CN105022403A - Method for determining the vertical locus control gain of gliding aircraft - Google Patents

Abstract

The invention discloses a method for determining the vertical locus control gain of a gliding aircraft. The method comprises: determining a simplified height control model, which is represented by a formula described in the specification, of the gliding aircraft according to a vertical control model of the gliding aircraft, wherein x1=h, x2= V*[theta], h is the height of the gliding aircraft, the h<.> is the height change rate of the gliding aircraft, V is speed, [theta] is the trajectory inclination angle of the gliding aircraft, m is the mass of the gliding aircraft, F is the aerodynamic force, namely the controlled quantity, borne by the gliding aircraft, the x1<.> and the x2<.> are first-order derivatives of the x1 and the x2 respectively; according to the simplified height control model, determining that the optimal controlled quantity of the simplified height control model satisfies F= -K*x<.>, wherein the K=[Kh K[theta]] is the optimal controlled quantity, Kh is height control gain, and K[theta] is trajectory inclination angle control gain. The method may fast design a height control gain parameter, effectively reduces design complexity, improves design universality, and can be directly used in a gliding aircraft vertical height control scheme.

Description

The defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle

Technical field

The present invention relates to flying vehicles control technology, the defining method of particularly longitudinal TRAJECTORY CONTROL gain of glide vehicle.

Background technology

For glide class aircraft, in order to keep aircraft by certain altitude profile gliding flight, the longitudinal TRAJECTORY CONTROL scheme of general employing carries out Altitude control, tracking control loop general adoption rate difference control and PD, and the design of PD ride gain is relevant with the characteristic of aircraft, need to set up aircraft altitude Controlling model and carry out parameter designing, design process is more complicated.

Therefore, in prior art, for the longitudinal TRAJECTORY CONTROL of glide vehicle, need the generation of the Altitude control loop PD ride gain completing aircraft according to vehicle mass characteristic fast, effectively to reduce computation complexity, for the Altitude control in the gliding flight process of aircraft provides suitable ride gain.

Summary of the invention

For the longitudinal TRAJECTORY CONTROL problem of glide vehicle, the invention provides a kind of longitudinal TRAJECTORY CONTROL gain design method being applicable to glide vehicle, the method can complete the generation of Altitude control loop PD ride gain fast according to vehicle mass characteristic, effective reduction computation complexity, for the Altitude control in gliding flight process provides suitable ride gain.

For solving the technical matters existed in prior art, embodiments of the invention provide a kind of defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle, comprising:

According to the simplification Altitude control model of longitudinal Controlling model determination glide vehicle of glide vehicle

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F$ Formula 1

Wherein, x ₁=h, x ₂=V Θ, h are the height of glide vehicle, for the altitude rate of glide vehicle, V is speed, and Θ is the trajectory tilt angle of glide vehicle, and m is the quality of glide vehicle, and F is the aerodynamic force that is subject to of glide vehicle and controlled quentity controlled variable, with be respectively x ₁and x ₂first order derivative;

According to simplification Altitude control model, determine that the controlled quentity controlled variable of the optimum of this simplification Altitude control model meets:

$F=-K\stackrel{.}{x}$

Wherein, K=[K _hk _Θ] be optimum controlled quentity controlled variable, k _hfor Altitude control gain, K _Θfor trajectory tilt angle ride gain.

Further, the defining method of longitudinal TRAJECTORY CONTROL gain of described glide vehicle comprises step:

Adopt linearquadratic regulator LQR algorithm, determine the Altitude control gain K in optimum controlled quentity controlled variable K _hwith trajectory tilt angle ride gain K _Θ.

Further, the defining method of longitudinal TRAJECTORY CONTROL gain of described glide vehicle also comprises:

According to the Altitude control gain K determined _hwith trajectory tilt angle ride gain K _Θ, according to longitudinal Trajectory Tracking Control rule of formula 6, glide vehicle is controlled,

$F_{\mathrm{yc}}=M\&CenterDot;g-M\&CenterDot;V_d^2/(a+H_x)-(K_h\&CenterDot;\mathrm{\&Delta;H}+K_{\mathrm{\&Theta;}}\&CenterDot;{\mathrm{\&Delta;\&theta;}}_d\&CenterDot;V_d)$ Formula 6

Wherein, M is glide vehicle quality, and g is acceleration of gravity, and Δ H is height error, Δ H=(H _x-H _cx), H _xfor practical flight height, H _cxfor command altitude, Δ θ _dfor local trajectory tilt angle error, Δ θ _d=(θ _d-θ _dcx), θ _dfor local trajectory tilt angle, θ _dcxfor local trajectory tilt angle instruction, a is semimajor axis of ellipsoid, V _dfor the real-time speed of glide vehicle, F _ycit is the control needed for short transverse of glide vehicle.

