CN105867399B - Method for determining multi-state tracking guidance parameters - Google Patents

Abstract

The invention discloses a method for determining multi-state tracking guidance parameters. The method includes the steps that a multi-state motion model of aircraft flight process reentry is established, small-deviation linear processing is carried out on the multi-state motion model, and a processed linear equation is obtained; based on the linear equation, a guidance equation is obtained; based on a linear quadratic regulator (LQR), an LQR tracking controller is designed, and a corresponding feedback control rule is obtained; according to the multi-state tracking requirement, a controller weighting matrix is selected; according to the controller weighting matrix and the guidance equation, the guidance parameters are obtained through calculation. By means of the method, tracking control over multiple state quantities can be achieved according to the determined guidance parameters, and mutual influences in tracking of multiple state quantities are reduced.

Description

Method for determining multi-state tracking guidance parameters

Technical Field

The invention relates to the technical field of lift type aircraft guidance, in particular to a method for determining a multi-state tracking guidance parameter.

Background

The lift-type aircraft is limited by various constraint conditions such as overload, dynamic pressure, stagnation point heat flow and the like in a balanced gliding section, so that the flight path of the lift-type aircraft has the requirements of process and terminal constraint and has higher precision. The guidance problem is a typical multiple-input multiple-output control problem, and the input control quantity has two states: namely roll angle and angle of attack, and considering the need for a lift aircraft to perform a large maneuver, the state quantities that need to be controlled are five variables: namely altitude, speed, ballistic inclination, heading angle, lateral position. Because the control quantity and the state quantity are not completely in one-to-one correspondence, and coupling and correlation exist among multiple states, decoupling control cannot be realized, and high requirements are provided for the design of the multi-state tracking guidance parameters.

However, a better method for determining the multi-state tracking guidance parameters has not yet been provided in the prior art, and therefore the problem needs to be solved.

Disclosure of Invention

In view of this, the present invention provides a method for determining a multi-state tracking guidance parameter, so as to realize tracking control over a plurality of state quantities according to the determined guidance parameter, and reduce mutual influence when tracking the plurality of state quantities.

The technical scheme of the invention is realized as follows:

a method of determining a multi-state tracking guidance parameter, the method comprising the steps of:

establishing a multi-state motion model of the reentry flight process of the aircraft, and carrying out small deviation linearization processing on the multi-state motion model to obtain a processed linearization equation;

obtaining a guidance equation based on the linearization equation;

designing an LQR tracking controller based on a linear quadratic regulator LQR to obtain a corresponding feedback control law;

selecting a controller weighting matrix according to a multi-state tracking requirement;

and calculating to obtain a guidance parameter according to the controller weighting matrix and the guidance equation.

Preferably, the establishing a multi-state motion model of the reentry flight process of the aircraft includes:

and establishing a dimensional multi-state motion model of the aircraft during reentry flight according to the longitudinal motion parameter height h, the geocentric radial r, the velocity v, the local ballistic inclination angle theta, the transverse position Z and the track deviation angle psi.

Preferably, the linearized equation after the processing is:

wherein, [ x ]]＝[r,v,θ,ψ,Z]^T＝[r－r_ref,v－v_ref,θ－θ_ref,ψ－ψ_ref,Z－Z_ref]^T，u＝[α,γ_V]^TA and B are time-varying matrices consisting of partial derivative terms of the system of characteristic point differential equations in the standard trajectory, r_refFor reference to the geocentric radial, v_refFor reference speed, θ_refFor reference to ballistic inclination angle, #_refFor reference to track drift angle, Z_refFor reference lateral position, α is angle of attack, γ_VIs the roll angle.

Preferably, the guidance equation may be:

wherein, α_refAnd gamma_VrefReference angle of attack and reference roll angle, α, respectively, for a predetermined standard trajectory_cxIs the current angle of attack, gamma_VcxAt the current roll angle, K_a1～K_a5First to fifth gain coefficients, K, of the angle of attack command, respectively_s1～K_s5The first to fifth feedback coefficients of the roll angle command respectively form a gain matrix K of 2 × 5_d。。

Preferably, the designing the LQR tracking controller to obtain the corresponding feedback control law includes:

aiming at the multi-state tracking control problem, introducing an LQR optimal control performance index;

and designing an LQR tracking controller to obtain a corresponding feedback control law.

