Stability Analysis Method for Adaptive Augmentation Controller of Launch Vehicle

Abstract

This invention provides a stability analysis method for an adaptive augmented controller (AAC) of a launch vehicle, relating to the field of spacecraft dynamics and control. The method includes: establishing a rocket control model based on rocket state variables, engine rudder deflection, a pre-set PD controller, and a correction network; determining the controller stability characteristics of the rocket control model; and then, combining error terms, elasticity terms, and regression terms, determining the rocket AAC control model and its necessary stability conditions; obtaining the adaptive control stability conditions based on the rocket AAC control model and its necessary stability conditions; and further obtaining the parameter tuning conditions that stabilize the rocket AAC control model. According to this invention, it can provide direct parameter tuning basis for the engineering application of AAC controllers, reduce reliance on batch simulations in engineering, improve the standardization, interpretability, and stability reliability of parameter design, and enhance the development efficiency of launch vehicle control systems.

Description

Technical Field

[0001] This invention relates to the field of spacecraft dynamics and control, and in particular to a stability analysis method for an adaptive augmented controller for launch vehicles. Background Technology

[0002] Currently, stability analysis of launch vehicle AAC controllers mainly includes methods such as modular stability analysis, describing function approximation analysis, and frequency sweep test analysis. Modular analysis typically addresses error, elastic, and regression terms separately, offering good applicability only when there are significant differences in magnitude between modules, thus limiting its application. While the describing function method can perform stability analysis on error and regression terms and incorporate the regression term into the stability analysis framework to approximate the nonlinear characteristics of the AAC controller, it still lacks a complete stability criterion, making it difficult to apply in engineering practice. Although frequency sweep test methods have been used in engineering to evaluate the applicability of controller design results, their theoretical support is insufficient, and stability and reliability still rely on batch simulations and target testing, resulting in a large workload. Therefore, the related technologies as a whole still struggle to form a unified stability analysis framework for AAC controllers, making it difficult to fully guarantee the stability and reliability of controller design results theoretically, lacking clear basis for parameter tuning, and incurring high engineering verification costs, ultimately affecting the design efficiency and reliability of launch vehicle control systems.

[0003] The information disclosed in the background section of this application is intended only to enhance the understanding of the general background of this application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0004] This invention provides a stability analysis method for adaptive augmented controllers (AACs) of launch vehicles, which can solve the technical problems in related technologies where AACs lack a complete stability analysis framework in launch vehicle applications, resulting in a lack of theoretical basis for controller parameter tuning, low engineering design efficiency and reliability, and high engineering verification costs.

[0005] According to a first aspect of the present invention, a method for stability analysis of an adaptive augmentation controller for a launch vehicle is provided, comprising: Based on the rocket state variables, engine rudder deflection, preset PD controller and correction network, a rocket control model is established, and the controller stability characteristics of the rocket control model are determined. Based on the rocket control model, as well as the error term, elasticity term, and regression term, the rocket AAC control model is determined, and based on the controller stability characteristics and the rocket AAC control model, the necessary conditions for the stability of the rocket AAC control model are determined. Based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model, the adaptive control stability conditions are obtained. Based on the adaptive control stability conditions, the parameter tuning conditions that stabilize the rocket AAC control model are obtained.

[0006] According to the present invention, a rocket control model is established based on rocket state variables, engine rudder deflection, a preset PD controller, and a correction network, and the controller stability characteristics of the rocket control model are determined, including: Based on the rocket state variables, engine rudder deflection, and state space matrix, set the rocket dynamics state space expression; The rocket dynamics state-space expression is processed by a preset PD controller to obtain the PD coefficient vector; The rocket control model is obtained by processing the PD coefficient vector through a calibration network. Lyapunov stability analysis was performed on the rocket control model to obtain the controller stability characteristics of the rocket control model.

[0007] According to the present invention, based on the rocket control model, and error terms, elasticity terms, and regression terms, a rocket AAC control model is determined, and based on the controller stability characteristics and the rocket AAC control model, the necessary conditions for the stability of the rocket AAC control model are determined, including: Based on the rocket control model, the error term is obtained; Based on the aforementioned error term, elasticity term, and regression term, the rocket AAC control model is determined; Based on the rocket AAC control model and controller stability characteristics, the Lyapunov function is obtained; Based on the Lyapunov function, determine the necessary stability conditions for the rocket AAC control model.

[0008] According to the present invention, based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model, adaptive control stability conditions are obtained, including: Based on the necessary stability conditions of the rocket AAC control model, intermediate variables are set; Based on the intermediate variables, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model, optional stability conditions are set. Based on the necessary stability conditions of the rocket AAC control model, set the necessary stability conditions; Based on the optional stability conditions and the necessary stability conditions, the adaptive control stability conditions are obtained.

[0009] According to the present invention, based on the intermediate variable, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model, optional stability conditions are set, including: Based on the rocket AAC control model, set the model parameter range; Based on the intermediate variables and the necessary stability conditions of the rocket AAC control model, selection conditions are set; Based on the necessary stability conditions of the rocket AAC control model, determine the stability conditions corresponding to each selection condition; Based on the range of model parameters, the selection conditions, and the stability conditions corresponding to each selection condition, the optional stability conditions are determined.

