Satellite attitude anti-windup control method and device, electronic equipment and storage medium

Abstract

The application provides a satellite attitude anti-saturation control method and device, electronic equipment and a storage medium, wherein the method comprises the following steps: establishing a nominal controller for being used as a system control input when being not limited based on a controlled object model of a satellite; establishing an actuator model with amplitude saturation and rate saturation; establishing and solving an anti-saturation compensator by using the controlled object model, the nominal controller and the actuator model; and performing anti-saturation control on the satellite attitude by using an anti-saturation closed-loop system; and the anti-saturation closed-loop system comprises the controlled object model, the nominal controller, the actuator model and the anti-saturation compensator. According to the scheme, when the actuator is saturated, the input is compensated by the anti-saturation compensator, so that the output of the controller and the input of the controlled object are as equal as possible, thereby the satellite attitude control precision and the stability of the closed-loop system can be improved.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, and in particular to a satellite attitude anti-saturation control method, device, electronic device, and storage medium. Background Technology

[0002] In practical control systems, controllers mostly drive the controlled object through actuators. As a physical system, the actuator's output amplitude and rate of change are limited; that is, the actuator's response amplitude and rate of change are always constrained. The development of spacecraft technology and the increasing complexity of space missions place higher demands on control capabilities. However, the control torque that actuators can output in spacecraft attitude control is limited, exhibiting saturation nonlinearity. If the controller design does not consider the saturation nonlinearity of the actuator, when the actuator saturates, the controller's output will not be equal to the input value of the controlled object, potentially leading to decreased spacecraft attitude control accuracy or instability of the closed-loop system.

[0003] Common direct anti-saturation design methods based on linear matrix inequalities require a linear controller when dealing with amplitude and rate saturation problems. Furthermore, solving for the anti-saturation compensation gain using linear matrix inequalities is complex and computationally intensive. Currently, there is no control method specifically designed for nonlinear systems.

[0004] It is evident that there is an urgent need to provide an anti-saturation control method for handling nonlinear systems. Summary of the Invention

[0005] This invention provides a satellite attitude anti-saturation control method, device, electronic device, and storage medium. It takes into account the saturation nonlinearity of the actuator and can make the output of the controller and the input of the controlled object as equal as possible when the actuator is saturated, thereby improving the satellite attitude control accuracy and the stability of the closed-loop system.

[0006] In a first aspect, embodiments of the present invention provide a satellite attitude anti-saturation control method, comprising:

[0007] Based on the satellite-based controlled object model, a nominal controller is established when the system control input is unrestricted.

[0008] Establish actuator models exhibiting both amplitude saturation and rate saturation;

[0009] Using the controlled object model, the nominal controller, and the actuator model, an anti-saturation compensator is established and solved;

[0010] An anti-saturation closed-loop system is used to perform anti-saturation control on the satellite attitude; the anti-saturation closed-loop system includes: the controlled object model, the nominal controller, the actuator model, and the anti-saturation compensator.

[0011] Secondly, embodiments of the present invention also provide a satellite attitude anti-saturation control device, comprising:

[0012] The controller establishment unit is used to establish a nominal controller for use as an unrestricted system control input based on a satellite-based controlled object model.

[0013] The actuator modeling unit is used to build actuator models that exhibit both amplitude saturation and rate saturation.

[0014] The compensator establishment unit is used to establish and solve the anti-saturation compensator using the controlled object model, the nominal controller and the actuator model;

[0015] A control unit is used to perform anti-saturation control on the attitude of a satellite using an anti-saturation closed-loop system; the anti-saturation closed-loop system includes: the controlled object model, the nominal controller, the actuator model, and the anti-saturation compensator.

[0016] Thirdly, embodiments of the present invention also provide an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method described in any embodiment of this specification.

[0017] Fourthly, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to perform the methods described in any embodiment of this specification.