Preferably, the LQR optimal control performance index J is:

q and R are respectively corresponding to a weighting matrix of the state vector and a weighting matrix of the control vector, and u is a feedback control law.

Preferably, the feedback control law u is as follows:

u＝[αγ_V]^T＝-R^-1B^TPx(t)＝-K_dx；

wherein, K_dFor the gain matrix, P is the Riccati equation PA + A^TP－PBR^-1B^TP + Q is 0 solution.

Preferably, the selecting the controller weighting matrix according to the multi-state tracking requirement includes:

determining a parameter design strategy of a weighting matrix of a state vector and a control vector according to a multi-state tracking requirement;

and selecting a controller weighting matrix according to the parameter design strategy and the maximum allowable state and control quantity deviation.

Preferably, the parameter design strategy is as follows:

wherein Q is₁、Q₂、Q₃、Q₄、Q₅Diagonal elements, R, of a weighting matrix Q of the state vectors in turn₁、R₂Diagonal elements of a weighting matrix R of the control vector are arranged in sequence, and the other off-diagonal elements are 0.

Preferably, the selecting the controller weighting matrix includes:

q in order parameter design strategy₁When 1, then Q₂、Q₃、Q₄、Q₅And R₁、R₂Expressed as:

wherein h is_max,v_max,θ_max,ψ_max,Z_max,α_max,γ_vmaxThe maximum allowable height deviation, speed deviation, trajectory inclination angle deviation, track deviation angle deviation, transverse position deviation, attack angle deviation and roll angle deviation are respectively.

Preferably, the calculating the guidance parameter according to the controller weighting matrix and the guidance equation includes:

selecting a certain motion parameter capable of representing a reentry flight process as a monotonous gain planning quantity;

calling a function lqr () for solving the Riccati equation, and calculating to obtain a gain matrix K_d；

Will K_dSubstituting the guidance equation to calculate and obtain the guidance parameters.

As can be seen from the above, in the method for determining a multi-state tracking guidance parameter in the present invention, since the multi-state motion model is established first, and then the small deviation linearization processing is performed on the multi-state motion model, the processed linearization equation is obtained; then based on the linearized equation, a guidance equation is obtained; then designing an LQR tracking controller to obtain a corresponding feedback control law; selecting a controller weighting matrix according to a multi-state tracking requirement; and finally, calculating to obtain the guidance parameters according to the controller weighting matrix and the guidance equation, thereby realizing the tracking control of a plurality of state quantities according to the determined guidance parameters, reducing the mutual influence when a plurality of state quantities are tracked, solving the problems of design and coordination of the multi-state tracking guidance parameters, and providing design basis and support for the design of the guidance parameters and the realization of the glide guidance.

Drawings

FIG. 1 is a flow chart illustrating a method for determining multi-state tracking guidance parameters in an embodiment of the invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and examples.

The embodiment provides a method for determining multi-state tracking guidance parameters, which is suitable for a balanced glide phase guidance process of a glide aircraft, so that the problems of design and coordination of the multi-state tracking guidance parameters can be solved, and design basis and support are provided for design of the guidance parameters and realization of glide guidance.

FIG. 1 is a flow chart illustrating a method for determining multi-state tracking guidance parameters in an embodiment of the invention. As shown in fig. 1, the method for determining a multi-state tracking guidance parameter in the embodiment of the present invention includes: .

Step 101, establishing a multi-state motion model of the reentry flight process of the aircraft, and performing small deviation linearization processing on the multi-state motion model to obtain a processed linearization equation.

In the technical scheme of the invention, a multi-state motion model of the reentry flight process of the aircraft can be established according to various specific implementation modes. The technical solution of the present invention will be described below by taking one of the specific implementation modes as an example.

For example, in a preferred embodiment of the present invention, the establishing the multi-state motion model of the reentry flight process of the aircraft includes:

and establishing a dimensional multi-state motion model of the aircraft during reentry flight according to the longitudinal motion parameter height h, the geocentric radial r, the velocity v, the local ballistic inclination angle theta, the transverse position Z and the track deviation angle psi.

