CN106802660B - A Composite Strong Anti-disturbance Attitude Control Method - Google Patents

Abstract

A composite strong anti-disturbance attitude control method, which is based on non-singular terminal sliding mode, backstepping method and observer, can realize fast and high-precision attitude tracking control of flexible aircraft system, and has strong anti-disturbance ability at the same time. Utilizing the fast and accurate estimation ability of ADRC for disturbance, combined with the strong robustness and rapidity of backstepping control technology and non-singular terminal sliding mode, the attitude tracking control of high-performance aircraft is realized.

Description

A Composite Strong Anti-disturbance Attitude Control Method

technical field

The invention relates to a composite strong anti-disturbance attitude control method, which belongs to the field of aircraft attitude control.

Background technique

The structure of modern aircraft is complex, and the increasingly diverse mission requirements put forward higher requirements for aircraft control performance (stability, anti-interference, rapidity, etc.). At the same time, with the continuous exploration of various new technologies and new methods, the development of aircraft control is facing many opportunities and challenges. Carrying out aircraft-related technology research has very important academic value, strategic significance and application prospects. How to develop advanced aircraft attitude control technology is one of the basic issues and key technologies of aircraft control technology.

Sliding mode variable structure control is a special kind of nonlinear discontinuous control method. This control method is different from other controls in that the structure of the system will change purposefully according to the current state of the system during the dynamic process, so that the system will run according to the state trajectory of the predetermined sliding mode. Since the sliding mode can be designed and has nothing to do with model parameters and disturbances, variable structure control has the advantages of fast response, insensitivity to parameter changes, insensitivity to disturbances, and simple physical implementation. At present, sliding mode variable structure control is used in aircraft It is widely used in the field of control and servo control. The backstepping method has the advantages of good stability and fast convergence speed, allows the preservation of the nonlinear or high-order characteristics of the controlled object, and can deal with a type of nonlinear and uncertain effects. Its application in the aviation field is highly valued by researchers. focus on. The active disturbance rejection control technology uses the extended state observer to transform all nonlinear uncertain objects with unknown external disturbances into integral series type with nonlinear state feedback, and then uses state error feedback to design an ideal controller. It fundamentally overcomes the inherent defects of classic PID. At the same time, there is no need to directly measure the external disturbance, and it is not necessary to know the law of the disturbance in advance, which can effectively improve the control accuracy.

Contents of the invention

The technical solution problem of the present invention is: overcome the deficiencies in the prior art, take the attitude control system of flexible aircraft as the background, provide a kind of flexible aircraft attitude tracking control based on non-singular terminal sliding mode, backstepping design method and observer The method realizes the fast attitude tracking control of the flexible aircraft, has high precision and strong anti-interference ability, and satisfies the attitude tracking requirements of the flexible aircraft to the greatest extent.

Technical solution of the present invention is:

A composite strong anti-disturbance attitude control method, the steps are as follows:

(1) Establish a flexible aircraft system model;

(2) utilize the described flexible vehicle system model that step (1) obtains, set up flexible vehicle kinematics error equation and dynamics error equation based on quaternion;

(3) According to the flexible vehicle system model obtained in steps (1), (2), the flexible vehicle kinematics error equation and the dynamics error equation, based on the backstepping method, determine the virtual control quantity;

(4) According to the kinematics error equation and the dynamics error equation of the flexible aircraft in the step (2), set up the finite-time non-singular terminal sliding mode surface;

(5) According to the flexible vehicle system model, flexible vehicle kinematics error equation and dynamic error equation obtained in steps (1) and (2), separate the total uncertainty item from the model, determine the extended state observer, and estimate Total uncertain items;

(6) Determine the controller based on the sliding mode and the extended state observer, so as to realize the composite strong anti-disturbance attitude control.

The beneficial effect of the present invention compared with prior art is:

(1) In the case of flexible vibration mode, uncertain moment of inertia, external disturbance and actuator saturation affecting the aircraft, it can realize fast and high-precision attitude tracking control of the aircraft, and has strong anti-interference ability.

(2) Give full play to the fast and accurate estimation ability of active disturbance rejection control, and combine the strong robustness and rapidity of backstepping control technology and non-singular terminal sliding mode to realize high-performance aircraft attitude tracking control.

