CN111290421A - Hypersonic aircraft attitude control method considering input saturation - Google Patents

Hypersonic aircraft attitude control method considering input saturation Download PDF

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CN111290421A
CN111290421A CN202010201787.3A CN202010201787A CN111290421A CN 111290421 A CN111290421 A CN 111290421A CN 202010201787 A CN202010201787 A CN 202010201787A CN 111290421 A CN111290421 A CN 111290421A
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attitude
angular rate
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aircraft
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罗世彬
吴瑕
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Hunan Airtops Intelligent Technology Co ltd
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Hunan Airtops Intelligent Technology Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

Abstract

The invention provides a hypersonic aircraft attitude control method considering input saturation, which comprises the following steps of: step 1: considering uncertainty of parameters, unmodeled dynamic state and external disturbance in a mathematical model of the unpowered reentry process of the hypersonic aircraft together as total disturbance, and establishing models of an attitude loop and an angular rate loop; step 2: designing a performance function to constrain the steady-state and transient performances of state variable tracking errors of an attitude loop and an angular rate loop of the aircraft; and step 3: converting the inequality constraint obtained in the step 2 into an equality constraint so as to facilitate the design of the controller; and 4, step 4: designing a linear extended state observer to obtain an output estimation value and a total disturbance estimation value of each loop; and 5: the controller is designed so that the tracking error of the system can converge to a predetermined region in the face of input saturation constraints. The design and parameter optimization of the linear active disturbance rejection controller of the hypersonic aircraft are realized, and the dynamic performance, the robust performance and the anti-interference performance of the hypersonic aircraft are improved.

Description

Hypersonic aircraft attitude control method considering input saturation
Technical Field
The invention relates to the technical field of control of hypersonic aircrafts, in particular to a hypersonic aircraft attitude control method considering input saturation.
Background
The hypersonic aircraft is an aircraft with or without wings, such as airplanes, missiles, shells and the like with flight speed of more than five times of sound speed, has important military status and wide civil prospect, and is a research hotspot in the technical field of aircraft control. The hypersonic aircraft has large flying airspace, high speed, long flying distance and high precision requirement, so the structural characteristics, the flying characteristics, the dynamic characteristics and the like of the hypersonic aircraft are more complex than those of a common aircraft.
The strong nonlinearity, strong coupling, fast time variation and uncertain characteristics of the hypersonic aircraft provide greater challenges for the design of a hypersonic aircraft control system. The traditional PID control is widely applied to control of the hypersonic flight vehicle due to simple structure, but the PID controller is poor in robustness and difficult to adapt to the fast time-varying characteristic and high-precision requirement of the hypersonic flight vehicle. Nowadays, some more complex modern control algorithms are also used in the controller design of the hypersonic aircraft to obtain the ideal performance, such as sliding mode variable structure controller, robust adaptive controller, predictive controller, etc. The control algorithm uses certain model information, and the algorithm design process is complex, so that the control algorithm is difficult to be widely applied to flight experiments of hypersonic aircrafts. In addition, most of the existing research methods do not consider the input saturation problem of the hypersonic flight vehicle, and if the problem is not considered explicitly in the design process of the controller, the performance of the controller is reduced, and even the stability of a closed-loop system is damaged. Meanwhile, due to the nonlinear characteristic of input saturation, the influence of the input saturation is difficult to overcome through a traditional linear control algorithm, so that the design of a high-performance feedback controller for a high-speed-of-sound aircraft with input saturation is a very challenging task.
In the design process of a controller of a practical system, the state quantity is expected to converge to the expected track at a faster speed (such as an exponential speed); the state quantity can not generate too high overshoot in the convergence process; furthermore, during steady state, the state quantities should remain bounded at all times under the influence of disturbances. Therefore, if the boundary of the convergence trajectory of the state quantity can be reasonably designed, and the controller is designed to ensure that the state quantity strictly converges within the boundary, the performance of the system state in the transient state and the steady state can be ensured, and the preset performance control algorithm is generated at the discretion. The preset performance means that the tracking error is guaranteed to be converged in a preset optional small area, meanwhile, the convergence speed and the overshoot are guaranteed to meet preset conditions, transient and steady-state performance is required to be met simultaneously, and the aim of improving the performance of the system is directly taken. The preset performance control method comprises the steps of firstly constructing an equivalent model by using a performance function and error transformation, and then designing a controller aiming at the equivalent model so as to ensure that the system meets the preset requirements on accuracy, rapidity and stability.