[0010] According to the present invention, the parameter tuning conditions for stabilizing the rocket AAC control model are obtained based on the adaptive control stability conditions, including: Based on the necessary stability conditions, set the necessary parameter tuning conditions; Based on the necessary parameter tuning conditions, the model parameter range, and the optional stability conditions, set the adaptive Lyapunov stability conditions; Based on the necessary parameter tuning conditions and the adaptive Lyapunov stability conditions, the parameter tuning conditions that stabilize the rocket AAC control model are obtained.

[0011] According to the present invention, adaptive Lyapunov stability conditions are set based on necessary parameter tuning conditions, model parameter ranges, and optional stability conditions, including: The gain parameter range is obtained based on the necessary parameter tuning conditions; Set the lower limit range of the gain parameter according to the optional stability conditions; Based on the range of the gain parameter, the lower limit range of the gain parameter, and the range of the model parameters, the adaptive Lyapunov stability conditions are obtained.

[0012] According to a second aspect of the present invention, a stability analysis system for an adaptive augmentation controller of a launch vehicle is provided, comprising: The stability feature acquisition module establishes a rocket control model based on rocket state variables, engine rudder deflection, a pre-set PD controller, and a correction network, and determines the controller stability features of the rocket control model. The first condition acquisition module determines the rocket AAC control model based on the rocket control model, as well as the error term, elasticity term, and regression term, and determines the necessary conditions for the stability of the rocket AAC control model based on the controller stability characteristics and the rocket AAC control model. The second condition acquisition module obtains the adaptive control stability conditions based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model. The third condition acquisition module obtains the parameter tuning conditions that stabilize the rocket AAC control model based on the adaptive control stability conditions.

[0013] According to a third aspect of the present invention, a stability analysis device for an adaptive augmentation controller of a launch vehicle is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to execute the stability analysis method for the adaptive augmentation controller of the launch vehicle.

[0014] According to a fourth aspect of the present invention, a computer-readable storage medium is provided having computer program instructions stored thereon, which, when executed by a processor, implement the stability analysis method for the adaptive augmentation controller of a launch vehicle.

[0015] By adopting the above technical solution, the present invention can achieve the following technical effects: The stability analysis method for the adaptive augmented controller (AAC) of launch vehicles proposed in this application comprehensively considers the error term, elasticity term, and regression term in the AAC control model to obtain the necessary stability conditions applicable to engineering practice. Furthermore, by combining the internal relationships of various parameters in the AAC control model, it obtains the parameter tuning conditions that ensure the stability of the AAC control model, thus guiding engineering parameter design. This method solves the problems of incomplete stability theory and weak adaptability in the design process of launch vehicle AAC control models. This method can provide direct parameter tuning basis for the engineering application of AAC controllers, reduce the reliance on batch simulations in engineering, improve the standardization, interpretability, and stability reliability of parameter design, and enhance the development efficiency of launch vehicle control systems.

[0016] This application presents a stability analysis method for adaptive augmented controllers (AACs) of launch vehicles. It uses state-space expressions to uniformly model the dynamics of large launch vehicles and integrates the PD controller and correction network into the same conventional control framework. By integrating variables, a holistic state-space model is formed. Based on this state space, a Lyapunov function is constructed, and the stability characteristics of the conventional controller are extracted. This achieves a theoretical and systematic characterization of the stability of conventional rocket control schemes. This application provides a reliable stability benchmark for the subsequent introduction of AAC control laws, comprehensive stability determination, and parameter tuning.

[0017] This application presents a stability analysis method for an adaptive augmented controller for launch vehicles. It incorporates the AAC control law into a traditional control block diagram, constructing a rocket AAC control model that comprehensively considers error, elastic, and regression terms. Based on the controller's stability characteristics, a Lyapunov analysis framework is further established to derive the necessary stability conditions for the AAC controller applicable to engineering practice. This method facilitates the transition from traditional control stability benchmarks to adaptive augmented control stability determination, providing a complete theoretical foundation for AAC controller stability analysis. It enhances the engineering interpretability and verifiability of controller design and provides a direct basis for subsequent adaptive control stability condition analysis and parameter tuning condition extraction.

[0018] The stability analysis method for the adaptive augmented controller (AAC) of launch vehicles proposed in this application, based on obtaining the necessary conditions for the stability of the AAC controller, comprehensively considers the error term, elastic term, and regression term in the AAC controller to complete the theoretical proof of stability. It transforms the complex Lyapunov stability inequality into a parameter constraint expression that is easy to judge, and then summarizes the adaptive control stability conditions between the various parameters of the AAC. This makes the stability analysis of the AAC controller clearer, more verifiable, and more engineering-oriented, and can effectively reduce the dependence on batch simulation in engineering and improve the efficiency of the rocket development process.

