CN106774379A - A kind of strong robust attitude control method of intelligent supercoil - Google Patents

Abstract

A kind of strong robust attitude control method of intelligent supercoil, the posture adjustment scheme of flexible aircraft is directed to using self adaptation to (Back Propagation, BP) neutral net combination supercoil sliding mode control algorithm, design is propagated.The program can meet the requirement such as flexible aerocraft system quick response, strong robustness, it will thus provide convergence rate more faster than standard super-twisting algorithm.Meanwhile, the program realizes parameter adaptive regulation, is effectively suppressed by being buffeted caused by high frequency switching behavior, and adaptive gain will also solve the problems, such as that hyperharmonic control gain chooses difficult.

Description

Intelligent supercoiled strong robust attitude control method

Technical Field

The invention relates to an intelligent supercoiled robust attitude control method, and belongs to the field of aircraft attitude control.

Background

With the continuous development of scientific technology and the continuous expansion of application fields, the structure and the task of the aircraft are increasingly complex and huge, and the flight environment is severe and changeable. How to accurately and quickly complete attitude control of a flexible aircraft system aiming at uncertain interior and external disturbance of an aircraft becomes an important problem in the design of a flight control system. The development of a flight control system with high speed, strong robustness and high precision to meet the high performance requirement has important academic value and application prospect.

Sliding mode variable structure control is a special nonlinear discontinuous control method. In the dynamic process, the control structure purposefully changes according to the current state of the system, so that the system runs according to the state track of the preset sliding mode. The variable structure control has the advantages of high reaction speed, insensitivity to parameter change, insensitivity to disturbance, simple physical implementation and the like. In order to improve engineering applicability, a supercoiled control algorithm adopts a series high-order sliding mode to ensure the continuity of control output and solve the problem of buffeting caused by high-frequency switching in sliding mode control, and the supercoiled control algorithm has the important characteristic that only the information of a sliding mode number needs to be known but the information of a first derivative of the sliding mode number is not needed, can eliminate the buffeting problem of a sliding mode control system with the correlation degree of 1, and has rapidity and robustness of a common sliding mode. However, the classical supercoiling control algorithm relies on an uncertain and disturbing upper bound that is not available in practical situations.

Intelligent algorithms are increasingly intensively studied, wherein neural network learning methods are increasingly widely applied. As an important feedforward neural network model, a Back Propagation (BP) neural network is a multi-layer feedforward network trained according to an error Back Propagation algorithm. The network has better large-scale nonlinear data parallel processing and fault-tolerant capability in practical application. As a basic learning algorithm of the neural network, the BP algorithm is the most common and effective learning method in the neural network, is widely applied to various fields, and has important theoretical and application values.

With the development of the adaptive technology, the gain coefficient of the controller can be dynamically calculated according to the actual conditions of uncertainty and interference characteristics. The idea of self-adaptive control is applied to a BP neural network combined with a second-order sliding mode supercoiling algorithm, a controller of dynamic gain is designed, dependence on external information is reduced, the action rule of disturbance does not need to be known in advance, and the applicability of the controller can be effectively improved.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and the posture adjusting method with accuracy, rapidness and strong robustness is provided. The accurate, fast and strong robust attitude tracking control of the flexible aircraft system with internal uncertainty and external disturbance is realized, and the attitude adjusting requirement of the flexible aircraft is met to the greatest extent.

The technical solution of the invention is as follows:

an intelligent supercoil strong robust attitude control method comprises the following steps:

(1) establishing a flexible aircraft system model;

(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);

(3) 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);

(4) and (4) determining a control law by using a BP self-adaptive neural network and combining a supercoiling algorithm according to the finite-time nonsingular terminal sliding mode surface established in the step (3), and realizing intelligent supercoiling strong robust attitude control.

Compared with the prior art, the invention has the beneficial effects that:

1. the method aims at realizing the fast tracking and stable control of the attitude of the flexible aircraft, and all the adjusting parameters realize intelligent self-adjustment, thereby overcoming the problem of difficult control gain selection.

2. The control output is absolutely continuous, and the buffeting problem caused by high-frequency switching in the traditional sliding mode control is effectively restrained.

3. The designed neural network adaptive gain supercoiled algorithm has strong robustness on external disturbance and uncertain and flexible vibration modes of time-varying and variable states, optimizes the classical supercoiled algorithm, and improves the convergence rate and the disturbance suppression range.

4. The designed control scheme does not depend on any prior information of the moment of inertia, external disturbance and derivatives thereof, and the adaptability of the attitude adjusting controller to the factors of the flexibility characteristic of the aircraft, uncertainty of the moment of inertia, external disturbance and the like is obviously improved.