The complicated flight environment of the hypersonic aircraft makes the hypersonic aircraft highly nonlinear and uncertain, and how to realize tracking control on attitude and angular rate under the condition that an aircraft model cannot be accurately known is another serious challenge to the design of the hypersonic aircraft controller. In recent years, due to the self-learning and self-adaptive capabilities of neural networks, the application and research of neural networks in nonlinear systems are increasingly wider. The structural form of the neural network multiple input and multiple output also makes the recognition of the unknown nonlinear part of the controlled object easy to realize. Fuzzy systems are another effective way to implement online identification of models. The general approximation property of neural network/fuzzy systems is only valid over a given bounded region.
In summary, it is urgently needed to design an attitude tracking control method for a hypersonic aircraft, so that the attitude and the angular rate of the aircraft can meet the preset requirements of rapidity, accuracy and stability under the conditions of input saturation, nonlinearity and uncertainty.
Disclosure of Invention
The invention aims to provide a hypersonic aircraft attitude control method considering input saturation, so that the hypersonic aircraft can track the attitude and the angular rate under the conditions of model uncertainty, external disturbance and input saturation, and the tracking performance meets the preset requirements on rapidity, accuracy and stability.
The invention adopts the following specific technical scheme:
the invention provides a hypersonic aircraft attitude control method considering input saturation, which comprises the following steps:
step 1: the parameter uncertainty, unmodeled dynamic state and external disturbance of a mathematical model of the unpowered reentry process of the hypersonic aircraft are taken together as total disturbance, mathematical models of an attitude loop and an angular rate loop of the hypersonic aircraft are established, and the mathematical models of the loops are written into a form suitable for the design of a linear active disturbance rejection controller;
step 2: according to the mathematical models of the attitude loop and the angular rate loop in the step 1, introducing a performance function to constrain the steady-state and transient performances of the state variable tracking errors of the attitude loop and the angular rate loop of the aircraft, so as to obtain inequality constraints;
and step 3: and (3) designing a controller according to the inequality constraint obtained in the step (2). In the design process of the controller, the inequality constraint (b.1) is directly processed with great difficulty, so that the inequality constraint is firstly considered to be converted into an equality constraint, and the converted equivalent system is processed;
and 4, step 4: designing a Linear Extended State Observer (Linear Extended State Observer-LESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting proper gains of the Linear Extended State Observer, and acquiring output estimation values and total disturbance estimation values of all loops;
and 5: according to the output estimation value and the total disturbance estimation value obtained in the step 4, aiming at the mathematical models of the attitude loop and the angular rate loop in the step 1, a control algorithm is designed, so that under the condition of facing input saturation constraint (a.2), the tracking error e of the system1、e2Can converge into a predetermined region (b.1).
Preferably, the expressions of the mathematical models of the attitude loop and the angular rate loop in the form suitable for the design of the linear active disturbance rejection controller in the step 1 are as shown in formulas (1) and (2):
Figure BDA0002419634230000031
Figure BDA0002419634230000032
wherein: x is the number of1＝[α β μ]T，x2＝[p q r]TThe state of the system, wherein α, β and mu are respectively the attack angle, the sideslip angle and the roll angle of the aircraft, p, q and r are respectively the roll rate, the yaw rate and the pitch rate, h1(t)、h2(t) total disturbances of the attitude loop and the angular rate loop, respectively, including model parameter uncertainty, unmodeled dynamics and external disturbances; delta is [ delta ]eδaδr]TIs a control input to the system, where δe、δa、δrRespectively representing the control surface deflection angles of an elevator, a rudder and an aileron, and the expression is as follows:
Figure BDA0002419634230000033
wherein: deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δminE (0, ∞) is the upper and lower bounds, g, respectively, for the known rudder surface deflection angle10、g20Are parameters to be designed.