[0019] The stability analysis method for the adaptive augmented controller of a launch vehicle proposed in this application can analyze the aforementioned adaptive control stability conditions one by one, transforming the necessary stability constraints into essential parameter tuning conditions. Furthermore, by combining the model parameter range and optional stability conditions, adaptive Lyapunov stability conditions are extracted, thereby obtaining the parameter tuning conditions that stabilize the rocket's AAC control model. This method can provide a direct basis for parameter tuning in the engineering application of AAC controllers, improving the standardization, interpretability, and stability reliability of parameter design, and enhancing the development efficiency of launch vehicle control systems.

[0020] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Other features and aspects of the invention will become clearer from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0021] 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 only some embodiments of the present invention. For those skilled in the art, other embodiments can be obtained based on these drawings without creative effort. Figure 1 A schematic flowchart of a stability analysis method for an adaptive augmented controller of a launch vehicle according to an embodiment of the present invention is shown as an example. Figure 2 A block diagram of a conventional control scheme for a large launch vehicle according to an embodiment of the present invention is shown as an example; Figure 3 An exemplary block diagram of an AAC control scheme for a large launch vehicle according to an embodiment of the present invention is shown; Figure 4 An exemplary diagram of a stability analysis system for an adaptive augmentation controller for a launch vehicle, according to an embodiment of the present invention, is shown. Detailed Implementation

[0022] 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 only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0024] Figure 1 An exemplary flowchart illustrates a stability analysis method for an adaptive augmentation controller of a launch vehicle according to an embodiment of the present invention, the method comprising: Step S1: Based on the rocket state variables, engine rudder deflection, preset PD controller and correction network, establish the rocket control model and determine the controller stability characteristics of the rocket control model. Step S2: Based on the rocket control model, as well as the error term, elasticity term, and regression term, determine the rocket AAC control model, and based on the controller stability characteristics and the rocket AAC control model, determine the necessary stability conditions of the rocket AAC control model. Step S3: Based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model, obtain the adaptive control stability conditions. Step S4: Based on the adaptive control stability conditions, obtain the parameter tuning conditions that stabilize the rocket AAC control model.

[0025] According to an embodiment of the present invention, a stability analysis method for an adaptive augmented controller (AAC) for launch vehicles comprehensively considers the error term, elasticity term, and regression term in the AAC control model to obtain the necessary stability conditions applicable to engineering practice. Furthermore, by combining the internal relationships of various parameters in the AAC control model, parameter tuning conditions that ensure the stability of the AAC control model are obtained, guiding engineering parameter design. This method solves the problems of incomplete stability theory and weak adaptability in the design process of launch vehicle AAC control models. This method can provide direct parameter tuning basis for the engineering application of AAC controllers, reduce reliance on batch simulations in engineering, improve the standardization, interpretability, and stability reliability of parameter design, and enhance the development efficiency of launch vehicle control systems.

[0026] Example 1: According to an embodiment of the present invention, in step S1, a rocket control model can first be established, and a PD controller and a correction network can be constructed to build a conventional control model of the launch vehicle, and a Lyapunov function can be constructed to derive the stability characteristics of the controller.

[0027] Figure 2 A block diagram of a conventional control scheme for a large launch vehicle according to an embodiment of the present invention is shown as an example.

[0028] According to an embodiment of the present invention, a rocket control model is established based on rocket state variables, engine rudder deflection, a preset PD controller, and a correction network, and the controller stability characteristics of the rocket control model are determined. This includes: setting a rocket dynamics state-space expression based on rocket state variables, engine rudder deflection, and a state-space matrix; processing the rocket dynamics state-space expression using a preset PD controller to obtain a PD coefficient vector; processing the PD coefficient vector using a correction network to obtain the rocket control model; and performing Lyapunov stability analysis on the rocket control model to obtain the controller stability characteristics of the rocket control model.

[0029] According to an embodiment of the present invention, firstly, the rocket dynamics state-space expression is set by means of rocket state variables, engine rudder deflection, and state-space matrix. This process is shown in formula (1).

[0030] (1) in, These are the rocket's state variables, including attitude, angular velocity, elastic modal generalized displacement, and fluid sloshing displacement. To control the engine rudder deflection in the pitch channel. and Both are state-space matrices, where A is an n×n matrix and B is an n×m matrix, where n is the number of state variables and m is the number of engines.

[0031] According to an embodiment of the present invention, after obtaining the rocket dynamics state-space expression, the expression is processed by a preset PD controller to obtain the PD coefficient vector. The PD controller only selects attitude and angular velocity from the rocket state variables for feedback processing; therefore, the output after passing through the PD controller is: ,in, It is an n×1 vector, that is, the PD coefficient vector.

[0032] According to an embodiment of the present invention, after obtaining the PD coefficient vector, the PD coefficient vector is further processed by a correction network. The output of the correction network is the engine rudder deflection controlling the pitch channel, and the correction network itself can be described by a transfer function. Assuming the transfer function of the correction network... for: (2) in, For the complex frequency domain variables in the Laplace transform, , , ..., , To correct the coefficients of the numerator polynomial of the network transfer function, ,… , To correct the coefficients of the denominator polynomial of the network transfer function, This represents the highest order of the numerator polynomial. The highest order of the denominator polynomial. To correct the output of the network's transfer function, To correct the input of the network's transfer function, here is .