In addition, preferably, in an embodiment of the present invention, the processed linearized equation may be:

wherein, [ x ]]＝[r,v,θ,ψ,Z]^T＝[r－r_ref,v－v_ref,θ－θ_ref,ψ－ψ_ref,Z－Z_ref]^T，u＝[α,γ_V]^TA and B are time-varying matrices consisting of partial derivative terms of the system of characteristic point differential equations in the standard trajectory, r_refFor reference to the geocentric radial, v_refFor reference speed, θ_refFor reference to ballistic inclination angle, #_refFor reference to track drift angle, Z_refFor reference lateral position, α is angle of attack, γ_VIs the roll angle.

Therefore, the above formula (1) can also be expressed as:

after the small deviation linearization process, the linearized equations after the process are actually a Linear state equation set that can be solved based on a Linear Quadratic Regulator (LQR).

In addition, in the technical solution of the present invention, the small deviation linearization processing can be performed by using a common small deviation linearization processing method in the prior art, and therefore, a specific processing procedure is not described in detail herein.

And 102, obtaining a guidance equation based on the linearization equation.

For example, in a preferred embodiment of the present invention, the guidance equations may be:

wherein, α_refAnd gamma_VrefReference angle of attack and reference roll angle, α, respectively, for a predetermined standard trajectory_cxIs the current angle of attack, gamma_VcxAt the current roll angle, K_a1～K_a5First to fifth gain factors, K, of angle of attack commands, respectively_s1～K_s5The first to fifth feedback coefficients of the roll angle command respectively form a gain matrix K of 2 × 5_d。

In the technical solution of the present invention, a standard trajectory can be pre-designed and corresponding reference attack angle and reference roll angle can be obtained by using a method commonly used in the prior art, and therefore, a detailed description thereof is omitted.

And 103, designing an LQR tracking controller based on a Linear Quadratic Regulator (LQR) to obtain a corresponding feedback control law.

In the technical solution of the present invention, the step 103 can be implemented according to various specific implementation manners. The technical solution of the present invention will be described below by taking one of the specific implementation modes as an example.

For example, in an embodiment of the present invention, the step 103 may specifically include:

step 31, aiming at the multi-state tracking control problem, introducing an LQR optimal control performance index;

preferably, in an embodiment of the present invention, the LQR optimal control performance index J is:

q and R are respectively corresponding to a weighting matrix of a state vector and a weighting matrix of a control vector, Q is a matrix of (5 multiplied by 5), and R is a matrix of (2 multiplied by 2); and u is a feedback control amount.

And step 32, designing an LQR tracking controller to obtain a corresponding feedback control law.

Preferably, in an embodiment of the present invention, the feedback control law u may be expressed as:

u＝[αγ_V]^T＝-R^-1B^TPx(t)＝-K_dx (4)

wherein, K_dFor the gain matrix, P is the Riccati (Riccati) equation PA + A^TP－PBR^-1B^TP + Q is 0 solution.

And 104, selecting a controller weighting matrix according to the multi-state tracking requirement.

In the technical solution of the present invention, the step 104 can be implemented according to various specific implementations. The technical solution of the present invention will be described below by taking one of the specific implementation modes as an example.

For example, in an embodiment of the present invention, the step 104 may specifically include:

and step 41, determining parameter design strategies of the weighting matrixes (namely Q matrix and R matrix) of the state vector and the control vector according to the multi-state tracking requirement.

Preferably, in an embodiment of the present invention, the parameter design policy is:

wherein Q is₁、Q₂、Q₃、Q₄、Q₅Diagonal elements, R, of a weighting matrix Q of the state vectors in turn₁、R₂Diagonal elements of a weighting matrix R of the control vector are arranged in sequence, and the other off-diagonal elements are 0.

And 42, selecting a controller weighting matrix according to the parameter design strategy and the maximum allowable state and control quantity deviation.

Preferably, in an embodiment of the present invention, the step 42 is:

let Q in formula (5)₁When 1, then Q₂、Q₃、Q₄、Q₅And R₁、R₂Can be expressed as:

wherein h is_max,v_max,θ_max,ψ_max,Z_max,α_max,γ_vmaxThe maximum permissible height deviation, velocity deviation, trajectory inclination deviation, track deviation angle, lateral position deviation, attack angle deviation, and roll angle deviation, respectively, i.e., the above-mentioned weighting matrix can be determined by intuitively setting the maximum permissible state quantity and control quantity deviation.

