CN110597068A - Hypersonic aircraft robust control method considering asymmetric constraint of attack angle - Google Patents

Abstract

The invention relates to a hypersonic aircraft robust control method considering asymmetric constraint of an attack angle, which considers a height tracking situation, takes the attack angle as a system state, designs a control law based on an asymmetric obstacle Lyapunov function, introduces asymmetric constraint information of an attack angle tracking error into the control law, ensures that the error is limited in a preset asymmetric interval, limits the attack angle virtual control, combines the attack angle and the control law to realize asymmetric constraint of the attack angle and ensures that a scramjet engine normally works. In consideration of uncertainty of the system, the method adds a robust term to estimate the upper bound of an unknown nonlinear function in the design of the controller, and compensates the influence caused by the uncertainty. And designing a PID controller aiming at the speed subsystem to realize speed tracking.

Description

Hypersonic aircraft robust control method considering asymmetric constraint of attack angle

Technical Field

The invention relates to an aircraft control method, in particular to a hypersonic aircraft robust control method considering asymmetric constraint of an attack angle, and belongs to the field of flight control.

Background

The hypersonic flight vehicle has the characteristics of high flying speed and strong penetration capability, makes global quick strike possible in the military aspect, and can be used for intercontinental quick transportation in the civil aspect, thereby gaining wide attention of all countries in the world. The air-breathing hypersonic aircraft is mainly powered by a scramjet engine, the requirement of normal air intake of the scramjet engine on the attack angle of the aircraft is strict, and the engine is easy to break down when the attack angle is a negative value, so that the amplitude value of the engine does not exceed a given range. In the prior art, the control of the hypersonic aircraft is designed by considering no attack angle constraint or only symmetrical constraint, so that the asymmetric constraint of the attack angle of the aircraft cannot be ensured, and the scramjet engine cannot work normally.

A Barrier Lyapunov function-based adaptive control for hypersonic flight vehicles (Hao An, Hongwei Xia, Changhong Wang, Nonlinear Dynamics,2017,88(3):1833 and 1853) aims at the problem of constraint of the attack angle of a hypersonic aircraft, a controller is designed based on the Barrier Lyapunov function, the tracking error of the pitch angle is limited, but the tracking error of the attack angle is not limited, only the Barrier Lyapunov function in a symmetrical form is considered, different constraints are not respectively introduced when the attack angle is a negative value and a positive value, and the fine adjustment capability is lacked.

Disclosure of Invention

Technical problem to be solved

In order to solve the problem of asymmetric constraint of the attack angle of the hypersonic aircraft caused by the air inlet requirement of the scramjet engine, the invention provides a hypersonic aircraft robust control method considering the asymmetric constraint of the attack angle.

Technical scheme

A hypersonic aircraft robust control method considering asymmetric constraint of an attack angle is characterized by comprising the following steps:

step 1: considering a longitudinal channel dynamics model of the hypersonic aircraft:

wherein,the thrust force is indicated by the expression,the expression lift force is shown as such,the resistance is represented by the amount of resistance,representing a pitch moment; v represents the speed, gamma represents the track inclination angle, h represents the height, alpha represents the attack angle, and q represents the pitch angle speed; delta_eThe rudder deflection angle is shown, and phi represents the throttle opening; representing the dynamic pressure, p representing the air density,represents the average aerodynamic chord length, S represents the aerodynamic reference area; m, I_yyAnd g represents mass, moment of inertia of pitch axis and acceleration of gravity, are all pneumatic parameters;

step 2: defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dFor the height instructions, given by the designer,is the first differential of the height command, k_h>0，k_i>0 is given by the designer; considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTaking the value as zero;

get x₁＝γ，x₂＝α，x₃Q; equations (3) - (5) can be written as strict feedback forms as follows:

wherein f is_i＝f_i0+Δf_i,i＝1,2,3，f_i0For a known nominal value,. DELTA.f_iIs system uncertainty and satisfies | Δ f_i|<Δf_im；g_iI ═ 1,2,3 is a known nonlinear function;

and step 3: step 1: defining the track angle tracking error as:

e₁＝x₁-γ_d (8)

the design attack angle virtual control quantity is as follows:

wherein z is₁To be designed forIs used to compensate for the error term of (a), as an estimate of the upper bound of uncertainty, k₁>0、λ₁>0、σ>0 is given by the designer;

in order to make the virtual control of the attack angle meet the given constraint condition, let x_2cX is obtained by the saturation function_2l：