Preferably, the attitude loop in step 1 corresponds to three state variables of an attack angle, a sideslip angle and a roll angle of the aircraft, and the angular rate loop in step 1 corresponds to three state variables of a roll rate, a yaw rate and a pitch rate of the aircraft.
Preferably, in said step 2, definition e1＝[e11,e12,e13]T＝x1-x1d，e2＝[e21,e22,e23]T＝x2-x2dTracking errors of the attitude loop and angular rate loop, respectively, where x1dIs a state variable x1Reference input of, x2dIs a state variable x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
Figure BDA0002419634230000034
wherein: kappaij∈(0,1]For the parameter to be designed, t ∈ [0, ∞), ρij(t) is a smooth, bounded, positive and strictly decreasing performance function, in general, the performance function ρij(t) may be designed in the form of:
Figure BDA0002419634230000041
wherein: k is a radical ofij,c＞0，
Figure BDA0002419634230000048
ρij,0Greater than 0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
Preferably, in step 3, the following error conversion function epsilon is definedij(t)：
εij(t)＝Φ(zij(t)) (6)
Wherein: phi (-) is a smooth function that increases strictly monotonically, such that
Figure BDA0002419634230000042
Herein, the form of the conversion function is designed to:
Figure BDA0002419634230000043
according to formula (6):
Figure BDA0002419634230000044
wherein:
Figure BDA0002419634230000045
Figure BDA0002419634230000046
let gamma bei＝diag(γi1,γi2,γi3),ηi＝diag(ηi1,ηi2,ηi3) Then, then
Figure BDA0002419634230000047
Preferably, in the step 4, a linear extended state observer shown in formulas (12) and (13) is designed, and an output estimation value and a total disturbance estimation value of each loop are obtained;
Figure BDA0002419634230000051
Figure BDA0002419634230000052
wherein β11、β12、β21、β22Is the gain of a linear extended state observer, z11＝[z11,1,z11,2,z11,3]TIs an estimate of the attitude loop output, z12＝[z12,1,z12,2,z12,3]TIs an estimate of the total disturbance of the attitude loop, eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs an estimate of the output of the angular rate loop, z22＝[z22,1,z22,2,z22,3]TIs an estimate of the total disturbance of the angular rate loop, eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
Preferably, in step 5, the controller design process is as follows:
the following virtual control law can be designed for the attitude loop
Figure BDA0002419634230000053
Wherein: c. C1＝diag(c11,c12,c13) Is the gain of the virtual control law.
In order to realize the compensation of the total disturbance of the attitude loop, the final control law of the system is designed into the following form:
Figure BDA0002419634230000054
regardless of input saturation (3), the diagonal rate loop can be designed as the following virtual control law
Figure BDA0002419634230000055
Wherein: c. C2＝diag(c21,c22,c23) Is the gain of the virtual control law.
Pair realization by dynamic surface control algorithm
Figure BDA0002419634230000056
The following first-order low-pass filter is selected as a filter form:
Figure BDA0002419634230000057
wherein: v. of2Is x2dThe differential signal of (2). Equation (16) can be rewritten as follows:
α2＝v2-γ2e2-c2ε2η2(18)
to achieve compensation for the total disturbance of the angular rate loop, the control input to be designed for the system can be written as follows:
Figure BDA0002419634230000061
due to the limitation of input saturation (3), this leads to designInput quantity delta ofcThere is a deviation from the actual control quantity δ, and therefore, the following auxiliary system is introduced to compensate for the deviation:
Figure BDA0002419634230000062
wherein:
Figure BDA0002419634230000063
for the anti-saturation compensation parameter, tanh (. cndot.) epsilon (-1,1) is a hyperbolic tangent function,
Figure BDA0002419634230000066
are parameters to be designed.
Then the control input delta is designed as shown in equation (21) taking into account the input saturationc：
Figure BDA0002419634230000064
At this time, virtual control law α2Can be written as
Figure BDA0002419634230000065
The invention also provides a hypersonic aircraft attitude control system considering input saturation, and the hypersonic aircraft attitude control method considering input saturation is adopted.
The technical scheme of the invention has the following beneficial effects:
(1) the invention provides a hypersonic aircraft attitude control method considering input saturation, which can realize the rapid tracking of attitude and angular rate under the conditions of model uncertainty, external disturbance and input saturation of a hypersonic aircraft, and the tracking performance meets the preset requirements of rapidity, accuracy and stability.