[0018] This invention provides a satellite attitude anti-saturation control method, device, electronic device, and storage medium. By establishing an actuator model with amplitude saturation and rate saturation and adding anti-saturation compensation design, an anti-saturation closed-loop system for anti-saturation control of satellite attitude is formed. When the actuator saturates, the anti-saturation compensator compensates for the input, making the output of the controller and the input of the controlled object as equal as possible, thereby improving the satellite attitude control accuracy and the stability of the closed-loop system. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of a satellite attitude anti-saturation control method provided in an embodiment of the present invention;

[0021] Figure 2 This is a block diagram of an anti-saturation closed-loop system provided in an embodiment of the present invention;

[0022] Figure 3 This is a schematic diagram of the system output response of an unrestricted system with amplitude rate saturation according to an embodiment of the present invention;

[0023] Figure 4 This is a schematic diagram of the output response of a closed-loop system after adding an anti-saturation compensator, provided in an embodiment of the present invention.

[0024] Figure 5 This is a comparative schematic diagram of the control inputs of an unrestricted system and an MRAW amplitude rate anti-saturation system provided in an embodiment of the present invention;

[0025] Figure 6 This is a comparative schematic diagram of the control input change rate of an unrestricted system and an MRAW amplitude rate anti-saturation system provided in an embodiment of the present invention;

[0026] Figure 7 This is a hardware architecture diagram of an electronic device provided in an embodiment of the present invention;

[0027] Figure 8 This is a structural diagram of a satellite attitude anti-saturation control device provided in an embodiment of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0029] Please refer to Figure 1 This invention provides a satellite attitude anti-saturation control method, which includes:

[0030] Step 100: Based on the satellite's controlled object model, establish a nominal controller for use as an unrestricted system control input;

[0031] Step 102: Establish an actuator model with amplitude saturation and rate saturation;

[0032] Step 104: Using the controlled object model, the nominal controller, and the actuator model, establish and solve the anti-saturation compensator;

[0033] Step 106: Use an anti-saturation closed-loop system to perform anti-saturation control on the satellite attitude; the anti-saturation closed-loop system includes: the controlled object model, the nominal controller, the actuator model, and the anti-saturation compensator.

[0034] In this embodiment of the invention, by establishing an actuator model with amplitude saturation and rate saturation, and adding an anti-saturation compensation design, an anti-saturation closed-loop system for anti-saturation control of satellite attitude is formed. When the actuator becomes saturated, the anti-saturation compensator compensates for the input, making the output of the controller and the input of the controlled object as equal as possible, thereby improving the accuracy of satellite attitude control and the stability of the closed-loop system.

[0035] The following description Figure 1 The execution method for each step is shown.

[0036] First, for step 100, based on the satellite's controlled object model, a nominal controller is established for use as an unrestricted system control input.

[0037] In this embodiment of the invention, taking the pitch axis of a flexible satellite as the controlled object as an example, the controlled object model of the satellite can be a simplified model of the dynamics of the pitch axis of the flexible satellite as follows:

[0038]

[0039]

[0040] Where J is the satellite's moment of inertia, ω is the pitch angular velocity, T is the control torque, and G = [g1 g2] T g i Let q be the coupling coefficient between the i-th mode of the flexible satellite and the satellite's pitch motion, where q = [q1 q2]. T Let Λ be the modal coordinates, Λ = diag(Λ1 Λ2) be the constrained modal frequencies, and q be the modal coordinates. i Λ i Let i and y represent the modal variables and constraint modal frequencies of the i-th mode of the flexible satellite, respectively, i = 1, 2.

[0041] Specifically, the method of establishing the nominal controller in step 100 may include the following steps 1001 and 1002:

[0042] 1001: The controlled object model of the satellite is represented using a second-order difference equation to obtain the characteristic model of the controlled object model;

[0043] In step 1001, the simplified model of the pitch axis dynamics of the above-mentioned flexible satellite can be expressed using a second-order difference equation of the following form to obtain the characteristic model of the controlled object model:

[0044] y(k+1)=f1(k)y(k)+f2(k)y(k-1)+g0(k)u(k) (3)

[0045] Where y(k+1) is the output feature variable of the feature model; y(k) and y(k-1) are the output feature variables of the system, which are also the actual output variables of the system; u(k) is the input control feature variable of the system at time k, which is also the input control variable of the actual object; f1(k), f2(k) and g0(k) are the feature parameters of the feature model, whose range can be predetermined and are within a known closed convex set.

