PGK guided missile rocket control method based on robust H∞ theory

Abstract

This invention belongs to the field of navigation and guidance, specifically relating to a PGK guided missile and rocket control method based on robust H∞ theory. It includes the following steps: Step (1) establishing a control system model for the PGK guided missile and rocket; Step (2) designing the autopilot of the PGK guided missile and rocket, simplifying it into a robust H∞ standard structure; Step (3) using robust H∞ theory to design a control method for the PGK guided missile and rocket autopilot. This invention employs hybrid control in the pitch and yaw channels of the missile and rocket autopilot, effectively suppressing the non-negligible coupling effect in both directions; by extending the state variables, a controller meeting the control requirements is designed; the method of this invention can track the overload signal of the guided missile and rocket autopilot, showing broad prospects in missile and rocket guidance control.

Description

Technical Field

[0001] This invention belongs to the field of navigation and guidance, specifically relating to a PGK-guided missile control method based on robust H∞ theory. Background Technology

[0002] In modern missile missions, improving the accuracy of the guidance system is the most important and challenging process. This paper mainly studies the design of the PGK (Precision Guidance Kit) guided missile and rocket control system, which directly affects the accuracy and stability of the mid-course flight of the guided missile and rocket. The aerodynamic parameters of the missile and rocket during flight are significantly affected by flight conditions such as altitude and speed. To achieve effective control of the missile and rocket, the missile body is usually severely underdamped, or even statically unstable. While this can greatly improve maneuverability, it also reduces the flight stability of the missile body. Therefore, an autopilot is needed to accelerate the missile body's response speed, improve damping, provide anti-interference capabilities, and accurately and robustly track input commands. The guided missile and rocket control system mainly refers to the closed-loop system composed of the missile and rocket's actuators, missile body, and corresponding controllers. The design of the missile and rocket control system is essentially the design of the autopilot.

[0003] Scholars at home and abroad have conducted a lot of research on different projectiles and rockets. The main research results can be divided into classical control theory, modern control theory and nonlinear control theory according to different design theories.

[0004] Classical control theory primarily studies linear time-invariant systems with single input and single output. Commonly used methods fall into two main categories: root locus methods and Bode plot methods. However, it also includes analytical and synthetic methods based on various algebraic stability criteria. While classical control theory is effective in solving the analysis and design problems of relatively simple control systems, it still has certain limitations, mainly in that it is only applicable to single-variable systems and is limited to the study of time-invariant systems.

[0005] Modern control theory, based on state-space models, uses state equations to describe multi-input, multi-output linear time-varying systems. It studies the intrinsic laws of these systems, including linear system analysis and synthesis, optimal control theory, system identification, and optimal estimation theory. Key concepts include controllability and observability. Modern control theory can handle a much wider range of control problems than classical control theory, including linear and nonlinear systems, time-invariant and time-varying systems, and single-variable and multi-variable systems. However, due to the different assumptions and methods of different control theories, there is a lack of consistency among them, resulting in a lack of a unified framework for modern control theory. Furthermore, there is insufficient communication between different control theories, making it difficult to combine them.

[0006] Robust control theory inherits previous robustness research methods and is characterized by a frequency design method based on state-space models. It proposes an effective method to fundamentally solve the problems of uncertainty in the controlled object model and uncertainty in external disturbances. It can not only be used for the robustness analysis and design of single-input single-output feedback control systems, but also can be successfully applied to multi-input multi-output situations, enabling the design of feedback control systems with better performance and robustness. Summary of the Invention

[0007] The purpose of this invention is to provide a control method for guided missiles, which aims to utilize robust H∞ theory to complete the design of a guided missile control system, achieve stable and accurate tracking of pitch and yaw channel input commands of the guided missile autopilot under overload, and improve the flight stability of the PGK guided missile.