Drawings

FIG. 1 is a flow chart of an intelligent supercoiled robust attitude control method of the present invention;

FIG. 2 is an attitude response curve of the system of the present invention;

FIG. 3 is an angular velocity response curve of the system of the present invention;

FIG. 4 is a slip form surface and control torque curve of the present invention;

FIG. 5 is a graph of neuron gain output according to the present invention;

FIG. 6 is a flexural mode frequency attenuation curve of the present invention.

Detailed Description

The following describes embodiments of the present invention in further detail with reference to the accompanying drawings. As shown in fig. 1, the intelligent supercoiled robust attitude control method provided by the invention specifically comprises the following steps:

(1) considering the influence of factors such as flexibility characteristics, uncertain moment of inertia, external disturbance and the like of the aircraft, establishing a flexible aircraft system model as follows:

wherein:d∈R³is an external disturbance, ∈ R^4×3Is a coupling matrix of rigid bodies and flexible attachments,^Tis that of (a), η is in a flexible 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; and u is an intelligent supercoiled strong robust attitude controller.

(2) Establishing a kinematic error equation and a dynamic error equation of the flexible aircraft based on quaternion by using the system model of the flexible aircraft obtained in the step (1), specifically

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_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_e1Ω_e2Ω_e3]^T＝[Ω_ei]^TI 1,2,3 is an angular velocity error vector established between the body coordinate system and the target coordinate system, Ω_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) Designing a finite-time nonsingular terminal sliding mode surface S according to the kinematic error equation and the dynamic error equation of the flexible aircraft in the step (2), specifically:

S＝Ω_e+K₁e_v+K₂S_c(5)

wherein S ═ S₁,S₂,S₃]^T∈R³，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); and define S_c＝[S_c1,S_c2,S_c3]^TThe following were used:

whereinr₁,r₂Is a positive odd number, and 0<r<1，l_1i、l_2i、_i,i＝1,2,3、ι₁、ι₂Is a design parameter, |, represents the absolute value, sign (a) is a sign function, defined as follows:

(4) determining an intelligent gain supercoiled strong robust attitude control law by utilizing a BP self-adaptive neural network and combining a supercoiled algorithm according to the finite time nonsingular terminal sliding mode surface established in the step (3), wherein the method specifically comprises the following steps:

u＝J₀[u₁,u₂,u₃]^T(7)

wherein:

the discrete form of u is:

wherein λ₁(k)、λ₂(j) J is 0, 1.. times, k is the corresponding gain coefficient, u (k) is the input value at the k-th sampling time; the increment of u (k) is:

Δu(k)＝u(k)-u(k-1)＝-λ₁(k)(_oi(k)-_oi(k-1))-λ₂(k)θ_i(k),i＝1,2,3 (13)

the neuron outputs are:

wherein x is₁(k)＝_oi(k)-_oi(k-1),x₂(k)＝θ_i(k) I-1, 2,3 correspond to two inputs of the neuron, w_i(k) Corresponding to the ith inputConnection weight, λ_i(k)＝(λ_i1,λ_i2,λ_i3) And i is 1, and 2 is a neuron gain, which has a great influence on the quick tracking and the anti-interference of the system.

Neuron gain lambda for intelligent supercoiled strong robust attitude controller_i(k) Designing an adaptive law, which specifically comprises the following steps:

wherein:

c is more than or equal to 0.025 and less than or equal to 0.05, H is more than or equal to 0.05 and less than or equal to 0.1, | represents an absolute value, S_i(k) I is 1,2,3 denotes the sliding mode face value of the k step, S_i(k-1), i ═ 1,2,3 denotes the sliding mode face value at step k-1, Δ S_i(k)＝S_i(k)-S_i(k-1)，i＝1,2,3，γ_i、κ_i、ν_iAre positive real numbers.

The significance of this is that when a neuron gains λ_1i(k)≤ν_iWhen it is monotonously increased, the neuron gain λ is increased_1i(k)>v_iThe method comprises the following steps: judgment S_i(k) If i is 1,2 and 3 are always the same number, and if the i is the same number, the sliding mode surface is not zero all the time, T is automatically adjusted_v(k) To gain neurons by lambda_i(k)＝(λ_i1,λ_i2,λ_i3) Acceleration with increased i-1, 2 and increased neuron gain is inversely proportional to T_v(k) (ii) a If S_i(k) When i is 1,2,3 opposite sign, i.e. swings around the slip form face, λ_i(k)＝(λ_i1,λ_i2,λ_i3) The i-1, 2 value drops to 75% of the previous time, the neuron gain decreases; the scheme comprises the advantages of a super-spiral sliding mode control algorithm and a BP neural network.

