction wheel generates a rotation speed ω and an electrical angle θ e The process is expressed as:

[0083]

[0084] Where J represents the moment of inertia of the wheel, c v represents the viscous friction coefficient of the bearing, p represents the pole pair number of the motor, mod(a,b) represents the remainder of a and b, Ω represents the square of the rotational speed. This scheme selects Ω as the differential variable to solve the singular phenomenon of the equation caused by the reaction wheel being stationary or reversing.

[0085] Finally, according to the electrical angle θ e The expression of back electromotive force e is obtained:

[0086]

[0087] Where, Wave represents the unit back electromotive force, K e represents the back electromotive force coefficient, f(θ e ) represents the trapezoidal wave function, and its formula is as follows:

[0088]

[0089] In summary, formula (1) to formula (9) give the reaction wheel drive model consisting of a three-phase inverter bridge-three-phase winding-reaction wheel body.

[0090] Step 2: Establish a rotor sector detection model based on Hall sensor

[0091] Hall sensor combined with information flow in the drive part of the reaction wheel drive model Figure 1 As shown above the dotted box, firstly, the electrical angle θ is detected e Generate the corresponding Hall signal H, the expression is as follows:

[0092]

[0093] Among them, h(θ e ) represents the measurement equation of the single-phase Hall sensor, which is expressed as:

[0094]

[0095] Secondly, according to the Hall signal H, a sector signal σ is generated to control the on / off of each MOS tube of the three-phase inverter bridge. s , the expression is as follows:

[0096]

[0097] Finally, according to the sector signal σ s The value of is used to obtain the on / off status of each MOS tube.

[0098] Step 3: Establish the reaction wheel linear switching system model based on steps 1 and 2

[0099] Due to the existence of the three-phase inverter bridge, the state space model of the reaction wheel is a linear switching system, which obeys two-layer switching rules: first, the sector signal σ s , the signal is measured by the Hall sensor and can be considered as the switching law of the known switching signal①; secondly, in each sector, the constraint is determined as formula (2) or formula (5) according to the specific value of the three-phase current i, which belongs to the state-dependent switching law②.

[0100] Let the state vector x = [i A ,i B ,i C ,ω] T , input vector u=V DC , the output vector y = ω, when it is in the freewheeling stage in a certain sector, the following linear transformation is introduced:

[0101]

[0102] Where diag[] represents a diagonal matrix consisting of the elements in brackets. According to formula (2), The state space representation of is:

[0103]

[0104] in, 1 k,j Represents a k-row and j-column matrix with all elements set to 1.

[0105] when After dropping to 0, the circuit enters the DC stage, and linear transformation is also introduced:

[0106]

[0107] at this time x The state space representation of is:

[0108]

[0109] In summary, the system has 12 subsystems. First, according to the switching rule ①, and The value of is then determined according to the switching rule ② to determine whether the system adopts formula (14) or formula (16).

[0110] In order to verify the high fidelity of the reaction wheel model proposed in this scheme, a reaction wheel physical verification platform is established to verify the model, as follows:

[0111] The same bus voltage is applied to the physical platform and the model, and the reaction wheel model parameters are set to the nominal parameters of the physical object, as shown in Table 1 below:

[0112] Table 1 Parameters of the reaction wheel physical platform

[0113]

[0114] The changes in the speed of the two are combined Figure 3 As shown, it can be seen that the speed curve of the reaction wheel model proposed in this scheme is highly matched with the actual speed curve and has good fidelity.

[0115] The reaction wheel model proposed in this scheme is modular and parameterized and can be adapted to different reaction wheels.

[0116] The drive circuit can adapt to three different forms of inverter power circuits: three-phase half-bridge, three-phase full-bridge and C-Dump; the motor winding can adapt to three connection methods: star connection, closed connection and multi-phase winding; the reaction wheel bearing can choose viscous, Coulomb or Dhal friction torque model according to different wheel bearings; the Hall sensor can adapt to three rotor position detection methods: three Hall sensors, multiple Hall sensors and back-EMF inductive position detection.

[0117] In addition, according to different reaction wheels, this model has a variety of adjustable parameters for adaptation, as shown in Table 2 below:

[0118] Table 2 Adjustable parameters of reaction wheel model

[0119]

[0120] This model has application-oriented functions such as testing controllers and simulating faults. Figure 4 As shown in the figure, this model has a controller interface for the reaction wheel. The sector signal output by the Hall sensor module can be used to design the outer ring speed controller, and then the inner ring speed controller can be designed using the output result of the outer ring speed controller and the three-phase current generated by the model. Finally, the result of the current loop is used as the bus voltage. The parameters involved in the two-ring controller can be debugged in the model and transferred to the real object for testing after the response is appropriate. In addition, thanks to the modular parameterized modeling method of this model, the component-level faults that may occur when the reaction wheel is working can be simulated. This model also has a motor fault interface, a wheel body fault interface, and a sensor fault interface. The state space model proposed in step three can be used to design the reaction wheel fault diagnosis algorithm, and the correctness of the algorithm can be verified by combining the data output by this model.