[0008] The technical solution to achieve the purpose of this invention is: a PGK-guided missile control method based on robust H∞ theory, comprising the following steps:

[0009] Step (1): Establish a control system model for the PGK guided missile;

[0010] Step (2): Design the autopilot of the PGK guided missile rocket and simplify it into a robust H∞ standard structure;

[0011] Step (3): Using robust H∞ theory, design the control method for the PGK guided missile autopilot.

[0012] Furthermore, step (1) specifically includes the following steps:

[0013] Step (11): Establish a 7DOF control system model for guided missiles and rockets.

[0014] The model includes 8 variables [α, β, ω]. z ω y n y n z δ y δ z T represents the angle of attack α, sideslip angle β, and pitch angular velocity ω, respectively. z yaw rate ω y Pitch overload n y Yaw overload z Equivalent pitch deflection δ z Equivalent yaw deflection δ y ;

[0015]

[0016] Step (12): Rewrite the system of differential equations of the model into state-space expressions.

[0017] Set the state variables: x = [α, ω] z ,β,ω y ] Τ Control variable: u = [δ z ,δ y ] Τ Output variable y = [n z ,n y ,ω z ,ω y ] Τ .

[0018]

[0019] The state matrix expression is as follows:

[0020]

[0021]

[0022] The output matrix is ​​decomposed into C = [C a C ω ] Τ This divides the acceleration and angular velocity variables into two subarrays.

[0023] Furthermore, step (2) specifically includes the following steps:

[0024] Step (21): Select the overload control autopilot for the guided missile.

[0025] The three-loop autopilot feedback control structure consists of a damping loop, a stabilization loop, and a guidance loop for controlling the stability of the projectile's attitude.

[0026] Step (22): Simplify the overload control autopilot structure of the guided missile rocket.

[0027] Organize the autopilot model into H ∞ The standard structure for robust control of autopilots.

[0028] Furthermore, step (3) specifically includes the following steps:

[0029] Step (31): Establish the H∞ canonical form state-space expression of the controlled system;

[0030] The standard structure of an autopilot is written as H with a perturbation w and a modulated output. ∞ State-space equations of the controlled model in the sense of:

[0031]

[0032] Step (32): Construct the input / output transfer equations of the open-loop system

[0033] Set the reference acceleration signal w = a zyc =[a zc ,a yc ] Τ Acceleration tracking deviation signal z = e zy =a zyc -a zy System state variable y c =[x e ,a zy ,ω zy ] Τ control variable u c =δ zy =[δ z ,δ y ] Τ .

[0034]

[0035] Add state dynamics integral x e =∫e yz The open-loop dynamics model is written as: (t)dt, where:

[0036]

[0037]

[0038] The dynamic equation for the augmented state vector is defined as follows:

[0039]

[0040] The open-loop dynamic equations above are recombinated and written in time-domain form:

[0041]

[0042] Step (33): Establish closed-loop feedback controller K

[0043] Define output feedback:

[0044] u c (s)=Ky c (s)

[0045] In the formula: K = [K e ,K a ,K ω ,K δ [K] is a 2x8 matrix; e ,K a ,K ω ,Kδ It is a 2x2 matrix, representing the control parameters in the pitch and yaw directions, respectively;

[0046] Step (34): Constructing the state feedback of the closed-loop system

[0047] Transform the output feedback into state feedback, and define y. c For the new state variables of the system; first, for y c Differentiating with respect to time t, we get Bring it in From the equation, we get:

[0048]

[0049] After rearranging the state equations of the open-loop system, we get:

[0050]

[0051] The state feedback controller u = Ky c Substituting into the above equation, we obtain the state equation of the closed-loop system, transforming the disturbance variable into a performance variable, and thus:

[0052]

[0053] Step (35): Solve for the closed-loop state feedback controller K.

[0054] By substituting the missile's aerodynamic parameters and using the LMI toolbox in Matlab, the H∞ controller coefficient matrix can be calculated as follows:

[0055]

[0056] Compared with the prior art, the significant advantages of this invention are:

[0057] (1) Compared with the traditional PID control method, the method of the present invention has the characteristics of high control accuracy and fast convergence speed.