Wherein, when the quality m of glide vehicle is 600kg, according to the optimum control amount that LQR algorithm is determined be: K=[K _hk _Θ]=[5.29 79.4].

Wherein, comprise according to the Altitude control model of longitudinal Controlling model determination glide vehicle of glide vehicle:

According to glide vehicle at the local trajectory tilt angle of glide section flight course close to the factor of zero, longitudinal Controlling model of glide vehicle that formula 3 represents is simplified, the longitudinal Controlling model (formula 4) be simplified,

$\begin{array}{c}\stackrel{.}{h}=V\sin \mathrm{\&Theta;}\\ V\&CenterDot;\stackrel{.}{\mathrm{\&Theta;}}=\frac{C_L\mathrm{\&rho;}{V}^{2}S}{2m}+\frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}$ Formula 3,

$\begin{array}{c}\stackrel{.}{h}=V\&CenterDot;\mathrm{\&Theta;}\\ V\&CenterDot;\stackrel{.}{\mathrm{\&Theta;}}=\frac{F}{m}+\frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}$ Formula 4

Wherein, c _lfor lift coefficient, ρ is atmospheric density, and S is aircraft area of reference, and m is glide vehicle quality, for trajectory tilt angle rate of change, h is the height of glide vehicle, and a is earth radius, and g is acceleration of gravity, and σ is the angle of heel of glide vehicle;

Make x ₁=h, x ₂=V Θ, ignores the impact of item, is converted into the state equation that formula 5 represents by the longitudinal Controlling model simplified:

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F+D$ Formula 5

Wherein, $D=\left[\begin{array}{c}0\\ \frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}\right]$ For constant;

Ignore the constant of the state equation that formula 5 is stated, determine the Altitude control model simplified:

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F$ Formula 1.

According to embodiments of the invention, by simplifying aircraft altitude Controlling model, obtain only relevant with vehicle mass simplification mathematical model, and then the gain parameter of the control of height ratio difference and PD control can be obtained by mathematical tool easily.Can the gain parameter of rapid Design Altitude control by method of the present invention, effectively reduce design complexities, improve design versatility, can be directly used in the longitudinal Altitude control conceptual design of glide vehicle.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the defining method of longitudinal TRAJECTORY CONTROL gain of the glide vehicle of the embodiment of the present invention.

Fig. 2 is the process flow diagram of the simplification Altitude control model of the longitudinal Controlling model determination glide vehicle according to glide vehicle according to the embodiment of the present invention.

Fig. 3 shows a condition responsive example plot as vehicle mass m=600kg

Embodiment

For making the technical problem to be solved in the present invention, technical scheme and advantage clearly, be described in detail below in conjunction with the accompanying drawings and the specific embodiments.

This method, for the longitudinal TRAJECTORY CONTROL problem of glide vehicle, by simplifying aircraft altitude Controlling model, obtains only relevant with vehicle mass simplification mathematical model, and then can be obtained the gain parameter of height PD control easily by mathematical tool.Can the gain parameter of rapid Design Altitude control by method of the present invention, effectively reduce design complexities, improve design versatility, can be directly used in the longitudinal Altitude control conceptual design of glide vehicle.

In aircraft flight process, longitudinal Trajectory Tracking Control rule of aircraft is general adopts following form:

$F_{yc}=M\&CenterDot;g-M\&CenterDot;V_d^2/(a+H_x)-(K_h\&CenterDot;\mathrm{\&Delta;}H+K_{\mathrm{\&Theta;}}\&CenterDot;{\mathrm{\&Delta;\&theta;}}_d\&CenterDot;V_d)$ Formula 6

Wherein, M is vehicle mass, and g is acceleration of gravity, and Δ H is height error, Δ H=(H _x-H _cx), H _xfor practical flight height, H _cxfor command altitude, Δ θ _dfor local trajectory tilt angle error, Δ θ _d=(θ _d-θ _dcx), θ _dfor local trajectory tilt angle, θ _dcxfor local trajectory tilt angle instruction, a is semimajor axis of ellipsoid, V _dfor the real-time speed of aircraft; F _ycit is the control needed for short transverse of aircraft.Obviously, in order to determine aircraft short transverse needed for control F _yc, first must determine Altitude control gain K _hwith trajectory tilt angle ride gain K _Θ.Determination Altitude control gain K of the present invention is described below in detail _hwith trajectory tilt angle ride gain K _Θmethod.