[0046] 1002: Design an adaptive golden section controller for the characteristic model represented by the second-order difference equation, and use the adaptive golden section controller as the nominal controller when the system control input is unrestricted.

[0047] Using the characteristic model represented by the second-order difference equation shown in formula (3) above, the following adaptive golden section controller can be designed as the nominal controller when the system control input is unrestricted, which can ensure the stability of the closed-loop system and meet the performance requirements:

[0048]

[0049] Where u(k) is the system input control characteristic variable at time k, l1 = 0.382, l2 = 0.618e(k) = y(k) - y r y(k) and y(k) are the system output characteristic variables, y r (k) is the reference input. and These are the feature parameters of the feature model obtained through parameter identification.

[0050] It should be noted that the feature parameters of the feature model can be identified using various existing parameter identification methods. Preferably, parameter identification can be performed using the following gradient projection algorithm:

[0051]

[0052] Where θ(k)=[f1(k) f2(k) g0(k)] T It is the feature model parameter vector. It is the estimated value of the feature model parameter vector θ(k) at time k, φ(k)=[y(k) y(k-1) u(k)] TIt is a data vector, λ1>0 and λ2>0 are adjustable parameters, and π{·} represents an orthogonal projection onto a known closed convex set.

[0053] Then, for step 102, an actuator model with amplitude saturation and rate saturation is established.

[0054] In this embodiment of the invention, an actuator model exhibiting both amplitude saturation and rate saturation can be established using the Model Recovery Anti-Windup (MRAW) control method based on feature modeling. In the MRAW control method, a suitable model is needed to characterize the amplitude and rate saturation features; that is, a rate and amplitude saturation equation that can be considered a small-signal identifier needs to be introduced. The actuator model exhibiting both amplitude and rate saturation can be described by equation (6):

[0055] u(k+1)=u(k)+sat R (sat M (u c (k))-u(k))(6)

[0056] Where u(k) is the system input control characteristic variable at time k; u c (k) is the output of the nominal controller; where... M and R are the upper limit of amplitude and the upper limit of rate, respectively.

[0057] Next, for step 104, the anti-saturation compensator is established and solved using the controlled object model, the nominal controller, and the actuator model.

[0058] Specifically, step 104 can be achieved in the following way:

[0059] Step 1041: Transform the characteristic model represented by the second-order difference equation to obtain the characteristic model in state-space form, and determine the steady-state characteristic model corresponding to the characteristic model in state-space form;

[0060] To facilitate subsequent design analysis, it can be made The characteristic model (Equation (3)) represented by the second-order difference equation can then be transformed into a state-space form:

[0061]

[0062] in,

[0063] C p =[0 1].

[0064] According to the anti-saturation design process, the first step is to design an adaptive golden section controller based on a feature model that does not consider control input saturation, thus obtaining the feature model in steady state. According to feature modeling theory, under steady-state conditions, the feature model of the controlled object and the actual controlled object are equal in output. Therefore, the steady-state feature model can be used in MRAW to replace the original controlled object to solve for the anti-saturation compensator, and the linear MRAW anti-saturation method can be used to implement the anti-saturation design of high-order or nonlinear objects.

[0065] Considering the reference signal for tracking control, the following steady-state characteristic model can be obtained according to equation (7):

[0066]

[0067] in,

[0068] C =

[01] ; and All are fixed values.

[0069] Step 1042: Using the steady-state characteristic model, the nominal controller, and the actuator model, establish an anti-saturation compensator to be solved, such that the anti-saturation compensator outputs a first compensation and a second compensation, wherein the first compensation is used to compensate the output of the controlled object model, and the second compensation is used to compensate the output of the nominal controller; the anti-saturation compensator has constraints.