Description of drawings

Fig. 1 is the flow chart of the control system based on sliding mode and observer of the present invention;

Fig. 2 is the attitude quaternion tracking error and the angular velocity tracking error of the PID controller of the present invention;

Fig. 3 is the attitude quaternion tracking error and the angular velocity tracking error of the composite strong anti-disturbance attitude controller of the present invention;

Fig. 4 is the input torque of PID controller of the present invention;

Fig. 5 is the input torque of composite strong anti-disturbance attitude controller of the present invention;

Fig. 6 is the simulation result of sliding mode surface of the present invention;

Fig. 7 is the estimation of the disturbance by the extended state observer of the present invention;

Fig. 8 is the frequency attenuation curve of the flexible mode of the present invention.

Fig. 9 shows attitude quaternion tracking error and angular velocity tracking error under the second situation of the present invention;

Fig. 10 is the estimation of the disturbance by the extended state observer in the second case of the present invention.

Detailed ways

Specific embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings. As shown in Figure 1, the concrete steps of a kind of composite strong anti-disturbance attitude control method that the present invention proposes are as follows:

(1) Considering the influence of aircraft flexibility characteristics, uncertain moment of inertia, external disturbance, actuator saturation and other factors, the following flexible aircraft system model is established:

in: d∈R ³ is the external disturbance, ^{δ∈R 4×3} is the coupling matrix of rigid body and flexible attachment, δT is the transpose of δ, η is the flexible mode, and are the first and second derivatives of η, respectively; J ₀ ∈ R ^3×3 is a known nominal inertia matrix, and is a positive definite matrix; ΔJ is the uncertain part of the inertia matrix, Ω=[Ω ₁ ,Ω ₂ ,Ω ₃ ] ^T is the angular velocity component of the aircraft in the body coordinate system, is the first-order derivative of Ω; × is an operation symbol, and applying × to vector b=[b ₁ ,b ₂ ,b ₃ ] ^T can be obtained:

L=diag{2ζ _i ω _ni ,i=1,2,...,N} and are the damping matrix and stiffness matrix respectively, N is the mode order, ω _ni ,i=1,2,...,N is the vibration mode frequency matrix, ζ _i ,i=1,2,...,N is the vibration modal damping ratio;

u=[u ₁ ,u ₂ ,u ₃ ] ^T is a controller based on sliding mode and extended state observer, sat(u)=[sat(u ₁ ),sat(u ₂ ),sat(u ₃ )] ^T is the actual control vector generated by the actuator, sat(u _i ), i=1,2,3 represents the nonlinear saturation characteristics of the actuator and satisfies sat(u _i )=sign(u _i ) min{u _mi , |u _i |}, i=1,2,3, |·| means to take the absolute value, sat(u _i ) is expressed as sat(u _i )=θ _oi +u _i ,i=1,2,3, where θ _oi , i=1,2,3 is:

u _mi , i=1, 2, 3 are actuator saturation values, the part exceeding the actuator saturation value is θ _o ＝[θ _o1 ,θ _o2 ,θ _o3 ] ^T , and satisfy ||θ _o ||≤l _δθ , l _δθ is a positive real number.

(2) Using the model obtained in step (1), the kinematics error equation and the dynamics error equation of the flexible aircraft are established based on the quaternion:

The kinematic error equation of flexible aircraft:

Where: (ev , e ₄ )∈R ³ × _R , _ev = [e ₁ , e ₂ , e ₃ ] ^T is the error quaternion vector part between the current aircraft attitude and the expected attitude, e ₄ is the scalar part, and satisfied and are the first-order derivatives of _ev and e ₄ respectively; (q _v ,q ₄ )∈R ³ ×R, q _v =[q ₁ ,q ₂ ,q ₃ ] ^T is the unit quaternion vector part describing the attitude of the aircraft , q ₄ is a scalar part, and satisfies q _dv =[q _d1 ,q _d2 ,q _d3 ] ^T is the unit quaternion vector part describing the desired attitude, q _d4 is the scalar part, and satisfies Ω _e ＝Ω-CΩ _d ＝[Ω _e1 Ω _e2 Ω _e3 ] ^T is the angular velocity error vector established between the body coordinate system and the target coordinate system, Ω _d ∈ R ³ is the desired angular velocity vector, is a transformation matrix, and satisfies ||C||=1, is the first derivative of C, and I ₃ is a 3×3 identity matrix;

The dynamic error equation of flexible aircraft is:

in, is the first derivative of Ω _e , Ω _d is the desired angular velocity, is the first derivative of Ω _d .