Wherein,and x_2cAre respectively x_2cUpper and lower bounds, given by the designer;

definition b₂＝x_2l-x_2c，z₁＝e₁-z₁₀Wherein z is₁₀Derived from the following adaptation law:

design ofThe adaptation law is as follows:

wherein eta is₁>0 and delta₁>0 is given by the designer;

the first order differentiator is designed as follows:

wherein p is₂₀>0、p₂₁>0 is given by the designer;

step 2: defining the tracking error of the attack angle as:

e₂＝x₂-x_2c (14)

constructing an asymmetric barrier Lyapunov function:

whereinIs an error e₂Upper bound of (c), -k_a<0 is the error e₂The lower bound of (1) is given by the designer;

definition ofDesigning a virtual control quantity of a pitch angle rate as follows:

wherein, as an estimate of the upper bound of uncertainty, k₂>0、λ₂>0 is given by the designer;

design ofThe adaptation law is as follows:

wherein eta is₂>0 and delta₂>0 is given by the designer；

The first order differentiator is designed as follows:

wherein p is₃₀>0、p₃₁>0 is given by the designer;

and 4, step 4: pitch rate tracking error is defined as:

e₃＝x₃-x_3c (19)

designing the deflection angle of the elevator as follows:

wherein, as an estimate of the upper bound of uncertainty, k₃>0、λ₃>0 is given by the designer;

design ofThe adaptation law is as follows:

wherein eta is₃>0 and delta₃>0 is given by the designer;

and 5: define velocity tracking error as:

wherein, V_dIs a speed reference command;

the design throttle opening phi is as follows:

wherein k is_pV>0、k_iV>0 and k_dV>0 is given by the designer;

step 6: according to the obtained deflection angle delta of the elevator_eAnd the throttle opening phi of the speed subsystem returns to the aircraft dynamics models (1) - (5) to carry out tracking control on the altitude and the speed.

Advantageous effects

The hypersonic aircraft robust control method considering the asymmetric constraint of the attack angle, provided by the invention, takes the attack angle as a system state in consideration of a height tracking situation, designs a control law based on an asymmetric obstacle Lyapunov function, introduces asymmetric constraint information of an attack angle tracking error into the control law, ensures that the error is limited in a preset asymmetric interval, limits the attack angle virtual control, realizes the asymmetric constraint of the attack angle by combining the attack angle virtual control and the control law, and ensures that a scramjet engine normally works. In consideration of uncertainty of the system, the method adds a robust term to estimate the upper bound of an unknown nonlinear function in the design of the controller, and compensates the influence caused by the uncertainty. And designing a PID controller aiming at the speed subsystem to realize speed tracking. Compared with the prior art, the beneficial effects are that:

(1) according to the method, by constructing the asymmetric obstacle Lyapunov function, different upper and lower bound constraints of the tracking error of the attack angle are directly introduced into the control law design, so that the tracking error of the attack angle is limited in a given asymmetric interval, and the tracking precision is ensured.

(2) According to the invention, while the tracking error of the attack angle is limited, the virtual control of the attack angle is realized by adopting an asymmetric amplitude limiting design, and the combination of the two, the attack angle can be constrained in an artificially given asymmetric range in the flight process, so that the air intake requirements of the scramjet engine under different flight conditions can be ensured.

