CN106802660B - A kind of compound strong anti-interference attitude control method - Google Patents
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Abstract
A kind of compound strong anti-interference attitude control method, this method are based on non-singular terminal sliding formwork, Backstepping and observer, be able to achieve flexible aerocraft system quickly, high-precision attitude tracing control, while there is strong interference rejection ability.High performance aircraft Attitude tracking control is realized in conjunction with the strong robustness and rapidity of Reverse Step Control technology and non-singular terminal sliding formwork to quick, the accurate estimated capacity of disturbance using Active Disturbance Rejection Control.
Description
Technical Field
The invention relates to a composite strong disturbance rejection attitude control method, and belongs to the field of aircraft attitude control.
Background
Modern aircraft are complex in structure, and increasingly diversified task requirements put higher requirements on aircraft control performance (stability, noise immunity, rapidity and the like). Meanwhile, with the continuous exploration of various new technologies and methods, the development of aircraft control faces many opportunities and challenges. The development of the relevant technical research of the aircraft has very important academic value, strategic significance and application prospect. How to develop an advanced aircraft attitude control technology is one of the fundamental problems and key technologies of the aircraft control technology.
Sliding mode variable structure control is a special nonlinear discontinuous control method. The control method is different from other control methods in that the structure of the system is purposefully changed according to the current state of the system in a dynamic process, so that the system operates according to the state track of a preset sliding mode. The sliding mode can be designed and is irrelevant to model parameters and disturbance, so that the variable structure control has the advantages of high reaction speed, insensitivity to parameter change, insensitivity to disturbance, simple physical realization and the like. The backstepping method has the advantages of good stability and high convergence speed, allows the non-linear or high-order characteristics of a controlled object to be retained, can treat the influence of non-linearity and uncertainty, and is concerned by researchers in the field of aviation. The active disturbance rejection control technology utilizes an extended state observer to feed back all nonlinear uncertain objects of unknown external disturbance into an integral series type by using a nonlinear state, then designs an ideal controller by using state error feedback, and fundamentally overcomes the inherent defects of classical PID by using a nonlinear structure. Meanwhile, the external disturbance action is not required to be directly measured, the action rule of disturbance is not required to be known in advance, and the control precision can be effectively improved.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art, takes an attitude control system of the flexible aircraft as a background, provides a flexible aircraft attitude tracking control method based on a nonsingular terminal sliding mode, a backstepping design method and an observer, realizes the rapid attitude tracking control of the flexible aircraft, has high precision and strong disturbance rejection capability, and meets the attitude tracking requirement of the flexible aircraft to the greatest extent.
The technical solution of the invention is as follows:
a composite strong anti-interference 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) 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);
(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.
Compared with the prior art, the invention has the beneficial effects that:
(1) under the conditions that the flexible vibration mode, the rotational inertia are uncertain, the external disturbance and the actuator saturation influence the aircraft, the fast and high-precision attitude tracking control of the aircraft is realized, and meanwhile, the high-precision attitude tracking control system has strong anti-disturbance capability.
(2) The fast and accurate estimation capability of active disturbance rejection control is fully exerted, and the high-performance aircraft attitude tracking control is realized by combining the backstepping control technology and the strong robustness and rapidity of the nonsingular terminal sliding mode.
Drawings
FIG. 1 is a flow chart of a control system based on a sliding mode and an observer according to the invention;
FIG. 2 is a diagram of attitude quaternion tracking error and angular velocity tracking error for a PID controller of the invention;
FIG. 3 is a diagram of the attitude quaternion tracking error and the angular velocity tracking error of the composite robust disturbance rejection attitude controller of the present invention;
FIG. 4 is an input torque of the PID controller of the invention;
FIG. 5 is an input torque of the composite robust disturbance rejection attitude controller of the present invention;
FIG. 6 is a simulation result of the slip form face of the present invention;
FIG. 7 is an estimation of disturbance by the extended state observer of the present invention;
FIG. 8 is a flexural mode frequency attenuation curve of the present invention.
FIG. 9 illustrates an attitude quaternion tracking error and an angular velocity tracking error under a second condition of the present invention;
FIG. 10 is an estimation of the disturbance by the extended state observer in the second case 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 method for controlling a composite strong anti-interference attitude provided by the present invention specifically comprises the following steps:
(1) considering the influence of factors such as flexibility characteristics, uncertain rotational inertia, external disturbance, actuator saturation and the like of the aircraft, establishing the following flexible aircraft system model:
wherein:d∈R3is an external disturbance, δ ∈ R4×3Being a coupling matrix of rigid bodies and flexible appendages, δTIs a transpose of delta, η is a flexural mode,andη first and second derivatives, respectively0∈R3×3Is 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; x is the sign of the operation, x is used for the vector b ═ b1,b2,b3]TThe following results were obtained:
L＝diag{2ζiωni1,2, N andrespectively damping matrix and rigidity matrix, N is modal order, omeganiN is a vibration mode frequency matrix, ζiN 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 actuatori) Where i is 1,2, and 3 represent nonlinear saturation characteristics of the actuator and satisfy sat (u)i)＝sign(ui)·min{umi,|uiI | }, i ═ 1,2,3, |, denotes the absolute value, sat (u)i) Expressed as sat (u)i)＝θoi+uiI is 1,2,3, wherein θoiI is 1,2, 3:
umiwhere i is 1,2,3 is the actuator saturation value, and the portion exceeding the actuator saturation value is θo＝[θo1,θo2,θo3]TAnd satisfy | | θo||≤lδθ，lδθAre positive real numbers.