(2) The embodiment of the invention aims at the unpowered reentry process of a hypersonic aircraft with saturated input, adopts a linear extended state observer to realize the estimation of an unknown part of a system, introduces a preset performance control algorithm to constrain the tracking errors of an attitude loop and an angular rate loop of the system, ensures that the tracking errors of the attitude loop and the angular rate loop are converged into a preset region, performs error conversion through a nonlinear mapping function, converts a constrained system into an error system in an unconstrained form, then designs a disturbance compensation controller aiming at a new unconstrained system based on a frame of a backstepping method, reduces the influence of the saturation characteristic of an aircraft executing mechanism on a closed-loop control system by introducing an auxiliary system, and realizes the tracking control of the attitude loop and the angular rate loop. The invention ensures the dynamic performance, stability and robustness of the control system by introducing the preset performance control algorithm.
(3) The embodiment of the invention introduces the auxiliary system to compensate the influence of input saturation, thereby effectively improving the input saturation suppression capability of the system; the uncertainty of the system is estimated by adopting the linear extended state observer, the design idea is simple compared with that a neural network and a fuzzy system are used for identifying nonlinearity and an interference observer is used for observing interference, and the defect that the neural network and the fuzzy system are only effective on some tight sets is not considered; the introduction of the preset performance control method can ensure that the steady-state tracking error converges to a preset region, and simultaneously, the convergence speed and the overshoot meet the preset conditions, thereby ensuring the convergence of the attitude and angular rate steady-state errors and simultaneously realizing the transient performance requirements of the convergence speed, the overshoot and the like.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic block diagram of a hypersonic aircraft attitude control method considering input saturation according to embodiment 1 of the present invention;
fig. 2 is a flowchart of a method for controlling an attitude of a hypersonic aircraft considering input saturation according to embodiment 1 of the present invention.
Detailed Description
The following is a detailed description of embodiments of the invention, but the invention can be implemented in many different ways, as defined and covered by the claims.
Example 1:
a hypersonic aircraft attitude control method considering input saturation comprises the following steps:
step 1: the method comprises the steps of considering parameter uncertainty, unmodeled dynamic state and external disturbance in a hypersonic aircraft unpowered reentry process mathematical model together as total disturbance, establishing mathematical models of an attitude loop and an angular rate loop of the hypersonic aircraft, and writing the mathematical models of the loops into a form suitable for the design of a linear active disturbance rejection controller; specifically, mathematical models of the attitude loop and the angular rate loop are written into a form suitable for the design of the linear active disturbance rejection controller.
The mathematical model of the unpowered reentry process of the hypersonic aircraft can be written as shown in the following formula (a):
Figure BDA0002419634230000081
wherein α, β, mu and gamma are respectively the attack angle, the sideslip angle, the roll angle and the track angle of the aircraft, p, q and r are respectively the roll angular velocity, the yaw angular velocity and the pitch angular velocity, M is the mass of the aircraft wing, g is the gravity acceleration, S is the reference area of the aircraft wing, I is the reference area of the aircraft wingx、Iy、IzIs the primary moment of inertia of the aircraft; l, D, Y are respectively the drag, lateral and lift forces of the aircraft, l, m, n are respectively the roll, yaw and pitch moments,
Figure BDA0002419634230000082
v is the velocity of the hypersonic aircraft, b is the span length, c is the mean aerodynamic chord length,
Figure BDA0002419634230000083
is a dynamic pressure; cL、CD、CY、Cl、Cm、CnIs the aerodynamic coefficient, the calculation formula is shown as the formula (a.1), deltae、δa、δrThe rudder surface deflection angles of the elevator, the rudder and the ailerons are respectively shown as a formula (a.2);
Figure BDA0002419634230000084
Figure BDA0002419634230000085
wherein: delta is the control input to the system, deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δminE (0, ∞) is the upper and lower bounds, respectively, for which the rudder surface deflection angle is known.