[0070] An anti-saturation compensator, from the perspective of a controller without control input saturation constraints, restores the system model without control input saturation. According to the anti-saturation design process, the nominal controller, when there are no control input saturation constraints, firstly demonstrates that the closed-loop system output can accurately track the input command signal, exhibiting good dynamic output response performance. This allows us to understand how an anti-saturation closed-loop control system with control input saturation constraints should respond under constrained conditions. By completely replicating the controlled object model, the MRAW anti-saturation compensator makes the closed-loop response of the saturated system as similar as possible to that of the unsaturated system. The design goal of anti-saturation is to minimize the output performance error between the anti-saturated system and the unconstrained system, which is quantitatively described using the L2 norm.

[0071] The design of an anti-saturation compensator can be summarized as constructing a state feedback controller that can make the response of the saturated system tend towards the desired response. An anti-saturation compensator is designed as shown in equation (9) to compensate for the control input when the closed-loop system becomes saturated. The first compensation y of the anti-saturation compensator output is... awThe main function of the anti-saturation compensator is to compensate for the output of the controlled object to ensure the normal operation of the nominal controller; while the second compensation υ1 of the anti-saturation compensator output is to restore the normal response of the unrestricted system as much as possible.

[0072]

[0073] Equation (9) above is subject to the following constraints:

[0074] y c (k)=y(k)-y aw (k) (10)

[0075] u(k) = sat M (δ(k)) (11)

[0076] Where, x aw (k), z aw (k) represents the state of the anti-saturation compensator and the output performance of the anti-saturation compensator, respectively; C =

[01] ; and All are fixed values; u c (k) is the output of the nominal controller; δ(k) is the new state obtained by integrating the difference of the output of the nominal controller and the second compensation υ1(k) together to satisfy the rate saturation limit; y aw (k) represents the first compensation, used to compensate the output of the controlled object model; y c (k) is the difference between the output of the controlled object model and the output of the anti-saturation compensator; M is the upper limit of the amplitude.

[0077] Since υ1(k) in the anti-saturation compensator shown in equation (9) is to be designed, it is necessary to solve equation (9) to obtain the designed anti-saturation compensator.

[0078] Step 1043: Based on the principle that the system state trajectory is the same when the system control input is restricted and when the system control input is unrestricted, the anti-saturation compensator is obtained by solving.

[0079] Please refer to Figure 2 This is a block diagram of the entire anti-saturation closed-loop system, consisting of... Figure 2It can be seen that it is necessary to be able to calculate the difference of the nominal controller output, and after this difference and the second compensation υ1 of the anti-saturation compensator jointly satisfy the rate saturation limit, the result is integrated to obtain a new state δ. This state then satisfies the amplitude saturation limit. Such a dynamic model meets the requirements. Thus, the input of the anti-saturation compensator consists of two parts: the output of the nominal controller and the newly added state δ. If it is necessary to obtain the difference of the nominal controller output, since the designed nominal controller is a strictly true controller, it can be solved directly.

[0080] For ease of analysis, δ is defined. aw (k)=δ(k)-u c (k), unrestricted controller state and output response Use superscripts to indicate this.

[0081] Analysis System x p -x aw From equations (8) and (9), we can see that:

[0082]

[0083] Therefore, the dynamics of systems (12) and (4) are the same as those of systems (8) and (4) for the initial conditions (xx). aw Since the two system state trajectories mentioned above are the same, based on the principle that the system state trajectories are the same whether the system control input is constrained or not, the following relationship can be obtained:

[0084]

[0085]

[0086]

[0087] Analyzing equation (13), it can be seen that when the actuator saturates, the system described by this equation depicts the state trajectory of an ideal system that has not saturated, which guides the control state to be restored. Therefore, it is necessary to design a suitable υ1 to make z aw →0, thus restoring the ideal output.

[0088] Consider an anti-saturation closed-loop system composed of the steady-state characteristic model (8) corresponding to the controlled object model, the adaptive golden section controller (4), the actuator model (6), the anti-saturation compensator (9) to be solved, and the constraint conditions (10) and (11). The controller state and output response (x) of the anti-saturation closed-loop system are given. c ,u c With unrestricted controller state and output response They are the same. And when At that time, there exist ρ > 0 and K types of functions γ(·) such that equation (14) holds, and for the initial conditions and Established:

[0089]

[0090] Among them, K aw It is a stabilized linear state feedback of the following system (15):

[0091] x aw (k+1)=Ax aw (k)+Bδ aw (k)

[0092]

[0093] Therefore, it is possible to take Such an anti-saturation compensator can be expressed as:

[0094]

[0095] Finally, for step 106, the satellite attitude is controlled by an anti-saturation closed-loop system; the anti-saturation closed-loop system includes: the controlled object model, the nominal controller, the actuator model, and the anti-saturation compensator.

