阅读说明：本技术 考虑舵机动态性能和攻击角约束的制导控制一体化方法 (Guidance control integration method considering steering engine dynamic performance and attack angle constraint ) 是由 张小跃 李志兵 王英竹 高远飞 齐明龙 于 2021-08-03 设计创作，主要内容包括：本发明提出一种考虑舵机动态性能和攻击角约束的制导控制一体化方法,主要用于STT导弹末制导阶段拦截机动目标。首先,建立了纵向平面的严反馈形式的非线性制导控制一体化模型。随后,基于反步法、全局终端滑模控制和线性反馈方法设计了制导控制一体化控制器,本发明考虑舵机动态性能及攻击角约束所设计制导控制一体化模型能够保证所有系统状态可直接测量。对制导子系统设计的全局终端滑模控制算法,可以保证滑模面的快速收敛及系统视线角快速收敛于期望的攻击角。同时,所设计控制命令无切换项的存在能够有效减缓“抖振”。采用降阶扩张状态观测器能够对系统的集成干扰进行估计,有效提高了系统的可靠性和鲁棒性。(The invention provides a guidance control integration method considering steering engine dynamic performance and attack angle constraint, which is mainly used for intercepting maneuvering targets at the terminal guidance stage of an STT missile. Firstly, a nonlinear guidance control integrated model in a strict feedback form of a longitudinal plane is established. And then, designing a guidance control integrated controller based on a back-stepping method, global terminal sliding mode control and a linear feedback method, wherein the guidance control integrated controller is designed by considering the dynamic performance of a steering engine and attack angle constraint, so that all system states can be directly measured. The global terminal sliding mode control algorithm designed for the guidance subsystem can ensure the rapid convergence of the sliding mode surface and the rapid convergence of the system line-of-sight angle to an expected attack angle. Meanwhile, the designed control command has no switching item, so that buffeting can be effectively relieved. The integration interference of the system can be estimated by adopting the reduced order extended state observer, and the reliability and robustness of the system are effectively improved.)

1. A guidance control integration method considering steering engine dynamic performance and attack angle constraint is characterized in that: the detailed steps are as follows:

establishing a missile-target motion relation of a longitudinal channel, a missile kinetic equation and a steering engine kinetic equation;

1.1, the elastic-visual relative motion relation equation of the longitudinal channel is as follows:

wherein R is the relative distance between the projectile and the eye, q is the visual angle of the projectile, V_MAnd theta_MIs the velocity vector and velocity dip, V, of the missile_TAnd theta_TIs the velocity vector and velocity dip of the target;

1.2, the kinetic equation of the missile in the longitudinal plane is as follows:

in the formula a_MAs normal acceleration, n_yIs the normal overload of the missile, g is the gravity acceleration, Y is the missile lift force, m is the missile mass, alpha is the attack angle,is a pitch angle, ω_zFor pitch angle rate, delta_zFor rudder deflection angle, J_zIs the moment of inertia of the z-axis, M₀Pitch moments related to angle of attack, pitch rate, rudder deflection angle;

is derived from the above formula

Wherein Q is dynamic pressure, S is characteristic area,is the partial derivative of the lift coefficient to angle of attack, a₁For the coefficient of lift to be related to the angle of attack,representing integrated interference, including perturbation caused by unmodeled dynamic and aerodynamic coefficient change and external interference;

1.3, the model of the missile in the lifting force and pitching moment of the longitudinal plane is as follows:

in the formula, M_αRepresenting a pitching moment component related to the angle of attack,representing a pitch moment component related to the pitch rate,representing pitch in relation to rudder deflection angleThe moment component, l, is the characteristic length,respectively the partial derivatives of the pitching moment coefficient to the attack angle, the pitch angle speed and the rudder deflection angle;

