CN111367182A - Hypersonic aircraft anti-interference backstepping control method considering input limitation - Google Patents
Hypersonic aircraft anti-interference backstepping control method considering input limitation Download PDFInfo
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Abstract
The invention provides an anti-interference backstepping control method of a hypersonic aircraft considering input limitation, which comprises the following steps of: step 1: establishing a model of an attitude loop and an angular rate loop; step 2: designing a preset performance function to constrain the steady-state and transient performance of the state variable tracking errors of the attitude loop and the angular rate loop of the aircraft; and step 3: designing a high-gain extended state observer to obtain an output estimation value and a total disturbance estimation value of each loop; and 4, step 4: based on a frame of a backstepping method, a disturbance compensation control method is designed, so that the tracking error of the system can be converged into a preset area under the condition of input saturation constraint. The invention realizes the tracking control of the attitude loop and the angular rate loop of the hypersonic aircraft, improves the dynamic performance and the steady-state performance of the whole control system by adopting a preset performance control method, and improves the anti-interference performance and the robustness of the whole system by adopting the design of the observer.
Description
Technical Field
The invention relates to the technical field of control of hypersonic aircrafts, in particular to an anti-interference backstepping control method of a hypersonic aircraft considering input limitation.
Background
The hypersonic aircraft is an aircraft with or without wings, such as airplanes, missiles, shells and the like with flight speed more than five times of sound speed, integrates the advantages of the traditional aircraft and spacecraft, and is the research focus of the current major strong countries in the world. However, the hypersonic flight vehicle has the characteristics of large flight envelope, nonlinear model height, uncertain parameters and the like, and has complex flight environment, unpredictable interference and uncertain factors exist in the flight process, so that great difficulty is brought to the design of the controller.
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, due to thermal blockage of the scramjet engine and rudder deflection angle control surface rotation angle limitation, the input of the hypersonic aircraft is limited, namely the actuator has physical upper and lower boundary constraints and cannot reach theoretical upper and lower boundaries. Moreover, if the actuator is in a saturated state for a long time, the performance of the actuator can be damaged, so that the problem of input limitation is considered when a hypersonic aircraft control system is designed, and the hypersonic aircraft control system has important value.
In the design process of a controller of an actual system, the output of the system is expected to obtain satisfactory dynamic and steady-state performance at the same time, and a preset performance control algorithm is generated accordingly. The preset performance means that the tracking error is guaranteed to be converged in a preset any small area, meanwhile, the convergence speed and the overshoot are guaranteed to meet preset conditions, and the preset requirements on accuracy, rapidity and stability are met by the system through the performance improvement of the system.
The complicated flight environment of the hypersonic aircraft makes the hypersonic aircraft have the characteristics of high model nonlinearity and uncertain parameters, and how to realize tracking control on the attitude and the angular rate under the condition 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 a tracking control method for a hypersonic aircraft, so that the attitude and angular rate of the aircraft can meet the preset transient and steady performance requirements under the conditions of external disturbance and limited input.
Disclosure of Invention
The invention aims to provide an anti-interference backstepping control method of a hypersonic aircraft considering input limitation, so that the hypersonic aircraft can track the attitude and the angular rate under the conditions of model uncertainty, external disturbance and input limitation, and the tracking performance meets the preset transient and steady performance requirements.
The invention adopts the following specific technical scheme:
one aspect of the invention provides an anti-interference backstepping control method for a hypersonic aircraft considering input limitation, which comprises the following steps:
step 1: the parameter uncertainty, unmodeled dynamic state and external disturbance of the hypersonic aircraft unpowered reentry process mathematical model 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 an anti-interference backstepping control method;
step 2: according to the mathematical models of the attitude loop and the angular rate loop in the step 1, introducing a preset 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: designing a High-gain Extended State Observer (High-gain Extended State Observer-HGESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting proper Observer gain, 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;
and 4, step 4: and (3) designing a disturbance compensation control method aiming at the mathematical models of the attitude loop and the angular rate loop in the step (1) based on a frame of a backstepping method according to the output estimation value and the total disturbance estimation value of the attitude loop and the angular rate loop obtained in the step (3), so that the tracking error of the system can be converged into a preset area under the condition of limited input.