Drawings

FIG. 1 is a flow chart of the present invention for robust control of hypersonic flight vehicles taking into account asymmetric constraints on angle of attack.

Detailed Description

The invention will now be further described with reference to the following examples and drawings:

referring to fig. 1, the hypersonic aircraft robust control considering the asymmetric constraint of the attack angle is applied to a hypersonic aircraft dynamics model, and is realized by the following steps:

(a) considering a longitudinal channel dynamics model of the hypersonic aircraft:

wherein,the thrust force is indicated by the expression,the expression lift force is shown as such,the resistance is represented by the amount of resistance,representing a pitch moment; v denotes velocity, γ denotes track pitch, h denotes altitude, α denotes angle of attack, and q denotes pitch angle velocity. Delta_eIndicating elevatorsThe deflection angle, Φ, represents the throttle opening. Denotes dynamic pressure, ρ 6.7429 × 10^-5Which represents the density of the air,represents the average aerodynamic chord length, and S-17 represents the aerodynamic reference area; m is 300, I_yy＝5×10⁵And g-32 represents mass, moment of inertia of pitch axis and acceleration of gravity,all are pneumatic parameters, and are specifically defined as follows:

(b) defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dFor the height instructions, given by the designer,is the first differential of the height command, k_h＝0.5，k_i0.05. Considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTake to zero.

Get x₁＝γ，x₂＝α，x₃Q; equations (3) - (5) can be written as strict feedback forms as follows:

wherein f is_i＝f_i0+Δf_i,i＝1,2,3，f_i0＝0.9f_iFor a known nominal value,. DELTA.f_iIs system uncertainty and satisfies | Δ f_i|<Δf_im；g_iI is 1,2,3, a known nonlinear function.

(c) Step 1: defining the track angle tracking error as:

e₁＝x₁-γ_d (8)

the design attack angle virtual control quantity is as follows:

wherein z is₁For the compensation error term to be designed, as an estimate of the upper bound of uncertainty, k₁＝0.8，λ₁1.5, σ is given by the designer.

In order to make the virtual control of the attack angle meet the given constraint condition, let x_2cX is obtained by the saturation function_2l：

Wherein,and x_2cEach occurrence of ═ 0.02 is x_2cUpper and lower bounds.

Definition b₂＝x_2l-x_2c，z₁＝e₁-z₁₀Wherein z is₁₀Derived from the following adaptation law:

design ofThe adaptation law is as follows:

wherein eta is₁＝0.1，δ₁＝0.001。

The first order differentiator is designed as follows:

wherein p is₂₀>0.9，p₂₁>1.2。

Step 2: defining the tracking error of the attack angle as:

e₂＝x₂-x_2c (14)

constructing an asymmetric barrier Lyapunov function:

whereinIs an error e₂Upper bound of (c), -k_aError e is-0.07₂The lower bound of (c).

Definition ofDesigning a virtual control quantity of a pitch angle rate as follows:

wherein, as an estimate of the upper bound of uncertainty, k₂＝1，λ₂＝30。

Design ofThe adaptation law is as follows:

wherein eta is₂＝0.1，δ₂＝0.001。

The first order differentiator is designed as follows:

wherein p is₃₀＝0.05，p₃₁＝2。

And 3, step 3: pitch rate tracking error is defined as:

e₃＝x₃-x_3c (19)

designing the deflection angle of the elevator as follows:

wherein, as an estimate of the upper bound of uncertainty, k₃＝35，λ₃＝10。

Design ofThe adaptation law is as follows:

wherein eta is₃0.1 and δ₃0.001 is given by the designer.

(d) Define velocity tracking error as:

wherein, V_dIs a speed reference command.

The design throttle opening phi is as follows:

wherein k is_pV＝5，k_iV＝1，k_dV＝0.01。

(e) According to the obtained deflection angle delta of the elevator_eAnd the throttle opening phi of the speed subsystem returns to the aircraft dynamics models (1) - (5) to carry out tracking control on the altitude and the speed.