1.4, simplifying a first-order dynamic model of the steering engine as follows:

in the formula, τ_zIs the time constant of the steering engine, delta_zFor rudder deflection angle, delta_zcAn input instruction of the controller;

step two, according to the missile-target motion relation and the missile body dynamic equation described in the step one, establishing a guidance control integrated model of a nonlinear missile longitudinal channel containing a non-matching uncertain strict feedback form, and preparing for the design of a controller in the next step;

to simplify the formula, define:

in the formula, a₂、a₃、a₄Representing the coefficient of the pitch moment in relation to the angle of attack, the pitch rate, the rudder deflection angle, respectively, a₅Represents a coefficient related to the steering engine time constant;

defining state variablesx_iI-1, 2,3,4,5 represents the system state, q_dAll state variables in the equation are directly measurable for the desired angle of attack; the established guidance control integrated model is as follows:

in the formula

In the formula (f)₂(x₂)、f₃(x₃)、f₄(x₄)、f₅(x₅) As a function term of the model, b₂、b₃、b₄、b₅As model state quantity coefficients, d₂、d₃、d₄For integrated disturbances of the system, including unmodeled dynamics of the system, external disturbances, perturbations due to changes in the aerodynamic parameters, and target maneuvers, a_TFor an unknown target normal acceleration,representing model uncertainty, u being the input to the controller;

dividing the model into a guidance subsystem, a normal overload subsystem, an attitude subsystem and a steering engine subsystem by using a back-stepping method, performing reverse recursive design, and designing a guidance control integrated controller by using a global terminal sliding mode control, linear feedback and dynamic surface method;

3.1, aiming at a guidance subsystem, defining a global terminal sliding mode surface and a corresponding approach law as follows:

in the formula s₁Being a global terminal sliding-mode surface, alpha₀、β₀Is a positive number, p₀And q is₀Is a positive odd number, and q₀>q₀，Gamma is a positive number, determining the arrival velocity, and lambda and eta are positive odd numbers;

substituting the derivative of the formula (7) into a second equation of the formula (6), and designing a virtual normal overload control command as

In order to avoid the phenomenon of differential explosion caused by an inversion control algorithm, a dynamic surface method is introduced, so that x is enabled to be_3dObtaining the filtered signal x by a first order filter_3cAnd

in the formula, τ₃Is the time constant of the filter;

3.2 design the expected normal overload for the normal overload subsystem using a linear feedback method

In the formula k₃Is a linear feedback coefficient; substituting the above equation (10) into equation (6) yields a virtual attitude control command of

For the same reason, x_4dObtaining the filtered signal x by a first order filter_4cAnd

τ₄is the time constant of the filter;

3.3, similarly, aiming at the attitude subsystem, designing the expected pitch angle speed as follows:

k₄for linear feedback coefficient, the above equation (13) is substituted into equation (6) to obtain the virtual rudder deflection angle control command as

For the same reason, x_5dObtaining the filtered signal x by a first order filter_5cAnd

τ₅is the time constant of the filter;

3.4 for the steering engine subsystem, the expected rudder deflection angle is designed to be

k₅For a linear feedback coefficient, the above equation (16) is substituted into equation (6) to give the controller command of

Fourthly, aiming at the integrated interference in the virtual control command designed in the third step, estimating and compensating the integrated interference by adopting a reduced order extended state observer;

in the formula p_iI-2, 3,4 is an auxiliary variable, β_i> 0, i-2, 3,4 is the gain of the observer,is an integrated disturbance d_iI is an estimated value of 2,3, 4;

and step five, combining the step three and the step four, the guidance control integrated controller is summarized as follows:

Technical Field

The invention relates to a design method of a guidance control system in the final guidance stage of a high-speed guidance weapon, in particular to a guidance control integrated design method considering the dynamic performance of a steering engine and attack angle constraint.

Background

The missile guidance control system is the key for accurately hitting the target by the missile. Based on the assumption of spectrum separation, the conventional design method is to design the pilot loop and the control loop independently and then perform matching joint tuning on the parameters of the two subsystems, which requires repeated design many times, which undoubtedly increases the design period and the design cost. And because the coupling influence of the control ring and the control ring is not considered, the projectile body is unstable and even missed in the final guidance stage due to high-speed maneuvering of the target.

The guidance control integrated design method regards the two subsystems as a whole, and directly solves a control instruction according to the self motion state of the projectile body and the relative motion relation of the projectile eyes. Because the coupling relation of the guidance system and the control system is fully considered, the guidance control integration is beneficial to improving the stability and the accurate hitting capability of the whole system. Another advantage is that the guidance control integration can enable the system to share one set of sensor system, so as to improve the economy and reliability of the system.