Formula (a) is abbreviated to the forms of formulae (a.3) and (a.4):
Figure BDA0002419634230000091
Figure BDA0002419634230000092
wherein x is1＝[α β μ]T，x2＝[p q r]T，δ＝[δeδaδr]T；f1(x1)、f2(x1,x2)、g11(x1)、g12(x1) And g2(x1) Is represented by formula (a.5):
Figure BDA00024196342300000914
Figure BDA0002419634230000101
wherein: cD,α、
Figure BDA0002419634230000102
CL,α、
Figure BDA0002419634230000103
CY,β、
Figure BDA0002419634230000104
Cl,β、Cl,δe、Cl,δa、Cl,δr、Cl,p、Cl,q、Cm,β、
Figure BDA0002419634230000105
Cm,p、Cm,q、Cn,α、
Figure BDA0002419634230000106
Figure BDA0002419634230000107
Cn,rIs the aerodynamic derivative.
The attitude loop and the angular rate loop can form a cascade system, the attitude loop is used as an outer ring of the cascade system and used for controlling the attitude angle of the hypersonic aircraft and eliminating the deviation of an aircraft control system, the angular rate loop is used as an inner ring of the cascade system and used for quickly compensating or inhibiting the influence of external disturbance, and meanwhile, the output of the inner ring is ensured to quickly and accurately track the output signal x of an outer ring controller2dFor convenience of controller design, equations (a.3) and (a.4) are abbreviated as the forms shown in equations (a.6) and (a.7):
Figure BDA0002419634230000108
Figure BDA0002419634230000109
wherein: h is1(t)＝f1(x1)+g12(x1)δ+(g11(x1)-g10)x2Is the total disturbance of the attitude loop, including uncertainty of model parameters in the attitude loop, unmodeled dynamics and external disturbance; h is2(t)＝f2(x1,x2)+(g2(x1)-g20) δ is the total disturbance of the angular rate loop, including uncertainty of model parameters in the angular rate loop, unmodeled dynamics, and external disturbances; because of g11And g2Related to aerodynamic parameters, not exact values, although there are related parameters that can be referenced, and therefore g11、g2Taking the reference pneumatic parameter g10、g20As an estimate thereof.
In the attitude loop in the step 1, the hypersonic aerocraft has three state variables of an attack angle, a sideslip angle and a roll angle, and in the angular rate loop in the step 1, the hypersonic aerocraft has three state variables of a rolling angular velocity, a yaw angular velocity and a pitch angular velocity.
Step 2: and (3) according to the mathematical models of the attitude loop and the angular rate loop in the step (1), introducing a performance function to constrain the steady-state and transient performances of the state variable tracking errors of the attitude loop and the angular rate loop of the aircraft, and obtaining an inequality constraint. The method specifically comprises the following steps:
definition e1＝[e11,e12,e13]T＝x1-x1d，e2＝[e21,e22,e23]T＝x2-x2dIs the tracking error of the attitude loop and angular rate loop, where x1dIs a state variable x1Reference input of, x2dIs a state variable x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
Figure BDA0002419634230000111
wherein: kappaij∈(0,1]For the parameter to be designed, t ∈ [0, ∞), ρij(t) is a smooth, bounded, positive and strictly decreasing performance function, in general, the performance function ρij(t) may be designed in the form of:
Figure BDA0002419634230000112
wherein: k is a radical ofij,c＞0，
Figure BDA0002419634230000113
ρij,0Greater than 0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
When inequality (b.1) is satisfied, eij(0) For example, ≧ 0, the tracking error curve is limited to- κijρij(t) and ρij(t) in the region surrounded by the first and second coupling functions, andijthe decreasing nature of (t) indicates that the tracking error will be at the function-kijρij(t) and ρij(t) rapidly converges to a small domain of 0. Constant rhoij,∞Representing an upper bound, p, of a predetermined steady state errorij(t) the decay rate is the tracking error eij(t) lower bound of convergence rate, while maximum overshoot of tracking error is not greater than kijρij,0. The steady-state and transient performance of the tracking error can be limited by selecting an appropriate performance function.