As shown in Figure 1, the process flow diagram of the defining method of longitudinal TRAJECTORY CONTROL gain of the glide vehicle of the embodiment of the present invention.

In step 100, according to the simplification Altitude control model of longitudinal Controlling model determination glide vehicle of glide vehicle

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F$ Formula 1

Wherein, x ₁=h, x ₂=V Θ, h are the height of glide vehicle, for the altitude rate of glide vehicle, V is speed, and Θ is the trajectory tilt angle of glide vehicle, and m is the quality of glide vehicle, and F is the aerodynamic force that is subject to of glide vehicle and controlled quentity controlled variable, with be respectively x ₁and x ₂first order derivative.

According to embodiments of the invention, as shown in Figure 2, in order to the simplification Altitude control model of the longitudinal Controlling model determination glide vehicle according to glide vehicle, first, in step 200, need the longitudinal Controlling model obtaining aircraft, as shown in Equation 3.

$\begin{array}{c}\stackrel{.}{h}=V\sin \mathrm{\&Theta;}\\ V\&CenterDot;\stackrel{.}{\mathrm{\&Theta;}}=\frac{C_L\mathrm{\&rho;}{V}^{2}S}{2m}+\frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}$ Formula 3.

The acquisition of longitudinal Controlling model of aircraft is known, does not repeat them here.

Those skilled in the art understand, and aircraft is in glide section flight course, and the local trajectory tilt angle of aircraft is close to zero.Therefore, in step 202, can simplify longitudinal Controlling model of the glide vehicle that formula 3 represents, the longitudinal Controlling model (formula 4) be simplified,

$\begin{array}{c}\stackrel{.}{h}=V\&CenterDot;\mathrm{\&Theta;}\\ V\&CenterDot;\stackrel{.}{\mathrm{\&Theta;}}=\frac{F}{m}+\frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}$ Formula 4

Wherein, c _lfor lift coefficient, ρ is atmospheric density, and S is aircraft area of reference, and m is glide vehicle quality, for trajectory tilt angle rate of change, h is the height of glide vehicle, and a is earth radius, and g is acceleration of gravity, and σ is the angle of heel of glide vehicle.

Next, x is made ₁=h, x ₂=V Θ, ignores the impact of item, is converted into the state equation (step 204) that formula 3 represents by the longitudinal Controlling model simplified:

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F+D$ Formula 5

Wherein, $D=\left[\begin{array}{c}0\\ \frac{V^2\&CenterDot;\cos \mathrm{\&Theta;}}{a+h}-\frac{g\&CenterDot;\cos \mathrm{\&Theta;}}{\cos \mathrm{\&sigma;}}\end{array}\right]$ For constant.

In step 206, ignore the constant of the state equation that formula 3 is stated, determine the Altitude control model simplified:

$\left[\begin{array}{c}{\stackrel{.}{x}}_1\\ {\stackrel{.}{x}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]\left[\begin{array}{c}{x}_1\\ x_2\end{array}\right]+\left[\begin{array}{c}0\\ \frac{1}{m}\end{array}\right]\&CenterDot;F$ Formula 1.

In step 102, according to simplification Altitude control model, determine that the controlled quentity controlled variable of the optimum of this simplification Altitude control model meets: wherein, K=[K _hk _Θ] be optimum controlled quentity controlled variable, k _hfor Altitude control gain, K _Θfor trajectory tilt angle ride gain.To those skilled in the art, the Altitude control model based on formula 1 is determined be known, be not described in detail in this.

In step 104, adopt linearquadratic regulator LQR algorithm, determine the Altitude control gain K in optimum controlled quentity controlled variable K _hwith trajectory tilt angle ride gain K _Θ.Such as, those skilled in the art can utilize the instruments such as Matlab, adopt the methods such as LQR to solve, can obtain satisfied feedback of status K value.As an example, Fig. 3 shows a condition responsive example plot as vehicle mass m=600kg, can obtain multiple K value corresponding to a Controlling model.Preferably, as vehicle mass m=600kg, if when adopting LQR algorithm, make R=30, Q=[840,0; 0,1], [K can be obtained _hk _Θ]=[5.29 79.4].During practical application, need consider aircraft manufacturing technology system rapidity limited case, the speed of response of Altitude control should be less than the adjustment speed of vehicle rate, and the dynamic perfromance chosen has longer regulating time.