Claims (1)

1. A hypersonic aircraft robust control method considering asymmetric constraint of an attack angle is characterized by comprising the following steps:

step 1: considering a longitudinal channel dynamics model of the hypersonic aircraft:

wherein,the thrust force is indicated by the expression,the expression lift force is shown as such,the resistance is represented by the amount of resistance,representing a pitch moment; v represents the speed, gamma represents the track inclination angle, h represents the height, alpha represents the attack angle, and q represents the pitch angle speed; delta_eThe rudder deflection angle is shown, and phi represents the throttle opening; dynamic pressure, and ρ nullThe air tightness of the air conditioner is improved,represents the average aerodynamic chord length, S represents the aerodynamic reference area; m, I_yyAnd g represents mass, moment of inertia of pitch axis and acceleration of gravity, are all pneumatic parameters;

step 2: defining a height tracking error e_h＝h-h_dDesign track angle command gamma_d：

In the formula, h_dFor the height instructions, given by the designer,is the first differential of the height command, k_h>0，k_i>0 is given by the designer; considering that the track angle change of the cruise section is small and the first-order differential of the track angle instructionTaking the value as zero;

get x₁＝γ，x₂＝α，x₃Q; equations (3) - (5) can be written as strict feedback forms as follows:

wherein f is_i＝f_i0+Δf_i,i＝1,2,3，f_i0For a known nominal value,. DELTA.f_iIs system uncertainty and satisfies | Δ f_i|<Δf_im；g_i,i＝1,2,3 are known non-linear functions;

and step 3: step 1: defining the track angle tracking error as:

e₁＝x₁-γ_d (8)

the design attack angle virtual control quantity is as follows:

wherein z is₁For the compensation error term to be designed, as an estimate of the upper bound of uncertainty, k₁>0、λ₁>0、σ>0 is given by the designer;

in order to make the virtual control of the attack angle meet the given constraint condition, let x_2cX is obtained by the saturation function_2l：

Wherein,andx _2care respectively x_2cUpper and lower bounds, given by the designer;

definition b₂＝x_2l-x_2c，z₁＝e₁-z₁₀Wherein z is₁₀Derived from the following adaptation law:

design ofThe adaptation law is as follows:

wherein eta is₁>0 and delta₁>0 is given by the designer;

the first order differentiator is designed as follows:

wherein p is₂₀>0、p₂₁>0 is given by the designer;

step 2: defining the tracking error of the attack angle as:

e₂＝x₂-x_2c (14)

constructing an asymmetric barrier Lyapunov function:

whereink_b>0 is the error e₂Upper bound of (c), -k_a<0 is the error e₂The lower bound of (1) is given by the designer;

definition ofDesigning a virtual control quantity of a pitch angle rate as follows:

wherein, as an estimate of the upper bound of uncertainty, k₂>0、λ₂>0 is given by the designer;

design ofThe adaptation law is as follows:

wherein eta is₂>0 and delta₂>0 is given by the designer;

the first order differentiator is designed as follows:

wherein p is₃₀>0、p₃₁>0 is given by the designer;

and 4, step 4: pitch rate tracking error is defined as:

e₃＝x₃-x_3c (19)

designing the deflection angle of the elevator as follows:

wherein, as an estimate of the upper bound of uncertainty, k₃>0、λ₃>0 is given by the designer;

design ofThe adaptation law is as follows:

wherein eta is₃>0 and delta₃>0 is given by the designer;

and 5: define velocity tracking error as:

wherein, V_dIs a speed reference command;

the design throttle opening phi is as follows:

wherein k is_pV>0、k_iV>0 and k_dV>0 is given by the designer;

step 6: according to the obtained deflection angle delta of the elevator_eAnd the throttle opening phi of the speed subsystem returns to the aircraft dynamics models (1) - (5) to carry out tracking control on the altitude and the speed.