And step 3: and (3) designing a controller according to the inequality constraint obtained in the step (2). In the design process of the controller, the inequality constraint (b.1) is directly processed with great difficulty, so that the inequality constraint is firstly considered to be converted into an equality constraint, and the converted equivalent system is processed, so that the following error conversion function epsilon is definedij(t)：
εij(t)＝Φ(zij(t)) (c.1)
Wherein: phi (-) is a smooth function that increases strictly monotonically, such that
Figure BDA0002419634230000114
Herein, the form of the design transfer function is:
Figure BDA0002419634230000115
then:
Figure BDA0002419634230000121
according to formula (c.1):
Figure BDA0002419634230000122
wherein:
Figure BDA0002419634230000123
Figure BDA0002419634230000124
let gamma bei＝diag(γi1,γi2,γi3),ηi＝diag(ηi1,ηi2,ηi3) Then, then
Figure BDA0002419634230000125
And 4, step 4: designing a Linear Extended State Observer (Linear Extended State Observer-LESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting a proper gain of the Linear Extended State Observer, and acquiring an output estimation value and a total disturbance estimation value of the attitude loop and an output estimation value and a total disturbance estimation value of the angular rate loop;
Figure BDA0002419634230000126
Figure BDA0002419634230000127
wherein β11、β12、β21、β22For the gain of the linear extended state observer, the bandwidth ω of the linear extended state observer can be usedoi＝[ωo1,i,ωo2,i,ωo3,i]TIs shown as z11＝[z11,1,z11,2,z11,3]TIs an estimate of the attitude loop output, z12＝[z12,1,z12,2,z12,3]TIs an estimate of the total disturbance of the attitude loop, eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs an estimate of the output of the angular rate loop, z22＝[z22,1,z22,2,z22,3]TIs an estimate of the total disturbance of the angular rate loop, eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
To simplify the parameter adjustment process, the gain of the linear extended state observer is designed as the following expression (d.3):
s2+β1s+β2＝(s+ωo)2......(d.4)
wherein: omegaoIs the bandwidth of a linear expansion state function, β1＝[β11,β21]，β2＝[β12,β22]，ωo＝[ωo1,ωo2]T. Thus, the gain of the linear extended state observer can be determined by the bandwidth ωoDetermination of ωoIs the only parameter to be adjusted in the linear extended state observer.
And 5: according to the output estimated values of the attitude loop and the angular rate loop obtained in the step 4And a total disturbance estimated value, aiming at the mathematical models of the attitude loop and the angular rate loop in the step 1, designing a control algorithm to ensure that the tracking error e of the system is under the condition of facing the input saturation constraint (a.2)1、e2Can converge into a predetermined region (b.1).
Designing a controller for an attitude loop, and defining an error surface:
Figure BDA0002419634230000131
according to equation (c.7), consider the lyapunov function as follows:
Figure BDA0002419634230000132
then:
Figure BDA0002419634230000133
according to the formula (e.3), to ensure
Figure BDA0002419634230000134
The following virtual control law can be designed
Figure BDA0002419634230000135
Wherein: c. C1＝diag(c11,c12,c13) Is the gain of the virtual control law.
In order to realize the compensation of the total disturbance of the attitude loop, the final control law of the system is designed into the following form:
Figure BDA0002419634230000136
controller design is carried out on the angular rate loop, and an error surface is defined:
Figure BDA0002419634230000137
the controller design is performed without considering the input saturation constraint (a.2):
according to equation (c.7), consider the lyapunov function as follows:
Figure BDA0002419634230000141
then:
Figure BDA0002419634230000142
according to formula (e.8), to ensure
Figure BDA0002419634230000143
The following virtual control law can be designed
Figure BDA0002419634230000144
Wherein: c. C2＝diag(c21,c22,c23) Is the gain of the virtual control law.
Pair realization by dynamic surface control algorithm
Figure BDA0002419634230000145
The following first-order low-pass filter is selected as a filter form:
Figure BDA0002419634230000146
wherein: v. of2Is x2dThe differential signal of (2). Equation (e.9) may be rewritten as follows:
α2＝v2-γ2e2-c2ε2η2(e.11)
to achieve compensation for the total disturbance of the angular rate loop, the control input to be designed for the system can be written as follows:
Figure BDA0002419634230000147
due to the limitation of input saturation (a.2), the designed input quantity delta is causedcThere is a deviation from the actual control quantity δ, and therefore, the following auxiliary system is introduced to compensate for the deviation:
Figure BDA0002419634230000148
wherein:
Figure BDA0002419634230000149
for the anti-saturation compensation parameter, tanh (. cndot.) epsilon (-1,1) is a hyperbolic tangent function,
Figure BDA00024196342300001413
are parameters to be designed.