[0096] In one embodiment of the present invention, when using an anti-saturation closed-loop system to perform anti-saturation control on satellite attitude, the anti-saturation compensator can provide compensation throughout the entire process, or it can be compensated in the following way:

[0097] When the output of the nominal controller does not exceed the set threshold, the anti-saturation compensator does not output compensation.

[0098] When the output of the nominal controller exceeds the set threshold, the anti-saturation compensator outputs compensation.

[0099] In other words, the anti-saturation compensator only provides compensation when the actuator becomes saturated, in order to ensure that the output of the controller and the input value of the controlled object are as equal as possible, thereby improving the attitude control accuracy of the spacecraft and the stability of the anti-saturation closed-loop system.

[0100] The following numerical simulation is performed on the design of an anti-saturation compensator for satellite attitude tracking control with constraints on control torque amplitude and rate saturation.

[0101] Please refer to Figure 3 This is a schematic diagram of the output response of an unconstrained system with amplitude and rate saturation. When the actuator exhibits both amplitude and rate saturation, the amplitude limit M = 1 and the rate limit R = 100. Figure 3 As can be seen, the control performance deteriorates, and it becomes difficult to track the reference signal during the adjustment phase.

[0102] With the anti-saturation compensator shown in equation (16) added, the closed-loop system output is as follows: Figure 4 As shown, the closed-loop system with the added anti-saturation compensator has regained its tracking of the reference signal. This can be seen from... Figure 5 and Figure 6 As can be seen, in a closed-loop system with an anti-saturation compensator, the amplitude and rate of change of the actuator's control output are within the required range while achieving the control objective.

[0103] like Figure 7 , Figure 8 As shown, this embodiment of the invention provides a satellite attitude anti-saturation control device. The device embodiment can be implemented through software, hardware, or a combination of both. From a hardware perspective, as... Figure 7 The diagram shown is a hardware architecture diagram of an electronic device for satellite attitude anti-saturation control provided in an embodiment of the present invention. (Except for...) Figure 7 In addition to the processor, memory, network interface, and non-volatile memory shown, the electronic device in the embodiment may also include other hardware, such as a forwarding chip responsible for processing packets. Taking software implementation as an example, such as... Figure 8 As shown, a logical device is formed by the CPU of its host electronic device reading the corresponding computer program from non-volatile memory into memory and running it. This embodiment provides a satellite attitude anti-saturation control device, including:

[0104] The controller establishment unit 801 is used to establish a nominal controller for use as an unrestricted system control input based on the satellite-based controlled object model.

[0105] Actuator establishment unit 802 is used to establish actuator models with amplitude saturation and rate saturation;

[0106] The compensator establishment unit 803 is used to establish and solve the anti-saturation compensator using the controlled object model, the nominal controller and the actuator model;

[0107] The control unit 804 is used to perform anti-saturation control on the satellite attitude using an anti-saturation closed-loop system; the anti-saturation closed-loop system includes: the controlled object model, the nominal controller, the actuator model, and the anti-saturation compensator.

[0108] In one embodiment of the present invention, the controller establishment unit is specifically used for: representing the controlled object model of the satellite using a second-order difference equation to obtain the characteristic model of the controlled object model; designing an adaptive golden section controller for the characteristic model represented by the second-order difference equation; and using the adaptive golden section controller as the nominal controller when the system control input is not limited.

[0109] In one embodiment of the present invention, the adaptive golden section controller is:

[0110]

[0111] Where u(k) is the system input control characteristic variable at time k, l1 = 0.382, l2 = 0.618, e(k) = y(k) - y r y(k) and y(k) are the system output characteristic variables, y r (k) is the reference input. and These are the feature parameters of the feature model obtained through parameter identification.