[0033] Furthermore, by performing an inverse Laplace transform on the transfer function, the corresponding time-domain expression can be obtained, as shown in equation (3). (3) in, To correct the input signal of the network, To correct the network's output signal, Indicates the input signal of the calibration network The first derivative with respect to time, Indicates the output signal of the calibration network The first derivative with respect to time.

[0034] According to an embodiment of the present invention, since the correction network is described in transfer function form while the rocket dynamics model is described in state-space form, in order to facilitate the subsequent unified integration of the correction network with the rocket dynamics model and PD controller, the correction network needs to be further converted into state-space form. Specifically, let the input of the correction network be... The output is Based on the order of the correction network transfer function, the output is selected. and input The state vector is composed of several derivatives of order . ,in, Let p be a vector of length 1. This is related to the order of the transfer function of the correction network. Therefore, the correction network can be written in state-space standard form, as shown in equation (4). (4) in, To correct the state matrix of the network, To correct the input matrix of the network, To correct the output matrix of the network, To correct the direct transfer matrix of the network, This represents the set of feasible PD gains that enable the traditional PD plus correction network control scheme to meet stability requirements. To correct the network's time-domain output.

[0035] According to an embodiment of the present invention, since the transfer function is converted into a state-space format, it is only necessary to describe the dynamic relationship between the input, state variables, and output, that is... ,therefore Except for the first line, the parameters mainly describe and The relationship between them , Just take Corresponding state , .

[0036] According to an embodiment of the present invention, by combining formulas (1), (4) and the aforementioned PD controller output relationship, a rocket control model can be obtained, as shown in formula (5). (5) in, , The extended state vector consists of rocket state variables and correction network state variables. and These are the system matrix and input matrix in the overall state-space model of the traditional control scheme, respectively.

[0037] According to an embodiment of the present invention, in engineering applications, through reasonable margin analysis, a set of parameters can be found that enables the closed-loop system to meet stability requirements and have the expected dynamic response characteristics, thus making the rocket body stable. This conclusion is expressed by the following formula (6) through Lyapunov stability: (6) According to an embodiment of the present invention, since the PD plus correction network controller can stabilize the rocket body, the derivative of the Lyapunov function must be less than 0, as shown in the following formula (7): (7) According to an embodiment of the present invention, a suitable , and , making It also possesses good dynamic characteristics. Furthermore, the gain... It is not unique, but rather there exists a set of feasible gains. .when The system remained stable at that time. Further introduction... To characterize the range of gain variation, the relationship shown in formula (8) can be obtained. (8) Among them, the upper bound of the derivative of the Lyapunov function within the gain perturbation range is: ,because ,therefore, , This represents the maximum perturbation amplitude of the gain parameter relative to its nominal value.

[0038] Therefore, within a certain gain perturbation range, the derivative of the Lyapunov function remains negative definite. By analyzing the result after converting the transfer function to a state-space format, the controller stability characteristics of the rocket control model are obtained, as shown in equation (9). (9) in, This indicates the change in engine rudder deflection in the pitch channel. Indicates the pitch channel angular velocity. This indicates the pitch channel attitude angle deviation. and This represents the coefficient in the PD controller that corresponds to the relationship between attitude angle deviation and angular velocity feedback.

[0039] In this way, the dynamics of large launch vehicles are uniformly modeled using state-space expressions. Based on this, the PD controller and correction network are integrated into the same conventional control framework. A holistic state-space model is formed through variable integration, and a Lyapunov function is constructed based on this state space to obtain the stability characteristics of the conventional controller. This achieves a theoretical and systematic characterization of the stability of conventional rocket control schemes. It provides a reliable stability benchmark for the subsequent introduction of AAC control laws, comprehensive stability determination, and parameter tuning.

[0040] Example 2: According to an embodiment of the present invention, in step S2, the rocket AAC control model and its necessary stability conditions can be obtained by considering the error term, elasticity term, and regression term, combined with the aforementioned rocket control model and Lyapunov function.

[0041] Figure 3 An exemplary block diagram of an AAC control scheme for a large launch vehicle according to an embodiment of the present invention is shown.

[0042] According to an embodiment of the present invention, a rocket AAC control model is determined based on a rocket control model, as well as an error term, an elasticity term, and a regression term. Furthermore, the necessary stability conditions for the rocket AAC control model are determined based on the controller stability characteristics and the rocket AAC control model. This process includes: obtaining an error term based on the rocket control model; determining the rocket AAC control model based on the error term, the elasticity term, and the regression term; obtaining a Lyapunov function based on the rocket AAC control model and the controller stability characteristics; and determining the necessary stability conditions for the rocket AAC control model based on the Lyapunov function.