(2) Establishing a flexible aircraft kinematic error equation and a dynamic error equation based on quaternion by using the model obtained in the step (1):
flexible aircraft kinematic error equation:
wherein (e)v,e4)∈R3×R，ev＝[e1,e2,e3]TIs a quaternion of the error between the current aircraft attitude and the desired attitudeVector portion, e4Is a scalar part, and satisfies Andare respectively ev、e4The first derivative of (a); (q) av,q4)∈R3×R，qv＝[q1,q2,q3]TIs a unit quaternion vector component, q, that describes the attitude of the aircraft4Is a scalar part, and satisfiesqdv＝[qd1,qd2,qd3]TIs a unit quaternion vector section, q, describing the desired posed4Is a scalar part, and satisfiesΩe＝Ω-CΩd＝[Ωe1Ωe2Ωe3]TIs an angular velocity error vector, omega, established between a body coordinate system and a target coordinate systemd∈R3Is the vector of the desired angular velocity and,is a transformation 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 omegaeFirst derivative of, omegadIt is the desired angular velocity of the beam,is omegadThe first derivative of (a).
(3) Determining a virtual control quantity α 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) and based on a backstepping method, wherein the virtual control quantity α specifically comprises the following steps:
α＝-K1ev-K2Sc (6)
wherein, Kj＝diag{kji}>0,i＝1,2,3,j＝1,2，diag(a1,a2,…,an) Represents a diagonal element of a1,a2,…,anA diagonal matrix of (a);
definition of Sc＝{Sc1,Sc2,Sc3}TThe following were used:
whereinp, q are positive odd numbers and 0<q/p<1，l1i、l2iI is a parameter 1,2, 3; e is the same asi,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), wherein S is ═ S1 S2 S3]TWherein:
Si＝Ωe+K1ev+K2Sc,i＝1,2,3 (8)
(5) separating the 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 specifically:
wherein Z is1Is the state error, F ═ F1,F2,F3]T＝-Ω×J0Ω+J0EΩ，EΩ＝(L1+L2Eq)Q(e)Ω，L1、L2Is a positive real number, define Eq：
fal(Z1,β1,γ)＝[fal1(Z1,β1,γ),fal2(Z1,β1,γ),fal3(Z1,β1,γ)]T (11)
X1And X2Is the output of the extended state observer, S is the system state, X1Tracking system state S, X2Expanded state G of tracking systemδ，GδIs 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, Z1iIs a vector Z1P and q are positive odd numbers, gamma, α and β1Is a design parameter, | · | represents an absolute value; by choosing appropriate rho1、ρ2Gamma and β1Extended state observer output X1And X2Will track to S and G respectively in a limited timeδ。
(6) According to the finite-time nonsingular terminal sliding mode surface and the extended state observer in the steps (4) and (5), establishing a controller u based on the sliding mode and the extended state observer, which specifically comprises the following steps:
wherein,
the controller can be viewed as the approach rate (J)0(-τS-σsignr(S))), known quantity of model (-J)0F) Unknown model estimator (-J)0X2) A combination of (1); wherein the approach rate (J)0(-τS-σsignr(S))) to achieve fast convergence of the controller; the model is knownAmount (-J)0F) Directly participate in the design of a controller, and reduce the estimated pressure of an observer; estimator for unknown model (-J)0X2) And the observer is used for accurate estimation and compensation, so that different disturbances can be suppressed, and the system is kept stable.
Example (b):
in order to verify the effectiveness of the aircraft attitude tracking controller based on the observer technology and the sliding mode control technology, the robustness of the controller in the aspect of aircraft attitude tracking control is verified through simulation under different conditions.