[0058] (2) Compared with traditional control methods, the method of the present invention can cope with the uncertainty and various changes of the system, including parameter changes, external disturbances, system coupling, etc., and has strong adaptability and robustness. Attached Figure Description

[0059] Figure 1 This is a diagram of the feedback control structure for an autopilot.

[0060] Figure 2 This is a schematic diagram of the open-loop controller for an autopilot.

[0061] Figure 3 The diagram shows the Simulink simulation model of the system.

[0062] Figure 4 This is a tracking diagram for the overload signal in the pitch channel.

[0063] Figure 5 This is a tracking diagram for the overload signal in the yaw channel. Detailed Implementation

[0064] A PGK-guided missile control method based on robust H∞ theory includes the following steps:

[0065] Step 1: Establish a control system model for the PGK guided missile.

[0066] Specifically as follows:

[0067] Step (11) Establish a 7DOF control system model for guided missiles and rockets.

[0068] The model includes 8 variables [α, β, ω]. z ω y n z n y δ z δ y ] Τ These are the angle of attack α, sideslip angle β, and pitch angular velocity ω, respectively. z yaw rate ω y Pitch overload n z Yaw overload y Equivalent pitch deflection δ z Equivalent yaw deflection δ y .

[0069]

[0070] Step (12) Rewrite the system of differential equations of the controlled model into a state-space expression.

[0071] Set the state variables: x = [α, ω] z ,β,ω y ] Τ Control variable: u = [δ z ,δ y ] Τ Output variable y = [n z ,n y ,ω z ,ω y ] Τ

[0072]

[0073] The state matrix expression is as follows:

[0074]

[0075]

[0076] The output matrix can be further decomposed into C = [C n C ω ] Τ This separates the acceleration and angular velocity variables into two sub-matrices, allowing for separate analysis of each variable.

[0077] Step 2: Design the autopilot for the PGK guided missile, simplifying it into a robust H∞ standard structure:

[0078] Specifically as follows:

[0079] Step (21): Select the overload control autopilot for the guided missile.

[0080] The feedback control structure of a three-loop autopilot is as follows: Figure 1 As shown, it consists of a damping circuit, a stabilization circuit, and a guidance circuit for controlling the attitude stability of the projectile.

[0081] Step (22): Simplify the overload control autopilot structure of the guided missile rocket.

[0082] Organize the autopilot model into H ∞ The standard structure of a robust control autopilot is as follows: Figure 2 As shown.

[0083] Step 3: Using robust H∞ theory, design the control method for the PGK guided missile autopilot:

[0084] Specifically as follows:

[0085] Step (31): Establish the H∞ canonical form state-space expression of the controlled system.

[0086] The standard structure of an autopilot is written as H with a perturbation w and a modulated output. ∞ The state-space equations of the controlled model in the sense of the word.

[0087]

[0088] Step (32): Construct the input / output transfer equations of the open-loop system

[0089] Set the reference acceleration signal w = a zyc =[a zc ,a yc ] Τ Acceleration tracking deviation signal z = e zy =a zyc -a zy System state variable yc =[x e ,a zy ,ω zy ] Τ control variable u c =δ zy =[δ z ,δ y ] Τ .

[0090]

[0091] Add state dynamics integral x e =∫e yz The open-loop dynamic model can be written as: (t)dt.

[0092]

[0093]

[0094] The dynamic equation for the augmented state vector is defined as follows:

[0095]

[0096] The open-loop dynamic equations above are recombinated and written in time-domain form:

[0097]

[0098] Step (33): Establish closed-loop feedback controller K

[0099] Define output feedback u c (s)=Ky c (s),

[0100] In the formula: K = [K e ,K a ,K ω ,K δ [K] is a 2x8 matrix; e ,K a ,K ω ,K δ It is a 2x2 matrix, representing the control parameters in the pitch and yaw directions, respectively.