According to embodiments of the invention, solving Altitude control gain K _hwith trajectory tilt angle ride gain K _Θ, the control of longitudinal track can be carried out to aircraft according to longitudinal Trajectory Tracking Control rule (formula 1) of aircraft,

$F_{yc}=M\&CenterDot;g-M\&CenterDot;V_d^2/(a+H_x)-(K_h\&CenterDot;\mathrm{\&Delta;}H+K_{\mathrm{\&Theta;}}\&CenterDot;{\mathrm{\&Delta;\&theta;}}_d\&CenterDot;V_d)$ Formula 6.

In the present invention, for the longitudinal TRAJECTORY CONTROL problem of glide vehicle, by simplifying aircraft altitude Controlling model, obtain only relevant with vehicle mass simplification mathematical model, and then the gain parameter of height PD control can be obtained by mathematical tool easily.Can the gain parameter of rapid Design Altitude control by the method, effectively reduce design complexities, improve design versatility, can be directly used in the longitudinal Altitude control conceptual design of glide vehicle.

The above is the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the prerequisite not departing from principle of the present invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (5)

1. a defining method for longitudinal TRAJECTORY CONTROL gain of glide vehicle, comprising:

According to the simplification Altitude control model of longitudinal Controlling model determination glide vehicle of glide vehicle

formula 1

Wherein, x ₁=h, x ₂=V Θ, h are the height of glide vehicle, for the altitude rate of glide vehicle, V is speed, and Θ is the trajectory tilt angle of glide vehicle, and m is the quality of glide vehicle, and F is the aerodynamic force that is subject to of glide vehicle and controlled quentity controlled variable, with be respectively x ₁and x ₂first order derivative;

According to simplification Altitude control model, determine that the controlled quentity controlled variable of the optimum of this simplification Altitude control model meets:

Wherein, K=[K _hk _Θ] be optimum controlled quentity controlled variable, k _hfor Altitude control gain, K _Θfor trajectory tilt angle ride gain.

2. the defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle according to claim 1, comprises step further:

Adopt linearquadratic regulator LQR algorithm, determine the Altitude control gain K in optimum controlled quentity controlled variable K _hwith trajectory tilt angle ride gain K _Θ.

3. the defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle according to claim 2, step comprises:

According to the Altitude control gain K determined _hwith trajectory tilt angle ride gain K _Θ, according to longitudinal Trajectory Tracking Control rule of formula 6, glide vehicle is controlled,

formula 6

Wherein, M is glide vehicle quality, and g is acceleration of gravity, and Δ H is height error, Δ H=(H _x-H _cx), H _xfor practical flight height, H _cxfor command altitude, Δ θ _dfor local trajectory tilt angle error, Δ θ _d=(θ _d-θ _dcx), θ _dfor local trajectory tilt angle, θ _dcxfor local trajectory tilt angle instruction, a is semimajor axis of ellipsoid, V _dfor the real-time speed of glide vehicle, F _ycit is the control needed for short transverse of glide vehicle.

4. the defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle according to claim 2, wherein, when the quality m of glide vehicle is 600kg, according to the optimum control amount that LQR algorithm is determined is:

K＝[K _hK _Θ]＝[5.29 79.4]。

5. the defining method of longitudinal TRAJECTORY CONTROL gain of glide vehicle according to claim 1, the Altitude control model according to longitudinal Controlling model determination glide vehicle of glide vehicle comprises:

According to glide vehicle at the local trajectory tilt angle of glide section flight course close to the factor of zero, longitudinal Controlling model of glide vehicle that formula 3 represents is simplified, the longitudinal Controlling model (formula 4) be simplified,

formula 3,

formula 4

Wherein, c _lfor lift coefficient, ρ is atmospheric density, and S is aircraft area of reference, and m is glide vehicle quality, for trajectory tilt angle rate of change, h is the height of glide vehicle, and a is earth radius, and g is acceleration of gravity, and σ is the angle of heel of glide vehicle;

Make x ₁=h, ignore the impact of item, is converted into the state equation that formula 5 represents by the longitudinal Controlling model simplified:

formula 5

Wherein, for constant;

Ignore the constant of the state equation that formula 5 is stated, determine the Altitude control model simplified:

formula 1.