[0043] According to an embodiment of the present invention, the error term can be obtained based on the above-described rocket control model. Since the PD controller controls attitude angle deviation and angular velocity during engineering implementation, the error term can be expressed as follows: ,in, This represents the state sub-vector composed of the attitude angle deviation and angular velocity deviation selected from the rocket's state variables. This represents the coefficient vector or matrix used to map the state subvectors to the error terms, which are used to select and weight the attitude angle deviations and angular velocity deviations to form the error terms. Then, based on the error terms, elastic terms, and regression terms, the rocket AAC control model is determined. Specifically, the AAC control law is shown in formula (10). (10) in, For a constant value, for rate of change, for rate of change, For gain parameters, This is the upper limit of the gain parameter. This is the lower limit of the gain parameter, and also... The initial value is given, and there is , If it is an elastic vibration signal, then It can be represented as an elasticity term. This is the regression term. , and This is an adjustable parameter. Furthermore, according to... Figure 3 The block diagram of the AAC control scheme for the large launch vehicle shown can be used to obtain the system expression of the rocket's AAC control model, as shown in formula (11). (11) According to an embodiment of the present invention, combining the controller stability characteristics obtained in formula (9) with the system expression of the rocket AAC control model, an adaptive control Lyapunov function analysis framework is constructed, wherein the Lyapunov function... The derivative is shown in formula (12). (12) According to an embodiment of the present invention, in order to further adapt the gain The dynamic changes are incorporated into a unified stability analysis framework, and an extended Lyapunov function is defined. Its derivative is shown in formula (13). (13) According to an embodiment of the present invention, based on formula (13), not only can the state changes of the rocket AAC control model be characterized, but also the adaptive gain can be... The change process is incorporated into the Lyapunov function, thus providing a foundation for the subsequent derivation of the necessary stability conditions. The PD control parameters are obtained through time interpolation. Considering that stability analysis in engineering applications typically focuses on short timescales, the PD control parameters can be considered approximately constant within a small time interval. time derivative It can be approximately ignored, that is Therefore, we can obtain the following formula (14). (14) According to an embodiment of the present invention, after obtaining the approximate condition shown in formula (14), it is necessary to further prove that the following inequality holds: (15) According to an embodiment of the present invention, if formula (15) holds, it can be proven that the derivative of the extended Lyapunov function satisfies This demonstrates that the rocket's AAC control model meets the stability requirements. Further analysis of formula (15) reveals that... Meanwhile, from the matrix definition of the above traditional control model, we can obtain... ,available .

[0044] Furthermore, due to ,remember ,Pick , As a constant, we have Therefore, formula (15) can be further simplified to formula (16), where, and These are the mapping coefficients for the AAC error term.

[0045] (16) According to an embodiment of the present invention, due to adaptive gain in engineering and All are positive, therefore we have If satisfied Then there is Under these conditions, if further satisfying This can prove .

[0046] Based on the above analysis, the necessary conditions for the stability of the rocket AAC control model can be determined as shown in the following formulas (17) and (18): (17) (18) According to an embodiment of the present invention, when the inequality conditions of formulas (17) and (18) are met, it can be guaranteed that the derivative of the extended Lyapunov function satisfies the negative definite requirement, thereby realizing the determination of the stability of the rocket AAC control model.

[0047] In this way, the AAC control law is incorporated into the traditional control block diagram, constructing a rocket AAC control model that comprehensively considers error, elasticity, and regression terms. Based on the controller's stability characteristics, a Lyapunov analysis framework is further established to derive the necessary stability conditions for the AAC controller applicable to engineering practice. This achieves a transition from traditional control stability benchmarks to adaptive augmented control stability criteria, providing a complete theoretical foundation for AAC controller stability analysis, enhancing the engineering interpretability and verifiability of controller design, and providing a direct basis for subsequent adaptive control stability condition analysis and parameter tuning condition extraction.

[0048] Example 3: According to an embodiment of the present invention, in step S3, the relationship between various parameters of the rocket AAC control model can be analyzed to obtain the adaptive control stability conditions.

[0049] According to an embodiment of the present invention, obtaining adaptive control stability conditions based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model includes: setting intermediate variables based on the necessary stability conditions of the rocket AAC control model; setting optional stability conditions based on the intermediate variables, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model; setting necessary stability conditions based on the necessary stability conditions of the rocket AAC control model; and obtaining adaptive control stability conditions based on the optional stability conditions and the necessary stability conditions.

[0050] According to an embodiment of the present invention, when obtaining the adaptive control stability conditions based on the rocket AAC control model and its necessary stability conditions, intermediate variables are first set according to the necessary stability conditions of the rocket AAC control model. Specifically, after obtaining the necessary stability conditions of the rocket AAC control model, to facilitate further simplification and classification discussion of these necessary stability conditions, intermediate variables are introduced... , Intermediate variables, among which, Represents the PD coefficient vector With state subvector The combined quantity constituted; This represents the quadratic form or squared modulus of the PD coefficient vector. Furthermore, it is related to proportional relationships. Therefore, we can obtain Therefore, the quadratic form of the error term can be derived. Rewritten as Through this process, the error term in the necessary conditions for stability can be replaced by an intermediate variable. This is expressed as follows. Further, based on the necessary stability conditions of the rocket AAC control model, necessary stability conditions are set. Specifically, the second of the necessary stability conditions of the rocket AAC control model (i.e., formula (18)) is denoted as... ,in, It is actually a straight line, so we need to find the condition that its maximum value is less than or equal to 0.