[0112] In one embodiment of the present invention, the compensator establishment unit is specifically used for:

[0113] The characteristic model represented by the second-order difference equation is formally transformed to obtain the characteristic model in state-space form, and the steady-state characteristic model corresponding to this characteristic model in state-space form is determined.

[0114] Using the steady-state characteristic model, the nominal controller, and the actuator model, an anti-saturation compensator to be solved is established, such that the anti-saturation compensator outputs a first compensation and a second compensation. The first compensation is used to compensate the output of the controlled object model, and the second compensation is used to compensate the output of the nominal controller. The anti-saturation compensator is subject to constraints.

[0115] Based on the principle that the system state trajectory is the same when the system control input is restricted and when the system control input is unrestricted, the anti-saturation compensator is obtained by solving.

[0116] In one embodiment of the present invention, the anti-saturation compensator is:

[0117]

[0118] Where, x aw (k), z aw (k) represents the state of the anti-saturation compensator and the output performance of the anti-saturation compensator, respectively; C = [0 1], and All are fixed values; uc (k) is the output of the nominal controller; δ(k) is the new state obtained by integrating the difference of the output of the nominal controller and the second compensation υ1(k) together to satisfy the rate saturation limit; y aw (k) represents the first compensation, used to compensate the output of the controlled object model; K aw To stabilize the linear state feedback gain;

[0119] The constraint condition for the existence of the anti-saturation compensator is:

[0120] y c (k)=y(k)-y aw (k)

[0121] u(k) = sat M (δ(k))

[0122]

[0123] Among them, y c (k) is the difference between the output of the controlled object model and the output of the anti-saturation compensator; M is the upper limit of the amplitude.

[0124] In one embodiment of the present invention, the actuator model exhibiting amplitude saturation and rate saturation is as follows:

[0125] u(k+1)=u(k)+sat R (sat M (u c (k))-u(k))

[0126]

[0127]

[0128] Where u(k) is the system input control characteristic variable at time k; u c (k) represents the output of the nominal controller; M and R represent the upper limit of amplitude and the upper limit of speed, respectively.

[0129] In one embodiment of the present invention, the control unit is specifically used to: perform anti-saturation control on the satellite attitude using an anti-saturation closed-loop system; when the output of the nominal controller does not exceed a set threshold, the anti-saturation compensator does not output compensation; when the output of the nominal controller exceeds the set threshold, the anti-saturation compensator outputs compensation.

[0130] It is understood that the structures illustrated in the embodiments of the present invention do not constitute a specific limitation on a satellite attitude anti-saturation control device. In other embodiments of the present invention, a satellite attitude anti-saturation control device may include more or fewer components than illustrated, or combine some components, or split some components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.

[0131] The information interaction and execution process between the modules in the above-mentioned device are based on the same concept as the method embodiment of the present invention, and the specific details can be found in the description of the method embodiment of the present invention, and will not be repeated here.

[0132] This invention also provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a satellite attitude anti-saturation control method according to any embodiment of this invention.

[0133] This invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform a satellite attitude anti-saturation control method according to any embodiment of this invention.

[0134] Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the embodiments described above is stored, and the computer (or CPU or MPU) of the system or apparatus may read and execute the program code stored in the storage medium.

[0135] In this case, the program code read from the storage medium can itself implement the function of any of the above embodiments, and therefore the program code and the storage medium storing the program code constitute part of the present invention.

[0136] Examples of storage media used to provide program code include floppy disks, hard disks, magneto-optical disks, optical disks (such as CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-RAM, DVD-RW, DVD+RW), magnetic tapes, non-volatile memory cards, and ROMs. Alternatively, program code can be downloaded from a server computer via a communication network.

[0137] Furthermore, it should be clear that not only can the program code read by the computer be executed, but also the operating system or other components operating on the computer can be instructed based on the program code to perform some or all of the actual operations, thereby realizing the function of any of the embodiments described above.

[0138] Furthermore, it is understood that the program code read from the storage medium is written to the memory set in the expansion board inserted into the computer or to the memory set in the expansion module connected to the computer. Then, based on the instructions of the program code, the CPU or other components installed on the expansion board or expansion module execute some and all of the actual operations, thereby realizing the function of any of the above embodiments.