Defining a tracking error of a correction state
Figure BDA00024196342300001410
The derivation can be:
Figure BDA00024196342300001411
the control input delta is designed according to equation (e.14)cComprises the following steps:
Figure BDA00024196342300001412
at this time, virtual control law α2Can be written as
Figure BDA0002419634230000151
The embodiment of the invention aims at the unpowered reentry process of a hypersonic aircraft with input saturation, a preset performance control function is adopted to constrain the tracking errors of a system attitude loop and an angular rate loop, so that the tracking errors of the system can be converged into a preset region, an error conversion function is adopted to convert a system with constraint into an unconstrained form for facilitating the design of a controller, then a linear expansion state observer is designed to realize the estimation of an unknown part of the system, a disturbance compensation controller is designed based on a frame of a backstepping method, and an auxiliary system is utilized to reduce the influence of the saturation characteristic of an aircraft executing mechanism on a closed-loop control system, so that the tracking control of the attitude loop and the angular rate loop is realized. The introduction of the preset performance control algorithm improves the dynamic performance and robustness of the whole control system, the uncertainty of the system is estimated by adopting the linear extended state observer, and compared with the design idea of identifying nonlinearity by using a neural network and a fuzzy system and observing interference by using an interference observer, the design idea is simple, and the defect that the neural network and the fuzzy system are only effective on some tight sets is not considered.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (8)

1. A hypersonic aircraft attitude control method considering input saturation is characterized by comprising the following steps:
step 1: the parameter uncertainty, unmodeled dynamic state and external disturbance of a mathematical model of the unpowered reentry process of the hypersonic aircraft are taken together as total disturbance, mathematical models of an attitude loop and an angular rate loop of the hypersonic aircraft are established, and the mathematical models of the loops are written into a form suitable for the design of a linear active disturbance rejection controller;
step 2: according to the mathematical models of the attitude loop and the angular rate loop in the step 1, introducing a performance function to constrain the steady-state and transient performances of the state variable tracking errors of the attitude loop and the angular rate loop of the aircraft, so as to obtain inequality constraints;
and step 3: performing corresponding conversion according to the inequality constraint obtained in the step 2 so as to facilitate subsequent controller design;
and 4, step 4: designing a Linear Extended State Observer (Linear Extended State Observer-LESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting proper gains of the Linear Extended State Observer, and acquiring output estimation values and total disturbance estimation values of all loops;
and 5: and (3) designing a control algorithm aiming at the mathematical models of the attitude loop and the angular rate loop in the step (1) according to the output estimation value and the total disturbance estimation value obtained in the step (4), so that the tracking error of the system can be converged into a preset area under the condition of facing input saturation constraint.
2. The attitude control method of hypersonic flight vehicle considering input saturation as claimed in claim 1, wherein the expressions of the mathematical models of attitude loop and angular rate loop suitable for the design form of linear active disturbance rejection controller in step 1 are as follows (1) and (2):
Figure FDA0002419634220000011
Figure FDA0002419634220000012
wherein: x is the number of1＝[α β μ]T，x2＝[p q r]T，δ＝[δeδaδr]Tα, β and mu are respectively the attack angle, the sideslip angle and the roll angle of the aircraft, p, q and r are respectively the roll angular velocity, the yaw angular velocity and the pitch angular velocity, h1(t)、h2(t) is the total disturbance of the attitude loop and angular rate loop, including model parameter uncertainty, unmodeled dynamics and external disturbances, respectively; g10、g20Is a parameter to be designed; deltae、δa、δrRespectively representing the control surface deflection angles of an elevator, a rudder and an aileron, and the expression is as follows:
Figure FDA0002419634220000021
wherein: deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δminE (0, ∞) is the upper and lower bounds, respectively, for which the rudder surface deflection angle is known.