[0051] According to an embodiment of the present invention, through further detailed analysis, optional stability conditions and necessary stability conditions are set, and the final adaptive control stability conditions are derived from this. The necessary stability conditions can be obtained based on the necessary stability conditions of the rocket AAC control model, as shown in the following formulas (19) and (20): (19) (20) According to an embodiment of the present invention, based on the intermediate variable, the rocket AAC control model, and the necessary stability condition of the rocket AAC control model, an optional stability condition can be obtained, namely: when When there are two cases, a and b, as shown in the following formula, only one of the optional stability conditions needs to be satisfied.

[0052] Case a: hour, like ,need ; like ,need ; like ,need ; Scenario b: and .

[0053] According to an embodiment of the present invention, the above necessary stability conditions and optional stability conditions are further summarized so that they together form the adaptive control stability conditions among the parameters of AAC. That is, the necessary stability conditions are the adaptive control stability conditions formulas (19) and (20), and the optional stability conditions are one of the two cases a or b mentioned above.

[0054] According to an embodiment of the present invention, setting optional stability conditions based on the intermediate variables, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model includes: setting a model parameter range based on the rocket AAC control model; setting selection conditions based on the intermediate variables and the necessary stability conditions of the rocket AAC control model; determining the stability conditions corresponding to each selection condition based on the necessary stability conditions of the rocket AAC control model; and determining optional stability conditions based on the model parameter range, the selection conditions, and the stability conditions corresponding to each selection condition.

[0055] According to an embodiment of the present invention, a model parameter range is set based on the rocket AAC control model, the model parameter range including: Furthermore, based on the intermediate variables and the necessary stability conditions of the rocket AAC control model, a detailed analysis of formula (20) in the necessary stability conditions of the rocket AAC control model is conducted, and then selection conditions and corresponding stability conditions are set for each selection condition. Specifically, there are three cases.

[0056] Scenario 1: When Sometimes, , , In this case, only ,Right now, Combining , can be obtained , and, because Therefore, the above inequality must be true, and no conditions need to be set.

[0057] Scenario 2: When Sometimes, ,exist When the maximum value is reached. Therefore, only , combined , can be obtained In this case, if Then it is necessary to make ;if Then it is necessary to make ;if Then it is necessary to make .

[0058] Scenario 3: In Sometimes, , ,exist At that moment, the maximum value is achieved. That is, only need to make , combined After sorting, we can obtain The right side is clearly greater than 0, and it is also known that... Since the left side is clearly less than zero, the expression must be true and no conditions need to be set.

[0059] In summary, scenarios one and three are automatically satisfied under the corresponding conditions, therefore no further constraints are needed. Scenario two, however, requires detailed analysis considering the relevant parameter symbols and value ranges to determine the selection criteria (i.e., regarding...). The conditions for stability (and their corresponding stability conditions) are then analyzed and summarized into optional stability conditions. The optional stability conditions are the same as those analyzed above and will not be repeated here.

[0060] In this way, based on obtaining the necessary conditions for the stability of the AAC controller, the theoretical proof of stability is completed by comprehensively considering the error term, elastic term, and regression term in the AAC controller. The complex Lyapunov stability inequality is transformed into a parameter constraint expression that is easy to judge. Then, the adaptive control stability conditions between the various parameters of the AAC are summarized, making the stability analysis of the AAC controller clearer, more verifiable, and more engineeringable. This can effectively reduce the dependence on batch simulation in engineering and improve the efficiency of the rocket development process.

[0061] Example 4: According to an embodiment of the present invention, in step S4, obtaining parameter tuning conditions that stabilize the rocket AAC control model based on the adaptive control stability conditions includes: setting necessary parameter tuning conditions based on the necessary stability conditions; setting adaptive Lyapunov stability conditions based on the necessary parameter tuning conditions, the model parameter range, and optional stability conditions; and obtaining parameter tuning conditions that stabilize the rocket AAC control model based on the necessary parameter tuning conditions and the adaptive Lyapunov stability conditions.

[0062] According to an embodiment of the present invention, after obtaining the adaptive control stability conditions of each parameter of the AAC, the stability conditions are analyzed one by one in an engineering manner to obtain parameter tuning rules that can be used for the design of the AAC controller. First, the necessary parameter tuning conditions are set according to the necessary stability conditions. Among them, the first necessary stability condition (formula (19)) in the adaptive control stability conditions is analyzed. Since the relevant parameters satisfy the same sign constraint, if stability is still required after the introduction of adaptive control, the corresponding gain relationship must also be satisfied. Furthermore, combined with the margin boundary after the system design is completed, it can be seen that the adaptive gain cannot be increased indefinitely, otherwise it will destroy the desired time domain response effect. Therefore, the adaptive gain needs to be limited to the value of 1 for adjustment, and its engineering expression is shown in formula (21): (twenty one) in: express The cases of taking positive and negative values.