(3) According to the flexible aircraft system model, flexible aircraft kinematics error equation and dynamic error equation obtained in steps (1), (2), based on the backstepping method, determine the virtual control variable α, specifically:

α＝-K ₁ e _v -K ₂ S _c (6)

Among them, K _j ＝diag{k _ji }>0, i=1,2,3, j=1,2, diag(a ₁ ,a ₂ ,…,a _n ) means that the diagonal elements are a ₁ , a ₂ ,…, a diagonal matrix of _n ;

Define S _c = {S _c1 , S _c2 , S _c3 } ^T as follows:

in p, q are positive odd numbers, and 0<q/p<1, l _1i , l _2i , i=1, 2, 3 are parameters; ∈ _i , i=1, 2, 3, ι ₁ , ι ₂ are design parameters , sign(a) is a sign function, defined as follows:

(4) According to the kinematics error equation and the dynamics error equation of the flexible vehicle in step (2), a finite-time non-singular terminal sliding mode surface is established, specifically S=[S ₁ S ₂ S ₃ ] ^T , where:

S _i =Ω _e +K ₁ e _v +K ₂ S _c ,i=1,2,3 (8)

(5) According to the flexible vehicle system model, flexible vehicle kinematics error equation and dynamic error equation obtained in steps (1) and (2), separate the total uncertainty item from the model, determine the extended state observer, and determine Extended state observer, specifically:

Among them, Z ₁ is the state error, F＝[F ₁ ,F ₂ ,F ₃ ] ^T ＝-Ω ^× J ₀ Ω+J ₀ E _Ω , E _Ω ＝(L ₁ +L ₂ E _q )Q(e) Ω, L ₁ and L ₂ are positive real numbers, define E _q :

fal(Z ₁ ,β ₁ ,γ)=[fal ₁ (Z ₁ ,β ₁ ,γ),fal ₂ (Z ₁ ,β ₁ ,γ),fal ₃ (Z ₁ ,β ₁ ,γ)] ^T ( 11)

X ₁ and X ₂ are the output of the extended state observer, S is the system state, X ₁ tracks the system state S, X ₂ tracks the extended state G _δ of the system, G _δ is the total uncertainty of the internal disturbance and external disturbance of the estimated system term, F is the known model, Ω is the angular velocity, ρ ₁ and ρ ₂ are the observation ability coefficients of the observer, Z ₁ is the state error, u is the controller based on the sliding mode and extended state observer, Z _1i is the vector Z The i- _th element of ₁ , _p , _q are positive odd numbers, γ, α, β ₁ are design parameters, || The outputs X ₁ and X ₂ track to S and G _δ respectively in a finite time.

(6) According to the finite-time non-singular terminal sliding mode surface and the extended state observer in steps (4) and (5), establish the controller u based on the sliding mode and the extended state observer, specifically:

in,

The controller can be regarded as a combination of approach rate (J ₀ (-τS-σsign ^r (S))), model known quantity (-J ₀ F), and unknown model estimator (-J ₀ X ₂ ); The close rate (J ₀ (-τS-σsign ^r (S))) realizes the fast convergence of the controller; the known model (-J ₀ F) directly participates in the controller design, reducing the pressure of the observer estimation; for the unknown model estimator ( -J ₀ X ₂ ), the observer is used to accurately estimate and compensate, so that different disturbances can be suppressed, so as to keep the system stable.

Example:

In order to verify the effectiveness of the aircraft attitude tracking controller designed above based on observer technology and sliding mode control technology, the robustness of the controller in aircraft attitude tracking control is proved through simulations under different conditions.