The guidance control integration is realized by considering the guidance subsystem and the control subsystem as a whole, so that the guidance control system is designed into a high-order nonlinear system, and the interception process has non-matching uncertainty due to perturbation and target mobility caused by aerodynamic parameters. In order to achieve a better damage effect, a missile interception process usually needs to consider numerous constraint conditions, such as fixed impact angle constraint, dynamic performance of an actuating mechanism, an attack angle and the like, which bring challenges to guidance and control integrated design.

Disclosure of Invention

Based on the characteristics of fast time change, strong nonlinearity and strong interference in the final guidance stage, the invention provides a guidance control integrated design method with high reliability and strong robustness, simultaneously considers the dynamic performance and the fixed impact angle constraint of a steering engine, and all state variables related to a guidance control integrated model can be directly measured.

The integrated design method for guidance control is provided based on a back-stepping method, global terminal sliding mode control, linear feedback and a dynamic surface method, and is mainly used for intercepting maneuvering targets at the end guidance stage of STT missiles. Firstly, a nonlinear guidance control integrated model in a strict feedback form of a longitudinal plane is established. And then designing a guidance control integrated controller based on a back-stepping method, global terminal sliding mode control and a linear feedback method, wherein integrated interference in the model is estimated and compensated by using a reduced order extended state observer. The specific steps are detailed as follows:

step one, establishing a missile-target motion relation of a longitudinal channel, a missile kinetic equation and a steering engine kinetic equation.

(a) The bullet-eye relative motion relation equation of the longitudinal channel is as follows:

wherein R is the relative distance between the projectile and the eye, q is the visual angle of the projectile, V_MAnd theta_MIs the velocity vector and velocity dip, V, of the missile_TAnd theta_TIs the velocity vector and velocity dip of the target.

(b) The kinetic equation of the missile in the longitudinal plane is as follows:

in the formula a_MAs normal acceleration, n_yIs the normal overload of the missile, g is the gravity acceleration, Y is the missile lift force, m is the missile mass, alpha is the attack angle,is a pitch angle, ω_zFor pitch angle rate, delta_zFor rudder deflection angle, J_zIs the moment of inertia of the z-axis, M₀As a function of angle of attack, pitch rate, rudder deflectionThe pitching moment of (a).

Can be pushed out from the above way

Wherein Q is dynamic pressure, S is characteristic area,is the partial derivative of the lift coefficient to angle of attack, a₁For the coefficient of lift to be related to the angle of attack,representing integrated disturbances including unmodeled dynamics, perturbations caused by aerodynamic coefficient changes, external disturbances, etc.

(c) The model of the missile on the lift force and the pitching moment of the longitudinal plane is as follows:

in the formula, M_αRepresenting a pitching moment component related to the angle of attack,representing a pitch moment component related to the pitch rate,representing the pitch moment component in relation to the rudder deflection angle, l is the characteristic length,the partial derivatives of the pitch moment coefficient to the angle of attack, pitch angle velocity and rudder deflection angle are respectively.

(d) The steering engine first order dynamics model can be simplified as follows:

in the formula, τ_zIs the time constant of the steering engine, delta_zFor rudder deflection angle, delta_zcAnd inputting instructions of the controller.

And step two, according to the missile-target motion relation and the missile body dynamic equation described in the step one, aiming at establishing a guidance control integrated model of a nonlinear missile longitudinal channel containing a non-matching uncertain strict feedback form, and preparing for the design of a controller in the next step.

To simplify the formula, define:

in the formula, a₂、a₃、a₄Representing the coefficient of the pitch moment in relation to the angle of attack, the pitch rate, the rudder deflection angle, respectively, a₅Representing coefficients related to the steering engine time constant.

Defining state variablesx_iI-1, 2,3,4,5 represents the system state, q_dAll state variables in the equation are directly measurable for the desired angle of attack. The established guidance control integrated model is as follows:

in the formula

In the formula (f)₂(x₂)、f₃(x₃)、f₄(x₄)、f₅(x₅) As a function term of the model, b₂、b₃、b₄、b₅As model state quantity coefficients, d₂、d₃、d₄For integrated disturbances of the system, including unmodeled dynamics of the system, external disturbances, perturbations due to changes in the aerodynamic parameters, and target maneuvers, a_TFor an unknown target normal acceleration,representing the model uncertainty and u is the input to the controller.