[0063] According to an embodiment of the present invention, the second necessary stability condition (formula (20)) in the adaptive control stability condition is analyzed. This conclusion corresponds to another necessary parameter tuning condition, where the relevant parameters are constant. This condition can be achieved by designing adaptive parameters and ensuring that the proportional relationship between angular deviation and angular velocity is consistent with that of the PD controller. At the same time, the corresponding initial conditions should also be guaranteed. Thus, the second necessary parameter tuning condition is obtained as shown in the following formula (22): (twenty two) in, ( (As constant), by designing adaptive parameters And ensure that the ratio of angular deviation to angular velocity is consistent with that of the PD controller. This can make the initial .

[0064] Furthermore, based on the necessary parameter tuning conditions, the model parameter range, and the optional stability conditions, adaptive Lyapunov stability conditions are set, including: obtaining the gain parameter range based on the necessary parameter tuning conditions; setting the lower limit range of the gain parameter based on the optional stability conditions; and obtaining the adaptive Lyapunov stability conditions based on the gain parameter range, the lower limit range of the gain parameter, and the model parameter range.

[0065] Specifically, after obtaining the adaptive control stability conditions among the various parameters of AAC, an engineering analysis of the optional stability conditions within the adaptive control stability conditions can be performed to obtain the gain parameter range of the optional stability conditions, i.e., the adaptive gain. It should be limited to between the preset upper and lower limits of gain, satisfying Based on the aforementioned necessary parameter tuning conditions, it can be seen that the adaptive gain should not deviate from the stability margin range of the traditional control system and should be adjusted around the value of 1 to avoid the adaptive gain being too large or too small, which would lead to a deterioration in the system's dynamic response or a reduction in the stability margin. Therefore, the overall range of the adaptive gain parameter can be obtained. Furthermore, combined with the model parameter range, i.e., .in, and This can be achieved through adaptive parameter design. This can be achieved by passing the elastic vibration signal through a high-pass filter, squaring it, and then passing it through a low-pass filter. This can be determined by combining the aforementioned gain parameter range. Therefore, the above constraints constitute the basic parameter range of the adaptive Lyapunov stability condition. Further, combining the optional stability conditions in step S3, an engineering comparison is performed on cases a and b; satisfying either one is sufficient. Since under the above conditions... ， Therefore, when the model parameter range satisfies There will inevitably be Therefore, it can be seen that the stability condition corresponding to case a is easier to satisfy in engineering than that of case b; therefore, case a should be analyzed in more detail first. Furthermore, since... ,and ,but This is necessarily true; therefore, it is only necessary to ensure that the following inequality (23) holds during the design phase in order to set the adaptive gain lower limit. The conditions that should be met are the adaptive Lyapunov stability conditions.

[0066] (twenty three) According to an embodiment of the present invention, by combining the above-mentioned necessary parameter tuning conditions and adaptive Lyapunov stability conditions, the necessary design conditions for the stability of the AAC controller after the system is stabilized by the traditional control method can be obtained in engineering. That is, the parameter tuning conditions for keeping the rocket AAC control model stable are as follows: 1. 2. 3. , , .

[0067] In this way, the aforementioned adaptive control stability conditions can be analyzed one by one, transforming the necessary stability constraints into essential parameter tuning conditions. Furthermore, by combining the model parameter range and optional stability conditions, adaptive Lyapunov stability conditions can be extracted, thereby obtaining the parameter tuning conditions that stabilize the rocket's AAC control model. This provides a direct basis for parameter tuning in the engineering application of AAC controllers, improving the standardization, interpretability, and stability reliability of parameter design, and enhancing the development efficiency of launch vehicle control systems.

[0068] Example 5: Figure 4 An exemplary diagram of a stability analysis system for an adaptive augmentation controller for a launch vehicle according to an embodiment of the present invention is shown, the system comprising: The stability feature acquisition module establishes a rocket control model based on rocket state variables, engine rudder deflection, a pre-set PD controller, and a correction network, and determines the controller stability features of the rocket control model. The first condition acquisition module determines the rocket AAC control model based on the rocket control model, as well as the error term, elasticity term, and regression term, and determines the necessary conditions for the stability of the rocket AAC control model based on the controller stability characteristics and the rocket AAC control model. The second condition acquisition module obtains the adaptive control stability conditions based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model. The third condition acquisition module obtains the parameter tuning conditions that stabilize the rocket AAC control model based on the adaptive control stability conditions.

[0069] According to an embodiment of the present invention, a stability analysis device for an adaptive augmentation controller of a launch vehicle is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to execute the stability analysis method for the adaptive augmentation controller of the launch vehicle.

[0070] According to an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored, wherein the computer program instructions, when executed by a processor, implement the stability analysis method of the adaptive augmentation controller for a launch vehicle.