And 105, calculating to obtain a guidance parameter according to the controller weighting matrix and the guidance equation.

In the technical solution of the present invention, the step 105 can be implemented according to various specific implementation manners. The technical solution of the present invention will be described below by taking one of the specific implementation modes as an example.

For example, in an embodiment of the present invention, the step 105 may specifically include:

and step 51, selecting a certain motion parameter capable of representing the reentry flight process as a monotonous gain planning quantity.

For example, in one embodiment of the present invention, a motion parameter that characterizes the reentry flight may be selected as a monotonic gain metric (e.g., velocity, energy, etc.) in the Matlab software environment.

Step 52, calling function lqr () for solving Riccati (Riccati) equation, and calculating to obtain gain matrix K_d。

In the technical solution of the present invention, the gain matrix K_dIs a matrix of 2 × 5.

Step 53, adding K_dSubstituting the guidance equation to calculate and obtain the guidance parameters.

In the technical solution of the present invention, the guidance equation is the formula (2). General K_dAfter substituting the guidance equation, the calculation can be carried outDeriving guidance parameters, e.g. control quantities α and gamma_V。

In summary, in the method for determining the multi-state tracking guidance parameters, the multi-state motion model is established first, and then the small deviation linearization processing is performed on the multi-state motion model to obtain the processed linearization equation; then based on the linearized equation, a guidance equation is obtained; then designing an LQR tracking controller to obtain a corresponding feedback control law; selecting a controller weighting matrix according to a multi-state tracking requirement; and finally, calculating to obtain the guidance parameters according to the controller weighting matrix and the guidance equation, thereby realizing the tracking control of a plurality of state quantities according to the determined guidance parameters, reducing the mutual influence when a plurality of state quantities are tracked, solving the problems of design and coordination of the multi-state tracking guidance parameters, and providing design basis and support for the design of the guidance parameters and the realization of the glide guidance.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A method of determining multi-state tracking guidance parameters, the method comprising the steps of:

establishing a multi-state motion model of the reentry flight process of the aircraft, and carrying out small deviation linearization processing on the multi-state motion model to obtain a processed linearization equation;

obtaining a guidance equation based on the linearization equation;

designing an LQR tracking controller based on a linear quadratic regulator LQR to obtain a corresponding feedback control law;

selecting a controller weighting matrix according to a multi-state tracking requirement;

calculating to obtain a guidance parameter according to the controller weighting matrix and the guidance equation; wherein,

the establishing of the multi-state motion model of the reentry flight process of the aircraft comprises the following steps:

according to the height h, the geocentric radial r, the speed v, the local trajectory inclination angle theta, the transverse position Z and the track deviation angle psi of the longitudinal motion parameters, establishing a dimensional multi-state motion model of the aircraft during reentry flight; and

the linearized equation after the processing is as follows:

$\[\mathrm{\δ}\stackrel{\·}{x}\]=\[A\]\[\mathrm{\δ}x\]+\[B\]\[\mathrm{\δ}u\];$

wherein, [ x ]]＝[r,v,θ,ψ,Z]^T＝[r－r_ref,v－v_ref,θ－θ_ref,ψ－ψ_ref,Z－Z_ref]^T，u＝[α,γ_V]^TA and B are time-varying matrices consisting of partial derivative terms of the system of characteristic point differential equations in the standard trajectory, r_refFor reference to the geocentric radial, v_refFor reference speed, θ_refFor reference to ballistic inclination angle, #_refFor reference to track drift angle, Z_refFor reference lateral position, α is angle of attack, γ_VIs a roll angle; and

the guidance equation is as follows:

$\left\{\begin{array}{c}{\mathrm{\α}}_{cx}={\mathrm{\α}}_{ref}+\mathrm{\δ}\mathrm{\α}={\mathrm{\α}}_{ref}-K_{a1}\mathrm{\δ}r-K_{a2}\mathrm{\δ}v-K_{a3}\mathrm{\δ}\mathrm{\θ}-K_{a4}\mathrm{\δ}\mathrm{\ψ}-K_{a5}\mathrm{\δ}Z\\ {\mathrm{\γ}}_{Vcx}={\mathrm{\γ}}_{Vref}+\mathrm{\δ}{\mathrm{\γ}}_V={\mathrm{\γ}}_{Vref}-K_{s1}\mathrm{\δ}r-K_{s2}\mathrm{\δ}v-K_{s3}\mathrm{\δ}\mathrm{\θ}-K_{s4}\mathrm{\δ}\mathrm{\ψ}-K_{s5}\mathrm{\δ}Z\end{array}\right.;$

wherein, α_refAnd gamma_{V ref}Reference angle of attack and reference roll angle, α, respectively, for a predetermined standard trajectory_cxIs the current angle of attack, gamma_{V cx}Is the current roll angle; k_a1～K_a5First to fifth gain coefficients, K, of the angle of attack command, respectively_s1～K_s5The first to fifth feedback coefficients of the roll angle command respectively form a gain matrix K of 2 × 5_d。

2. The method according to claim 1, wherein the designing the LQR tracking controller to derive the corresponding feedback control laws comprises:

aiming at the multi-state tracking control problem, introducing an LQR optimal control performance index;

and designing an LQR tracking controller to obtain a corresponding feedback control law.

3. The method according to claim 2, wherein the LQR optimal control performance index J is:

$J=\frac{1}{2}{\∫}_{t_0}^{t_f}\[{\mathrm{\δx}}^T\left(t\right)Q\mathrm{\δ}x\left(t\right)+{\mathrm{\δu}}^T\left(t\right)R\mathrm{\δ}u\left(t\right)\]dt;$

wherein, Q and R are respectively corresponding to a weighting matrix of a state vector and a weighting matrix of a control vector, and u is a feedback control quantity.

4. The method according to claim 3, wherein the feedback control amount u is:

u＝[α γ_V]^T＝-R^-1B^TPx(t)＝-K_dx；

wherein, K_dFor the gain matrix, P is the Riccati equation PA + A^TP－PBR^-1B^TP + Q is 0 solution.

5. The method of claim 4, wherein selecting the controller weight matrix based on the multi-state tracking requirement comprises:

determining a parameter design strategy of a weighting matrix of a state vector and a control vector according to a multi-state tracking requirement;

and selecting a controller weighting matrix according to the parameter design strategy and the maximum allowable state and control quantity deviation.

6. The method of claim 5, wherein the parameter design policy is:

$Q_1{\mathrm{\δh}}_{max}^2=Q_2{\mathrm{\δv}}_{max}^2=Q_3{\mathrm{\δ\Θ}}_{max}^2=R_1{\mathrm{\δ\α}}_{max}^2=R_2{\mathrm{\δ\γ}}_{v\_max}^2;$

wherein Q is₁、Q₂、Q₃、Q₄、Q₅Diagonal elements, R, of a weighting matrix Q of the state vectors in turn₁、R₂Diagonal elements of a weighting matrix R of the control vector are arranged in sequence, and the other off-diagonal elements are 0.

7. The method of claim 6, wherein selecting the controller weight matrix comprises:

q in order parameter design strategy₁When 1, then Q₂、Q₃、Q₄、Q₅And R₁、R₂Expressed as:

$\begin{array}{c}{Q}_2=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δv}}_{\max }^2},Q_3=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δ\θ}}_{\max }^2},Q_4=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δ\ψ}}_{\max }^2},Q_5=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δZ}}_{\max }^2}\\ R_1=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δ\α}}_{\max }^2},R_2=\frac{{\mathrm{\δh}}_{\max }^2}{{\mathrm{\δ\γ}}_{v\_\max }^2}\end{array};$

wherein h is_max,v_max,θ_max,ψ_max,Z_max,α_max,γ_vmaxThe maximum allowable height deviation, speed deviation, trajectory inclination angle deviation, track deviation angle deviation, transverse position deviation, attack angle deviation and roll angle deviation are respectively;

the step of calculating and obtaining the guidance parameters according to the controller weighting matrix and the guidance equation comprises the following steps:

selecting a certain motion parameter capable of representing a reentry flight process as a monotonous gain planning quantity;

calling a function lqr () for solving the Riccati equation, and calculating to obtain a gain matrix K_d；

Will K_dSubstituting the guidance equation to calculate and obtain the guidance parameters.