Considering the kinematics error equation and the dynamics error equation of the flexible vehicle, the nominal inertia matrix is

The uncertain part in the inertia matrix is:

ΔJ=diag(50,30,20)kg·m ² ;

The external disturbance d∈R ³ is a function of time t, which can be expressed as d(t), specifically taken as:

Situation 1: d(t)=0.5[sin(t), sin(2t), sin(3t)] ^T ;

Situation 2: d(t)=[200*sin(0.1t), 220*sin(0.2t), 300*sin(0.3t)] ^T ;

The initial quaternion value of the aircraft attitude is q=[0.3,-0.2,-0.3,0.8832] ^T and the initial angular velocity is Ω=[0,0,0] ^T , and the effectiveness of the control algorithm is verified by numerical simulation, assuming the desired The initial value of the attitude quaternion is q _d =[0,0,0,1] ^T , and the expected angular velocity is a function of time t, which can be expressed as Ω _d (t), specifically taken as:

Ω _d (t)=0.05[sin(πt/100), sin(2πt/100), sin(3πt/100)] ^T ;

In the presence of uncertain inertia matrix and external disturbance, Fig. 2 shows the attitude quaternion tracking error and angular velocity tracking error of the PID controller; Fig. 3 shows the attitude quaternion tracking error and angular velocity of the composite strong anti-disturbance attitude controller Tracking error; Fig. 4 is the input torque of PID controller; Fig. 5 is the input torque of composite strong anti-disturbance attitude controller; As can be seen from Table 1, compared with PID control, the present invention proposes based on sliding mode and extended state observer The controller can ensure that the trajectory of the aircraft system can quickly and accurately track the reference attitude.

Table 1 Comparison results of composite strong anti-disturbance attitude controller and PID control

controller Quaternion angular velocity Composite strong anti-disturbance attitude controller ±9.54e-6 ±2.17e-5 PID controller ±9.02e-3 ±3.92e-3 Increase ratio, % 99.8 99.4

Figure 6 shows the simulation results of the sliding surface, based on the parameter μ=15I ₃ , The system trajectory of β ₁ =0.50, K ₁ =2I ₃ , K ₂ =I ₃ and q/p=0.9 can quickly reach the sliding mode surface, and the extended state observer can accurately estimate the uncertainty and external disturbance, thereby effectively suppressing The chattering phenomenon caused by the sliding mode control is shown in Fig. 7. The estimation performance of the extended state observer to the total disturbance G _δi , i=1,2,3; by selecting the appropriate parameters ρ ₁ =4.5, ρ ₂ =8.5 and γ=1, the observer outputs each component X ₂ (i),i=1,2,3 which can effectively track the disturbance components G _δi ,i=1,2,3, which verifies that the extended state observer has a good Observation performance, so that the controller has fast convergence and high-precision tracking capabilities.

Figure 8 shows the attitude quaternion tracking error and angular velocity tracking error in the second disturbance condition, and Figure 9 and Figure 10 show the estimation performance of the extended state observer for the total disturbance. It can be seen that the designed sliding mode controller can also guarantee Good convergence speed and precision, with strong anti-interference ability. The content that is not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims (4)

1. A composite strong anti-interference attitude control method is characterized by comprising the following steps:

(1) establishing a flexible aircraft system model;

the flexible aircraft system model specifically is as follows:

wherein:d∈R³is an external disturbance, δ ∈ R^4×3Being a coupling matrix of rigid bodies and flexible appendages, δ^TIs a transpose of delta, η is a flexural mode,andη first and second derivatives, respectively₀∈R^3×3Is a known nominal inertia matrix and is a positive definite matrix; Δ J is an uncertainty in the inertia matrix, Ω ═ Ω₁,Ω₂,Ω₃]^TIs the angular velocity component of the aircraft in the body coordinate system,is the first derivative of Ω;^×is a sign of operation, will^×For vector b ═ b₁,b₂,b₃]^TThe following results were obtained:

L＝diag{2ζ_iω_ni1,2, N andrespectively damping matrix and rigidity matrix, N is modal order, omega_niN is a vibration mode frequency matrix, ζ_iN is a vibration mode damping ratio;

u＝[u₁,u₂,u₃]^Tis based on a controller of sliding mode and extended state observer, sat (u) ═ sat (u)₁),sat(u₂),sat(u₃)]^TIs the actual control vector, sat (u), generated by the actuator_i) Where i is 1,2, and 3 represent nonlinear saturation characteristics of the actuator and satisfy sat (u)_i)＝sign(u_i)·min{u_mi,|u_i|},i＝1,2,3，sat(u_i) Expressed as sat (u)_i)＝θ_oi+u_iI is 1,2,3, wherein θ_oiI is 1,2, 3:

u_miwhere i is 1,2,3 is the actuator saturation value, and the portion exceeding the actuator saturation value is θ_o＝[θ_o1,θ_o2,θ_o3]^TAnd satisfies | θ_o‖≤l_δθ，l_δθIs a positive real number;