[0071] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0072] Those skilled in the art should understand that the embodiments of the present invention described above and shown in the accompanying drawings are merely examples and do not limit the present invention. The objectives of the present invention have been fully and effectively achieved. The functions and structural principles of the present invention have been demonstrated and explained in the embodiments, and any variations or modifications may be made to the implementation of the present invention without departing from the stated principles.

[0073] 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 or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A stability analysis method for an adaptive augmented controller of a launch vehicle, characterized in that, include: Based on the rocket state variables, engine rudder deflection, preset PD controller and correction network, a rocket control model is established, and the controller stability characteristics of the rocket control model are determined. Based on the rocket control model, as well as the error term, elasticity term, and regression term, the rocket AAC control model is determined, and based on the controller stability characteristics and the rocket AAC control model, the necessary conditions for the stability of the rocket AAC control model are determined. Based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model, the adaptive control stability conditions are obtained. Based on the adaptive control stability conditions, the parameter tuning conditions that stabilize the rocket AAC control model are obtained.

2. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 1, characterized in that, Based on rocket state variables, engine rudder deflection, a pre-set PD controller, and a correction network, a rocket control model is established, and the controller stability characteristics of the rocket control model are determined, including: Based on the rocket state variables, engine rudder deflection, and state space matrix, set the rocket dynamics state space expression; The rocket dynamics state-space expression is processed by a preset PD controller to obtain the PD coefficient vector; The rocket control model is obtained by processing the PD coefficient vector through a calibration network. Lyapunov stability analysis was performed on the rocket control model to obtain the controller stability characteristics of the rocket control model.

3. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 1, characterized in that, Based on the rocket control model, as well as the error term, elasticity term, and regression term, the rocket AAC control model is determined. Furthermore, based on the controller stability characteristics and the rocket AAC control model, the necessary stability conditions for the rocket AAC control model are determined, including: Based on the rocket control model, the error term is obtained; Based on the aforementioned error term, elasticity term, and regression term, the rocket AAC control model is determined; Based on the rocket AAC control model and controller stability characteristics, the Lyapunov function is obtained; Based on the Lyapunov function, determine the necessary stability conditions for the rocket AAC control model.

4. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 1, characterized in that, Based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model, the adaptive control stability conditions are obtained, including: Based on the necessary stability conditions of the rocket AAC control model, intermediate variables are set; Based on the intermediate variables, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model, optional stability conditions are set. Based on the necessary stability conditions of the rocket AAC control model, set the necessary stability conditions; Based on the optional stability conditions and the necessary stability conditions, the adaptive control stability conditions are obtained.

5. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 4, characterized in that, Based on the intermediate variables, the rocket AAC control model, and the necessary stability conditions of the rocket AAC control model, optional stability conditions are set, including: Based on the rocket AAC control model, set the model parameter range; Based on the intermediate variables and the necessary stability conditions of the rocket AAC control model, selection conditions are set; Based on the necessary stability conditions of the rocket AAC control model, determine the stability conditions corresponding to each selection condition; Based on the range of model parameters, the selection conditions, and the stability conditions corresponding to each selection condition, the optional stability conditions are determined.

6. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 5, characterized in that, Based on the aforementioned adaptive control stability conditions, the parameter tuning conditions that stabilize the rocket's AAC control model are obtained, including: Based on the necessary stability conditions, set the necessary parameter tuning conditions; Based on the necessary parameter tuning conditions, the model parameter range, and the optional stability conditions, set the adaptive Lyapunov stability conditions; Based on the necessary parameter tuning conditions and the adaptive Lyapunov stability conditions, the parameter tuning conditions that stabilize the rocket AAC control model are obtained.

7. The stability analysis method for the adaptive augmented controller of a launch vehicle according to claim 6, characterized in that, Based on the necessary parameter tuning conditions, model parameter range, and optional stability conditions, adaptive Lyapunov stability conditions are set, including: The gain parameter range is obtained based on the necessary parameter tuning conditions; Set the lower limit range of the gain parameter according to the optional stability conditions; Based on the range of the gain parameter, the lower limit range of the gain parameter, and the range of the model parameters, the adaptive Lyapunov stability conditions are obtained.

8. A stability analysis system for an adaptive augmented controller of a launch vehicle, characterized in that, include: The stability feature acquisition module establishes a rocket control model based on rocket state variables, engine rudder deflection, a pre-set PD controller, and a correction network, and determines the controller stability features of the rocket control model. The first condition acquisition module determines the rocket AAC control model based on the rocket control model, as well as the error term, elasticity term, and regression term, and determines the necessary conditions for the stability of the rocket AAC control model based on the controller stability characteristics and the rocket AAC control model. The second condition acquisition module obtains the adaptive control stability conditions based on the rocket AAC control model and the necessary stability conditions of the rocket AAC control model. The third condition acquisition module obtains the parameter tuning conditions that stabilize the rocket AAC control model based on the adaptive control stability conditions.

9. A stability analysis device for an adaptive augmentation controller of a launch vehicle, characterized in that, include: processor; A memory for storing processor-executable instructions; wherein the processor is configured to invoke the instructions stored in the memory to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, It stores computer program instructions that, when executed by a processor, implement the method of any one of claims 1-7.

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