And step three, establishing a guidance control integrated model containing a non-matching uncertain strict feedback form, dividing the model into a guidance subsystem, a normal overload subsystem, an attitude subsystem and a steering engine subsystem by using a back-stepping method, performing reverse recursion design, and designing a guidance control integrated controller by using a global terminal sliding mode control, linear feedback and dynamic surface method.

(a) For a guidance subsystem, a global terminal sliding mode surface and a corresponding approach law are defined as follows

In the formula s₁Being a global terminal sliding-mode surface, alpha₀、β₀Is a positive number, p₀And q is₀Is a positive odd number, and q₀>q₀，Gamma is a positive number, determining the arrival velocity, and lambda and eta are positive odd numbers.

Substituting the derivative of the formula (7) into a second equation of the formula (6), and designing a virtual normal overload control command as

In order to avoid the phenomenon of differential explosion caused by an inversion control algorithm, a dynamic surface method is introduced, so that x is enabled to be_3dObtaining the filtered signal x by a first order filter_3cAnd

in the formula, τ₃Is the time constant of the filter.

(b) For the normal overload subsystem, a linear feedback method is used to design the expected normal overload as

In the formula k₃Is a linear feedback coefficient. Substituting the above equation (10) into equation (6) yields a virtual attitude control command of

For the same reason, x_4dObtaining the filtered signal x by a first order filter_4cAnd

τ₄is the time constant of the filter.

(c) Similarly, for the attitude subsystem, the desired pitch rate is designed as:

k₄for linear feedback coefficient, the above equation (13) is substituted into equation (6) to obtain the virtual rudder deflection angle control command as

For the same reason, x_5dObtaining the filtered signal x by a first order filter_5cAnd

τ₅is the time constant of the filter.

(d) For the steering engine subsystem, the desired rudder deflection angle is designed to be

k₅For a linear feedback coefficient, the above equation (16) is substituted into equation (6) to give the controller command of

And step four, aiming at the integrated interference in the virtual control command designed in the previous step, because the integrated interference belongs to an unknown item in the actual process, the integrated interference is estimated and compensated by adopting a reduced order extended state observer, and the integrated interference control method has the advantages of few parameters and convenience in debugging.

In the formula p_iI-2, 3,4 is an auxiliary variable, β_i> 0, i-2, 3,4 is the gain of the observer,is an integrated disturbance d_iAnd i is an estimated value of 2,3 and 4.

In conclusion, in combination with the third and fourth steps, the designed guidance control integrated controller can be summarized as follows:

the invention has the following beneficial effects and advantages:

1. the invention designs a guidance control integrated model by considering the dynamic performance of the steering engine and the attack angle constraint, which can ensure that all system states can be directly measured.

2. The invention designs a global terminal sliding mode control algorithm aiming at a guidance subsystem, and can ensure that the sliding mode surface and the system line-of-sight angle can be converged to an expected attack angle quickly. Meanwhile, the designed control command has no switching item, so that buffeting can be effectively relieved.

3. The invention adopts the reduced order extended state observer to estimate the integrated interference of the system, thereby effectively improving the reliability and robustness of the system.

Drawings

Fig. 1 is a schematic diagram of the bullet-eye relative motion relationship of the present invention.

FIG. 2 is a flow chart of the guidance control integrated design method of the present invention.

FIG. 3 is a diagram of the trajectory of a missile intercepting maneuvering target under an example of the present invention.

FIG. 4 is a view angle curve of a missile based on an example of the present invention.

FIG. 5 is a missile normal overload curve based on an example of the invention.

Fig. 6 is a missile pitch velocity profile based on an example of the present invention.

Fig. 7 is a missile rudder deflection angle curve based on the example of the invention.

Fig. 8 is a controller command output curve based on an example of the present invention.

Detailed Description

The embodiments of the present invention will be further explained with reference to the drawings.

Fig. 1 is a schematic diagram of the bullet-target relative movement relationship of the invention, and fig. 2 is a flow chart of the guidance control integrated design method of the invention.

Firstly, establishing a missile-target motion relation of a longitudinal channel, a missile kinetic equation and a steering engine kinetic equation.

(a) The bullet-eye relative motion relation equation of the longitudinal channel is as follows:

wherein R is the relative distance between the projectile and the eye, q is the visual angle of the projectile, V_MAnd theta_MIs the velocity vector and velocity dip, V, of the missile_TAnd theta_TIs the velocity vector and velocity dip of the target.