(2) establishing a flexible aircraft kinematic error equation and a dynamic error equation based on quaternion by using the flexible aircraft system model obtained in the step (1);

the flexible aircraft kinematic error equation and the dynamic error equation are specifically as follows:

flexible aircraft kinematic error equation:

wherein (e)_v,e₄)∈R³×R，e_v＝[e₁,e₂,e₃]^TIs the error quaternion vector component, e, of the current aircraft attitude to the desired attitude₄Is a scalar part, and satisfies Andare respectively e_v、e₄The first derivative of (a); (q) a_v,q₄)∈R³×R，q_v＝[q₁,q₂,q₃]^TIs a unit quaternion vector component, q, that describes the attitude of the aircraft₄Is a scalar part, and satisfiesq_dv＝[q_d1,q_d2,q_d3]^TIs a unit quaternion vector section, q, describing the desired pose_d4Is a scalar part, and satisfiesΩ_e＝Ω-CΩ_d＝[Ω_e1 Ω_e2 Ω_e3]^TIs an angular velocity error vector, omega, established between a body coordinate system and a target coordinate system_d∈R³Is the vector of the desired angular velocity and,is a conversion matrix, and satisfies | C | 1, is the first derivative of C, I₃Is a 3 × 3 identity matrix;

the flexible aircraft dynamic error equation is as follows:

wherein,is omega_eFirst derivative of, omega_dIt is the desired angular velocity of the beam,is omega_dThe first derivative of (a);

(3) determining a virtual control quantity based on a back stepping method according to the flexible aircraft system model, the flexible aircraft kinematic error equation and the dynamic error equation obtained in the steps (1) and (2);

the virtual control amount α is specifically:

α＝-K₁e_v-K₂S_c；

wherein, K_j＝diag{k_ji}>0,i＝1,2,3,j＝1,2，diag(a₁,a₂,…,a_n) Represents a diagonal element of a₁,a₂,…,a_nA diagonal matrix of (a);

definition of S_c＝{S_c1,S_c2,S_c3}^TThe following were used:

whereinp, q are positive odd numbers and 0<q/p<1，k_1i、k_2iI is a parameter 1,2, 3; epsilon_i,i＝1,2,3、ι₁、ι₂Is a design parameter, sign (a) is a sign function, defined as follows:

(4) establishing a finite-time nonsingular terminal sliding mode surface according to the kinematic error equation and the dynamic error equation of the flexible aircraft in the step (2);

(5) separating a total uncertainty from the model according to the flexible aircraft system model, the flexible aircraft kinematic error equation and the dynamic error equation obtained in the steps (1) and (2), determining an extended state observer, and estimating the total uncertainty;

(6) and determining a controller based on the sliding mode and the extended state observer, thereby realizing the composite strong disturbance rejection attitude control.

2. The composite strong disturbance rejection attitude control method according to claim 1, wherein: the finite time nonsingular terminal sliding mode surface is as follows: s ═ S₁S₂S₃]^TWherein:

S_i＝Ω_e+K₁e_v+K₂S_c,i＝1,2,3。

3. the composite strong disturbance rejection attitude control method according to claim 2, wherein: the expansion state observer specifically comprises:

wherein Z is₁Is the state error, F ═ F₁,F₂,F₃]^T＝-Ω^×J₀Ω+J₀E_Ω，E_Ω＝(L₁+L₂E_q)Q(e)Ω，L₁、L₂Is a positive real number, define E_q：

fal(Z₁,β₁,γ)＝[fal₁(Z₁,β₁,γ),fal₂(Z₁,β₁,γ),fal₃(Z₁,β₁,γ)]^T；

X₁And X₂Is the output of the extended state observer, S is the system state, X₁Tracking system state S, X₂Expanded state G of tracking system_δ，G_δIs the total uncertainty term for estimating the internal and external disturbances of the system, F is the known model, Ω is the angular velocity, ρ₁、ρ₂Is the observation capability coefficient of the observer, Z₁Is the state error, u is the controller based on sliding mode and extended state observer, Z_1iIs a vector Z₁P and q are positive odd numbers, gamma, A and β₁Is a design parameter.

4. The composite strong disturbance rejection attitude control method according to claim 3, wherein: the controller u based on the sliding mode and the extended state observer specifically comprises the following components:

wherein,