[0139] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0140] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of satellite attitude anti-windup control, characterized in that, The method comprises the following steps: a satellite-based controlled object model is used to establish a nominal controller when system control input is not limited; an actuator model with amplitude saturation and rate saturation is established; the actuator model introduces a rate-amplitude saturation equation which can be regarded as a small signal identifier; an anti-saturation compensator is established and solved by using the controlled object model, the nominal controller and the actuator model; anti-saturation control is performed on the satellite attitude by using an anti-saturation closed-loop system; the anti-saturation closed-loop system comprises the controlled object model, the nominal controller, the actuator model and the anti-saturation compensator; the actuator model with amplitude saturation and rate saturation is as follows: wherein, is k the system input control feature variable at the time instant; is the output quantity of the nominal controller; , are the amplitude upper limit and the rate upper limit, respectively; is the difference between the output quantity of the nominal controller and the second compensation the new state after the common satisfaction of the rate saturation limit, the integration of the difference between the output quantity of the nominal controller and the first compensation the anti-saturation compensator is as follows: wherein , are the state of the antisaturation compensator and the output performance of the antisaturation compensator, respectively; , , , , and are fixed values; is a first compensation for compensating the output of the controlled object model; is a stabilizing linear state feedback gain.

2. The method of claim 1, wherein, the satellite-based controlled object model is used to establish a nominal controller when system control input is not limited, which comprises the following steps: a characteristic model of the controlled object model is obtained by using a second-order difference equation to represent the satellite-based controlled object model; an adaptive golden section controller is designed for the characteristic model represented by the second-order difference equation, and the adaptive golden section controller is used as the nominal controller when system control input is not limited.

3. The method of claim 2, wherein, the adaptive golden section controller is as follows: wherein , , , is a system output feature variable, is a reference input, , and is a feature variable of a feature model identified by parameters.

4. The method of claim 3, wherein, the anti-saturation compensator is established and solved by using the controlled object model, the nominal controller and the actuator model, which comprises the following steps: the characteristic model in the state space form is obtained by performing formal transformation on the characteristic model represented by the second-order difference equation, and a steady-state characteristic model corresponding to the characteristic model in the state space form is determined; an anti-saturation compensator to be solved is established by using the steady-state characteristic model, the nominal controller and the actuator model, so that the anti-saturation compensator outputs a first compensation and a second compensation, wherein the first compensation is used to compensate the output of the controlled object model, and the second compensation is used to compensate the output of the nominal controller; the anti-saturation compensator has a constraint condition; the anti-saturation compensator is solved based on the principle that the system state trajectory is the same when system control input is limited and when system control input is not limited.

5. The method according to claim 4, wherein the constraint condition of the anti-saturation compensator is as follows: wherein, outputs the difference between the controlled object model output and the anti-windup compensator output.

6. The method according to any one of claims 1 to 5, characterized in that, anti-saturation control is performed on the satellite attitude by using an anti-saturation closed-loop system, wherein when the output of the nominal controller does not exceed a set threshold, the anti-saturation compensator does not output compensation; when the output of the nominal controller exceeds the set threshold, the anti-saturation compensator outputs compensation. The method according to any one of claims 1-6 is implemented by using the following device:

7. A satellite attitude anti-windup control apparatus characterized by comprising: a controller establishing unit is configured to establish a nominal controller based on a satellite-based controlled object model when system control input is not limited; an actuator establishing unit is configured to establish an actuator model with amplitude saturation and rate saturation; a compensator establishing unit is configured to establish and solve an anti-saturation compensator by using the controlled object model, the nominal controller and the actuator model. ​ The control unit is configured to perform anti-windup control on the satellite attitude by using an anti-windup closed loop system, wherein the anti-windup closed loop system comprises the controlled object model, the nominal controller, the actuator model and the anti-windup compensator. 8.An electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method according to any one of claims 1-6. 9.A computer readable storage medium storing a computer program, wherein the computer program, when executed in a computer, causes the computer to perform the method according to any one of claims 1-6.

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