(b) The kinetic equation of the missile in the longitudinal plane is as follows:

can be pushed out from the above way

In the formula, n_yIs the normal overload of the missile, Q is dynamic pressure, S is a characteristic area,is the partial derivative of lift coefficient to angle of attack, m is missile mass, J_zIs the z-axis moment of inertia.

(c) The model of the missile on the lift force and the pitching moment of the longitudinal plane is as follows:

in the formula, l is a characteristic length,the partial derivatives of the pitch moment coefficient to the angle of attack, pitch angle velocity and rudder deflection angle are respectively.

(d) The steering engine first order dynamics model can be simplified as follows:

in the formula, τ_zIs the time constant of the steering engine, delta_zFor rudder deflection angle, delta_zcAnd inputting instructions of the controller.

And step two, establishing a non-linear guided missile longitudinal channel guidance control integrated model containing a non-matching uncertain strict feedback form.

Selecting a state variableq_dIs the desired angle of attack. The established guidance control integrated model is as follows:

in the formula

Wherein d is₂、d₃、d₄The system integration interference comprises unmodeled dynamics of the system, external interference, perturbation caused by pneumatic parameter change and target maneuvering.

And step three, designing a guidance control integrated controller based on a back-stepping method, global terminal sliding mode control, linear feedback and a dynamic surface method.

(a) Aiming at a guidance subsystem, defining a global terminal sliding mode surface and an approach law as follows

In the formula of alpha₀、β₀Is a positive number, p and q are positive odd numbers, and q is a positive odd number₀>q₀，Gamma > 0 determines the arrival velocity and lambda and eta are positive odd numbers.

Designing the virtual normal overload control command as

In order to avoid the phenomenon of differential explosion caused by an inversion control algorithm, a dynamic surface method is introduced, so that x is enabled to be_3dObtaining x by a first order filter_3cAnd

in the formula, τ₃Is the time constant of the filter.

(b) For the normal overload subsystem, a linear feedback method is used to design the expected normal overload as

The virtual attitude control command is

For the same reason, x_4dObtaining x by a first order filter_4cAnd

(c) similarly, for the attitude subsystem, the desired pitch rate is designed as:

the virtual rudder deflection angle control command is

For the same reason, x_5dObtaining x by a first order filter_5cAnd

(d) for the steering engine subsystem, the desired rudder deflection angle is designed to be

The command of the controller is obtained as

And fourthly, aiming at the integrated interference in the virtual control command, the integrated interference is unknown in the actual process, and therefore the integrated interference is estimated and compensated by adopting a reduced order extended state observer.

In the formula p_iI-2, 3,4 is an auxiliary variable, β_i> 0, i-2, 3,4 is the gain of the observer,is an integrated disturbance d_iAnd i is an estimated value of 2,3 and 4.

Step five, combining the step three and the step four, the designed guidance control integrated controller is

Step six, verifying simulation examples

The initial conditions for the simulation are given as: initial coordinates of missile (0,0), initial position of targetV_M＝600m/s，V_T300m/s, missile and target initial speed dip angle theta_M0＝60°，θ_T00 °, initial pitch rate ω_z00 °/s, initial pitch angleInitial rudder deflection angle delta_z0＝0°。

Assuming a desired angle of attack q_d＝20°。

Unknown target acceleration a_T50sin (0.25t), unknown integrated interference d₃＝0.5sin(t)，d₄＝0.2sin(t)。

The system pneumatic parameter is a₁＝3.1166,a₂＝-82.6918,a₃＝-0.9749,a₄＝-128.6316,a₅＝10。

The parameters of the controller in the fifth step are as follows:

α₀＝1，β₀＝1，q₀＝3,p₀＝5，γ＝1，λ＝1，η＝3，

k₃＝10.0,k₄＝0.3,k₅＝8.5,τ₃＝τ₄＝τ₅＝0.01。

the parameter of the step four middle reduced order extended observer is beta₂＝12,β₃＝25,β₄＝20。

Fig. 3 shows a trajectory curve of a ballistic interception excited target, with a miss amount of 0.13 m.

Figure 4 shows the line of sight angle curve for a missile with a final attack angle of 20.15.

Fig. 5-7 show the system state change curves, and fig. 8 shows the controller command output curves.