[0121] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0122] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for designing a high-fidelity digital model of a satellite reaction wheel, characterized in that: The following steps are involved: Step 1: Establish a reaction wheel drive model consisting of a three-phase inverter bridge-three-phase winding-reaction wheel body The brushless DC motor consists of a three-phase inverter bridge and a three-phase winding. Its input includes the inverter bridge bus voltage V DC , sector signal σ s and the back EMF e=[e A e B e C ] T , whose output is electromagnetic power P m , the reaction wheel body is in the electromagnetic power P m Under the action of the self-inertia and bearing friction characteristics, the output speed ω and electrical angle θ e ; In the brushless DC motor, each sector is divided into the freewheeling phase and the DC phase, and a model that uniformly describes the three-phase current i is established using linear transformation, as follows: In the freewheeling stage, a linear transformation P1(k) is introduced, and its expression is as follows: P1(k)=(E 1,3 E 1,2 ) k (1) Among them, E i,j represents a third-order elementary matrix, that is, the matrix obtained by exchanging the i-th and j-th rows of the identity matrix; Then, the linear transformation P1(k) is used for the back electromotive force e and combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the freewheeling stage of different sectors: Among them, R represents the phase resistance of the motor winding, L represents the phase inductance of the motor winding, and The intermediate variables representing the three-phase current i and the back electromotive force e in the freewheeling stage; In the DC stage, a linear transformation P2(k) is introduced, and its recursive method is described as follows: P2(k)=E(k)P2(k-1) (3) When k = 1, P2(0) is a third-order unit matrix, and the value of E(k) is determined by the sector, expressed as: Then, the linear transformation P2(k) of the back electromotive force e is combined with the equivalent circuit of the brushless DC motor to obtain the model of the three-phase current i in the DC phase of different sectors: Among them, i and e represent the intermediate variables of the three-phase current i and the back electromotive force e in the DC stage; After obtaining the three-phase current i, the electromagnetic power P output by the brushless DC motor is m It is expressed as: P m =e T ·i (6) The reaction wheel generates a rotation speed ω and an electrical angle θ e The process is expressed as: Where J represents the moment of inertia of the wheel, c v represents the viscous friction coefficient of the bearing, p represents the number of pole pairs of the motor, mod(a,b) represents the remainder of a and b, and Ω represents the square of the rotation speed; Finally, according to the electrical angle θ e The expression of back electromotive force e is obtained: Where, Wave represents the unit back electromotive force, K e represents the back electromotive force coefficient, f(θ e ) represents the trapezoidal wave function, and its formula is as follows: In summary, formula (1) to formula (9) give the reaction wheel drive model consisting of three-phase inverter bridge-three-phase winding-reaction wheel body; Step 2: Establish a rotor sector detection model based on Hall sensor The Hall sensor detects the electrical angle θ e Generate the corresponding Hall signal H, the expression is as follows: Among them, h(θ e ) represents the measurement equation of the single-phase Hall sensor, which is expressed as: Secondly, according to the Hall signal H, a sector signal σ is generated to control the on / off of each MOS tube of the three-phase inverter bridge. s , the expression is as follows: Finally, according to the sector signal σ s The value of is used to obtain the on / off status of each MOS tube; Step 3: Establish the reaction wheel linear switching system model based on steps 1 and 2 The state space model of the reaction wheel obeys the two-layer switching law: the sector signal σ s The switching law of the known switching signal measured by the Hall sensor is ①; in each sector, the switching law constrained to the state-dependent switching law of formula (2) or formula (5) is determined according to the specific value of the three-phase current i; Let the state vector x = [i A ,i B ,i C ,ω] T , input vector u=V DC , the output vector y = ω, when it is in the freewheeling stage in a certain sector, a linear transformation is introduced: Where diag[] represents a diagonal matrix consisting of the elements in brackets. According to formula (2), The state space representation of is: in, 1 k,j represents a k-row and j-column matrix with all elements set to 1; when After dropping to 0, the circuit enters the DC stage and introduces linear transformation: at this time x The state space representation of is: In summary, first of all, according to the switching rule ①, and The value of is then determined according to the switching rule ② to determine whether the system adopts formula (14) or formula (16).

2. The method for designing a high-fidelity digital model of a single satellite reaction wheel according to claim 1, characterized in that: The Hall sensor is developed to set up a sensor fault interface, the brushless DC motor is developed to set up a controller interface and a motor fault interface, and the reaction wheel is developed to set up a wheel body fault interface.

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