[0101] Step (34): Constructing the state feedback of the closed-loop system

[0102] Transform the above output feedback into state feedback, and define y. c This is the new state variable for this system. First, let's consider y. c Differentiating with respect to time t, we get Bring it in From the equation, we obtain

[0103]

[0104] After rearranging the state equations of the open-loop system, we get:

[0105]

[0106] The state feedback controller u = Ky c Substituting into the above equation, we obtain the state equation of the closed-loop system, transforming the disturbance variable into a performance variable, and thus:

[0107]

[0108] Step (35): Solve for the closed-loop state feedback controller K.

[0109] By substituting the missile's aerodynamic parameters and using the LMI toolbox in Matlab, the H∞ controller coefficient matrix can be calculated as follows:

[0110]

[0111] Conclusion: Building system simulations in Simulink is as follows Figure 3 As shown in the simulation results Figure 4 , Figure 5 It can be seen that when a square wave signal with an amplitude of 1 is input to the pitch channel and the overload signal of the yaw channel is 0, the output signal az can effectively track the input signal azc, and the yaw channel can effectively suppress coupling, achieving the effect of system decoupling. When a square wave signal with an amplitude of 1 is input to the yaw channel and the overload signal of the pitch channel is 0, the output signal ay can effectively track the input signal ayc, and the pitch channel can effectively suppress coupling, achieving the effect of system decoupling.

Claims

1. A PGK-guided missile control method based on robust H∞ theory, characterized in that, Includes the following steps: Step (1): Establish a control system model for the PGK guided missile; Step (2): Design the autopilot of the PGK guided missile rocket and simplify it into a robust H∞ standard structure; Step (3): Using robust H∞ theory, design the control method for the PGK guided missile autopilot; Step (1) specifically includes the following steps: Step (11): Establish a 7DOF control system model for guided missiles and rockets. The model includes 8 variables. ] T The angle of attack is respectively Sideslip angle β, pitch angular velocity yaw rate Pitch overload Yaw overload Equivalent pitch deflection Equivalent yaw deflection ; ， Step (12): Rewrite the system of differential equations of the model into state-space expressions. Set state variables: Control variables: Output variables ; ， The state matrix expression is as follows: ， ， The output matrix decomposition is so that the acceleration and angular velocity variables are split into two sub-matrices; Step (2) specifically includes the following steps: Step (21): Select the overload control autopilot for the guided missile. The three-loop autopilot feedback control structure consists of a damping loop, a stabilization loop, and a guidance loop for controlling the stability of the projectile's attitude. Step (22): Simplify the overload control autopilot structure of the guided missile rocket. The autopilot model is arranged as a standard structure of a robust control autopilot; Step (3) specifically includes the following steps: Step (31): Establish the H∞ canonical form state-space expression of the controlled system; The standard structure of an autopilot is written as a state space equation of the controlled model with disturbance w and the regulated output y: x = Ax + Bu + w Step (32): Construct the input / output transfer equations of the open-loop system Set reference acceleration signal Acceleration tracking deviation signal System state variables Control variables ; ， Joining state dynamics integration The open-loop dynamics model is written as: where the dynamics of the augmented state vector is defined as The open-loop dynamic equations above are recombinated and written in time-domain form: Step (33): Establish closed-loop feedback controller K Define output feedback: In the formula: It is a 2x8 matrix; It is a 2x2 matrix, representing the control parameters in the pitch and yaw directions, respectively; Step (34): Constructing the state feedback of the closed-loop system Transform the output feedback into state feedback, define... For the new state variables of the system; firstly, for Differentiating with respect to time t, we get Bring it in From the equation, we get: After rearranging the state equations of the open-loop system, we get: The state feedback controller Substituting into the above equation, the state equation of the closed-loop system is obtained, and the disturbance variable is changed into a performance variable, and the following is obtained: Step (35): Solve for the closed-loop state feedback controller K. By substituting the missile's aerodynamic parameters and using the LMI toolbox in Matlab, the H∞ controller coefficient matrix can be calculated as follows: 。

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