Considering a kinematic error equation and a dynamic error equation of the flexible aircraft, the nominal inertia matrix is
The uncertainty in the inertia matrix is:
ΔJ＝diag(50,30,20)kg·m2；
external disturbance d ∈ R3Is a function of time t, which can be expressed as d (t), and is specifically taken as:
the first condition is as follows: d (t) 0.5[ sin (t), sin (2t), sin (3t)]T；
Case two: d (t) ([ 200 × sin (0.1 t)), 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]TAnd initial angular velocity of [0,0 ]]TThe effectiveness of the control algorithm is verified by numerical simulation, and the initial value of the quaternion of the expected attitude is assumed to be qd＝[0,0,0,1]TThe desired angular velocity is a function of time t, which can be expressed as Ωd(t), specifically taking:
Ωd(t)＝0.05[sin(πt/100),sin(2πt/100),sin(3πt/100)]T；
under the condition of inertia matrix uncertainty and external disturbance, fig. 2 shows an attitude quaternion tracking error and an angular velocity tracking error of the PID controller; FIG. 3 is a diagram of the attitude quaternion tracking error and the angular velocity tracking error of the composite robust disturbance rejection attitude controller; FIG. 4 is an input torque for the PID controller; FIG. 5 is an input torque of the composite robust disturbance rejection attitude controller; as can be seen from Table 1, compared with PID control, the controller based on the sliding mode and the extended state observer provided by the invention can better ensure that the track of the aircraft system can track the reference attitude quickly and accurately.
TABLE 1 comparison of composite robust immunity attitude controller with PID control
| Controller | Quaternion | Angular velocity |
| Composite strong anti-interference attitude controller | ±9.54e-6 | ±2.17e-5 |
| PID controller | ±9.02e-3 | ±3.92e-3 |
| Increase the proportion% | 99.8 | 99.4 |
FIG. 6 shows the simulation result of the sliding mode surface, based on the parameter μ ═ 15I3,β1＝0.50,K1＝2I3，K2＝I3The system track with q/p being 0.9 can quickly reach the sliding mode surface, the extended state observer accurately estimates uncertain and external disturbance, and therefore buffeting caused by sliding mode control is effectively restrained, and fig. 7 shows that the extended state observer can be used for total disturbance GδiI-1, 2, 3; by selecting a suitable parameter rho1＝4.5,ρ2The observer outputs each component X, 8.5 and γ 12(i) I 1,2,3 can effectively track each component G of the disturbanceδiAnd i is 1,2 and 3, which verifies that the extended state observer has good observation performance, so that the controller has quick convergence and high-precision tracking capability.
Fig. 8 shows the attitude quaternion tracking error and the angular velocity tracking error under the second disturbance condition, fig. 9 and fig. 10 show the estimation performance of the extended state observer on the total disturbance, and it can be seen that the designed sliding mode controller can also ensure good convergence speed and precision under the large disturbance condition, and has strong disturbance rejection capability. Those skilled in the art will appreciate that the invention may be practiced without these specific details.
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 ∈ R4×3Being a coupling matrix of rigid bodies and flexible appendages, δTIs a transpose of delta, η is a flexural mode,andη first and second derivatives, respectively0∈R3×3Is 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{2ζiωni1,2, N andrespectively damping matrix and rigidity matrix, N is modal order, omeganiN is a vibration mode frequency matrix, ζiN 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 actuatori) Where i is 1,2, and 3 represent nonlinear saturation characteristics of the actuator and satisfy sat (u)i)＝sign(ui)·min{umi,|ui|},i＝1,2,3，sat(ui) Expressed as sat (u)i)＝θoi+uiI is 1,2,3, wherein θoiI is 1,2, 3:
umiwhere i is 1,2,3 is the actuator saturation value, and the portion exceeding the actuator saturation value is θo＝[θo1,θo2,θo3]TAnd satisfies | θo‖≤lδθ，lδθIs 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，ev＝[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 ev、e4The first derivative of (a); (q) av,q4)∈R3×R，qv＝[q1,q2,q3]TIs a unit quaternion vector component, q, that describes the attitude of the aircraft4Is a scalar part, and satisfiesqdv＝[qd1,qd2,qd3]TIs a unit quaternion vector section, q, describing the desired posed4Is a scalar part, and satisfiesΩe＝Ω-CΩd＝[Ωe1 Ωe2 Ωe3]TIs an angular velocity error vector, omega, established between a body coordinate system and a target coordinate systemd∈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 omegaeFirst derivative of, omegadIt is the desired angular velocity of the beam,is omegadThe 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＝-K1ev-K2Sc；
wherein, Kj＝diag{kji}>0,i＝1,2,3,j＝1,2，diag(a1,a2,…,an) Represents a diagonal element of a1,a2,…,anA diagonal matrix of (a);
definition of Sc＝{Sc1,Sc2,Sc3}TThe following were used:
whereinp, q are positive odd numbers and 0<q/p<1，k1i、k2iI is a parameter 1,2, 3; epsiloni,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:
Si＝Ωe+K1ev+K2Sc,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+J0EΩ，EΩ＝(L1+L2Eq)Q(e)Ω，L1、L2Is a positive real number, define Eq：
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 systemδ，GδIs 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, Z1iIs 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,
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