3. The method as claimed in claim 1, wherein the attitude loop of step 1 corresponds to three state variables of the aircraft, namely, the angle of attack, the sideslip angle and the roll angle, and the angular rate loop of step 1 corresponds to three state variables of the aircraft, namely, the roll rate, the yaw rate and the pitch rate.
4. The hypersonic aircraft attitude control method taking input saturation into account as claimed in claim 2, wherein in said step 2, e is defined1＝[e11,e12,e13]T＝x1-x1d，e2＝[e21,e22,e23]T＝x2-x2dTracking errors of the attitude loop and angular rate loop, respectively, where x1dIs a state variable x1Reference input of, x2dIs a state variable x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
Figure FDA0002419634220000022
wherein: kappaij∈(0,1]For the parameter to be designed, t ∈ [0, ∞), ρij(t) is a smooth, bounded, positive and strictly decreasing performance function, the performance function ρij(t) is designed in the form of:
Figure FDA0002419634220000023
wherein: k is a radical ofij,c＞0，
Figure FDA0002419634220000024
ρij,0Greater than 0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
5. The method for controlling the attitude of a hypersonic aircraft considering input saturation according to claim 4, characterized in that in step 3, the following error transfer function ε is definedij(t)：
εij(t)＝Φ(zij(t)) (6)
Wherein: phi (-) is a smooth function that increases strictly monotonically, such that
Figure FDA0002419634220000025
The form of the transfer function is designed as:
Figure FDA0002419634220000031
according to formula (6):
Figure FDA0002419634220000032
wherein: epsiloni＝[εi1,εi2,εi3]T,γi＝diag(γi1,γi2,γi3),ηi＝diag(ηi1,ηi2,ηi3)，
Figure FDA0002419634220000033
Figure FDA0002419634220000034
6. The method for controlling the attitude of a hypersonic aircraft considering input saturation according to claim 5, characterized in that in the step 4, a linear extended state observer is designed as shown in formulas (12) and (13):
Figure FDA0002419634220000035
Figure FDA0002419634220000036
wherein β11、β12、β21、β22Is the gain of a linear extended state observer, z11＝[z11,1,z11,2,z11,3]TIs an estimate of the attitude loop output, z12＝[z12,1,z12,2,z12,3]TIs an estimate of the total disturbance of the attitude loop, eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs an estimate of the output of the angular rate loop, z22＝[z22,1,z22,2,z22,3]TIs an estimate of the total disturbance of the angular rate loop, eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
7. The hypersonic aircraft attitude control method taking input saturation into account as claimed in claim 6, wherein in said step 5, the controller design process is as follows:
the following virtual control law can be designed for the attitude loop
Figure FDA0002419634220000041
Wherein: c. C1＝diag(c11,c12,c13) Is the gain of the virtual control law.
In order to realize the compensation of the total disturbance of the attitude loop, the final control law of the system is designed into the following form:
Figure FDA0002419634220000042
due to the limitation of input saturation (3), the designed input quantity delta is causedcThere is a deviation from the actual control quantity δ, and therefore, the following auxiliary system is introduced to compensate for the deviation:
Figure FDA0002419634220000043
wherein:
Figure FDA0002419634220000044
for the anti-saturation compensation parameter, tanh (. cndot.) epsilon (-1,1) is a hyperbolic tangent function,
Figure FDA0002419634220000045
are parameters to be designed.
Then virtual control law α for input saturation2Is designed into
Figure FDA0002419634220000046
To achieve compensation of the total disturbance of the angular rate loop, the system has to be designed with a control input δcThe design is as follows:
Figure FDA0002419634220000047
wherein: c. C2＝diag(c21,c22,c23) Is the gain of the virtual control law;
pair realization by dynamic surface control algorithm
Figure FDA0002419634220000048
The following first-order low-pass filter is selected as a filter form:
Figure FDA0002419634220000049
wherein: v. of2Is x2dThe differential signal of (a); then equation (17) is rewritten as follows:
Figure FDA00024196342200000410
the formula (19) is substituted for the formula (3) to obtain the actual control law δ of the whole system.
8. An attitude control system of a hypersonic aerocraft considering input saturation, which is characterized in that the attitude control method of the hypersonic aerocraft considering input saturation is adopted, and the attitude control system is as claimed in any one of claims 1 to 7.
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