Example (b):

in order to verify the rationality of the attitude adjustment scheme of the flexible aircraft and the effectiveness of the designed controller on the problems of uncertainty, disturbance and the like, numerical simulation is carried out on the flexible aircraft under the Matlab environment, and a nominal rotational inertia matrix is as follows:

the uncertainty in the inertia matrix is:

ΔJ＝diag[50 120 35]kg·m²；

considering external disturbance d ∈ R³Is a function of time t, which can be expressed as d (t), and is specifically taken as:

d(t)＝[10*sin(0.1t),15*sin(0.2t),20*sin(0.2t)]^T；

the initial value of quaternion is selected to be q ═ 0.3, -0.2, -0.3,0.8832]^TInitial angular velocity is [0,0 ═ q]^TAssuming the initial value of the quaternion of the expected attitude is q_d＝[0,0,0,1]^TDesired angular velocity is Ω_d＝[0,0,0]^T。

Flexible accessory parameters:

ω_n＝(1.0973 1.2761 1.6538 2.2893)；

η＝(0.01242 0.01584 -0.01749 0.01125)；

ζ_n＝(0.05 0.06 0.08 0.025)；

TABLE 1 comparison of Intelligent supercoiled robust attitude control and PID control

Controller	Time of convergence	Accuracy of convergence
			The invention relates to an attitude controller	8s	2e-5
PID controller	70s	1e-2
			Increase the proportion%	88.5	99

The intelligent supercoiling strong robust attitude controller performance is shown in fig. 2-6. As can be seen from fig. 2 and 3, the control scheme completes high-performance large-angle satellite attitude stabilization maneuver within about 10s of limited time, the flexible vibration mode is effectively suppressed, and the accurate satellite stabilization control capability of the control scheme is verified; compared with PID control, the performance is greatly improved; FIG. 4 is a response of the fast terminal sliding mode surface, illustrating that the buffeting problem of control can be effectively suppressed; neuron gain As shown in FIG. 5, neuron gain λ₁(k)＝(λ₁,λ₂,λ₃) Is a positive bounded function value with small fluctuations; fig. 6 is a flexural mode frequency attenuation curve showing that flexural mode vibration is effectively suppressed.

Those skilled in the art will appreciate that the invention may be practiced without these specific details.

Claims (6)

1. An intelligent supercoil strong robust attitude control method is characterized by comprising the following steps:

(1) establishing a flexible aircraft system model;

(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);

(3) 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);

(4) and (4) determining a control law by using a BP self-adaptive neural network and combining a supercoiling algorithm according to the finite-time nonsingular terminal sliding mode surface established in the step (3), and realizing intelligent supercoiling strong robust attitude control.

2. The intelligent supercoiled robust attitude control method according to claim 1, characterized in that: the flexible aircraft system model specifically is as follows:

$\begin{array}{c}(J_0+\mathrm{\&Delta;}J)\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=-{\mathrm{\&Omega;}}^{\&times;}(J_0+\mathrm{\&Delta;}J)\mathrm{\&Omega;}+u+\tilde{d}\\ \stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}+L\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+K\mathrm{\&eta;}+\mathrm{\&delta;}\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=0\end{array};$

wherein:d∈R³is an external disturbance, ∈ R^3×3Is a coupling matrix of rigid bodies and flexible attachments,^Tis that of (a), η is in a flexible 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 the operator sign, × is used for the vector b ═ b₁,b₂,b₃]^TThe following results were obtained:

$b^{\&times;}=\left[\begin{array}{ccc}0& -b_3& b_2\\ b_3& 0& -b_1\\ -b_2& b_1& 0\end{array}\right];$

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; and u is an intelligent supercoiled strong robust attitude controller.

3. The intelligent supercoiled robust attitude control method according to claim 2, characterized in that: the flexible aircraft kinematic error equation and the dynamic error equation are specifically as follows:

flexible aircraft kinematic error equation:

$\begin{array}{cc}{e}_v=q_{d4}{q}_v-q_{dv}^{\&times;}{q}_v-q_4{q}_{dv}& e_4=q_{dv}^T{q}_v+q_4{q}_{d4}\end{array};$

$\begin{array}{cc}{\stackrel{\&CenterDot;}{e}}_v=\frac{1}{2}(q_4{I}_3+q_v^{\&times;}){\mathrm{\&Omega;}}_e& {\stackrel{\&CenterDot;}{e}}_4=-\frac{1}{2}{q}_v^T{\mathrm{\&Omega;}}_e\end{array};$

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_e1Ω_e2Ω_e3]^T＝[Ω_ei]^TI 1,2,3 is an angular velocity error vector established between the body coordinate system and the target coordinate system, Ω_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:

$\begin{array}{c}(J_0+\mathrm{\&Delta;}J){\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_e=-{({\mathrm{\&Omega;}}_e+{\mathrm{C\&Omega;}}_d)}^{\&times;}(J_0+\mathrm{\&Delta;}J)({\mathrm{\&Omega;}}_e+{\mathrm{C\&Omega;}}_d)\\ +(J_0+\mathrm{\&Delta;}J)({\mathrm{\&Omega;}}_e^{\&times;}{\mathrm{C\&Omega;}}_d-C{\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}}_d)+u+\tilde{d}\end{array};$

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

4. The intelligent supercoiled robust attitude control method according to claim 3, characterized in that: the finite-time nonsingular terminal sliding mode surface S specifically comprises the following steps:

S＝Ω_e+K₁e_v+K₂S_c；

wherein S ═ S₁,S₂,S₃]^T∈R³，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); and define S_c＝[S_c1,S_c2,S_c3]^TThe following were used:

whereinr₁,r₂Is a positive odd number, and 0<r<1，l_1i、l_2i、_i,i＝1,2,3、ι₁、ι₂Is a design parameter, sign (a) is a sign function, defined as follows:

$sign\left(a\right)=\left\{\begin{array}{cc}1& a>0\\ 0& a=0\\ -1& a<0\end{array}\right..$

5. the intelligent supercoiled robust attitude control method according to claim 4, characterized in that: the intelligent supercoiled strong robust attitude controller specifically comprises:

u＝J₀[u₁,u₂,u₃]^T；

$u_i=-{\mathrm{\&lambda;}}_1{\mathrm{\&Gamma;}}_{oi}-{\&Integral;}_0^t{\mathrm{\&lambda;}}_2{\mathrm{\&theta;}}_{i}dt;$

wherein:

${\mathrm{\&Gamma;}}_{oi}={\left|S_i\right|}^{\frac{1}{2}}sign\left(S_i\right)+S_i,i=1,2,3;$

${\mathrm{\&theta;}}_i={\mathrm{\&sigma;}}_i{\mathrm{\&Gamma;}}_{oi}=\frac{1}{2}sign\left(S_i\right)+\frac{3}{2}{\left|S_i\right|}^{\frac{1}{2}}sign\left(S_i\right)+S_i,i=1,2,3;$

${\mathrm{\&sigma;}}_i=\frac{1}{2}{\left|S_i\right|}^{-\frac{1}{2}}+1,i=1,2,3;$

the discrete form of u is:

$u\left(k\right)=-{\mathrm{\&lambda;}}_i\left(k\right){\mathrm{\&Gamma;}}_{oi}\left(k\right)-\underset{j=0}{\overset{k}{\&Sigma;}}{\mathrm{\&lambda;}}_2\left(j\right){\mathrm{\&theta;}}_i\left(j\right),i=1,2,3;$

wherein λ₁(k)、λ₂(j) J is 0,1, k is the corresponding gainCoefficient u (k) is the input value at the k-th sampling time; the increment of u (k) is:

Δu(k)＝u(k)-u(k-1)＝-λ₁(k)(_oi(k)-_oi(k-1))-λ₂(k)θ_i(k),i＝1,2,3；

the neuron outputs are:

$u\left(k\right)=u(k-1)+{\mathrm{\&lambda;}}_i\left(k\right)\underset{i=1}{\overset{2}{\&Sigma;}}{w}_i\left(k\right)x_i\left(k\right),i=1,2,3;$

wherein x is₁(k)＝_oi(k)-_oi(k-1),x₂(k)＝θ_i(k) I-1, 2,3 correspond to two inputs of the neuron, w_i(k) Corresponding to the connection weight, lambda, of the ith input_i(k)＝[λ_i1,λ_i2,λ_i3]And i is 1 and 2 is the neuron gain.

6. The intelligent supercoiled robust attitude control method according to claim 5, characterized in that: the neuron gain λ_i(k) The adaptive law of (1) is as follows:

wherein:

$T_v\left(k\right)=T_v(k-1)+H\&CenterDot;sign\left(\right|{\mathrm{\&Delta;S}}_i\left(k\right)|-T_v(k-1\left)\right|{\mathrm{\&Delta;S}}_i^2\left(k\right)\left|\right),i=1,2,3;$

c is more than or equal to 0.025 and less than or equal to 0.05, H is more than or equal to 0.05 and less than or equal to 0.1, | represents an absolute value, S_i(k) I is 1,2,3 denotes the sliding mode face value of the k step, S_i(k-1), i ═ 1,2,3 denotes the sliding mode face value at step k-1, Δ S_i(k)＝S_i(k)-S_i(k-1)，i＝1,2,3，γ_i、κ_i、ν_iAre positive real numbers.