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 anti-interference backstepping control method in the step 1 are as shown in formulas (1) and (2):
wherein: x is the number of1＝[x11,x12,x13]T＝[α,β,μ]T，x2＝[x21,x22,x23]T＝[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:
wherein: deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δmin∈ (0, ∞) are 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 x1d＝[x1d,1,x1d,2,x1d,3]TIs a state variable x1Reference input of, x2d＝[x2d,1,x2d,2,x2d,3]TIs a state variable x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
-ρij(t)<eij(t)<ρij(t)，(i＝1,2；j＝1,2,3) (4)
t ∈ [0, ∞), rhoij(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:
wherein: k is a radical ofij,c>0，
ρij,0>0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
Preferably, in the step 3, a high-gain extended state observer shown in formulas (6) and (7) is designed:
wherein: a is11、a12、a21、a22Design satisfies s2+a11s+a12＝(s+ωo1)2、s2+a21s+a22＝(s+ωo2)2Wherein ω iso1、ωo2For high gain extended state observer bandwidth, z11＝[z11,1,z11,2,z11,3]TIs attitude loop output x1Estimate of, mui∈ (0,1) (i ═ 1,2) is the parameter to be designed, z12＝[z12,1,z12,2,z12,3]TIs the total disturbance h of the attitude loop1Estimated value of eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs the angular rate loop output x2Estimate of z22＝[z22,1,z22,2,z22,3]TIs the total disturbance h of the angular rate loop2Estimated value of eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
Preferably, in step 4, the controller design process is as follows:
firstly, the attitude loop is designed by a controller, and a preset performance function is selectedNumber rho1j(t) is represented by the formula (5) and ρ1jThe initial value of (t) satisfies rho1j(0)>|x1j(0)-x1d,j(0) (j ═ 1,2,3) to achieve performance constraints on attitude loop tracking errors; meanwhile, the following virtual control law can be designed
Wherein: k is a radical of1jIs the gain of the attitude loop virtual control law.
In order to realize the compensation of the total disturbance of the attitude loop, the final control law of the attitude loop is designed into the following form:
x2d＝-z12+α1(9)
α therein1＝[α11,α12,α13]T。
Designing a controller for a diagonal rate loop, and selecting a preset performance function rho2j(t) is represented by the formula (5) and ρ2jThe initial value of (t) satisfies rho2j(0)>|x2j(0)-x2d,j(0) (j ═ 1,2,3) to achieve performance constraints on the angular rate loop tracking error; meanwhile, the following virtual control law can be designed
Wherein: k is a radical of2jIs the gain of the attitude loop virtual control law.
Final control law δ of the system for compensation of total disturbance of the diagonal rate loopcThe design is as follows:
δc＝-z22+α2(11)
α therein2＝[α21,α22,α23]T. The system actual control law δ can be obtained by substituting equation (11) into equation (3).
The invention also provides an anti-interference backstepping control system of the hypersonic aircraft considering input limitation, and the control method is adopted.
The invention has the beneficial effects that:
(1) the invention provides an anti-interference backstepping control method of a hypersonic aircraft considering input limitation, which enables the hypersonic aircraft to realize accurate tracking of attitude and angular rate under the conditions of model uncertainty, external disturbance and input limitation.
(2) Aiming at the unpowered reentry process of a hypersonic aircraft with limited input, the embodiment of the invention firstly considers the internal uncertainty and the external disturbance of the aircraft together as the total disturbance, adopts a high-gain extended state observer to realize the estimation of the total disturbance, introduces a preset performance control algorithm to constrain the tracking errors of a system attitude loop and an angular rate loop, ensures that the tracking errors of the attitude loop and the angular rate loop are converged into a preset area, and then designs a disturbance compensation controller based on a frame of a backstepping method to realize the tracking control of the attitude loop and the angular rate loop; the introduction of the preset performance control method can ensure that the steady-state error, the convergence speed and the overshoot of the system meet the preset conditions, thereby ensuring that the attitude and the angular rate of the aircraft meet the requirements of transient and steady-state performance in the tracking process.
(3) Compared with the traditional extended state observer, the high-gain extended state observer has more accurate estimation and smaller estimation error, but the high-gain observer can cause a peak phenomenon, and researches show that the influence of the peak phenomenon on the system performance can be effectively inhibited by adopting input limitation, and the input limitation is a problem which needs to be considered in the design process of an aircraft tracking controller, so that the control method provided by the invention fully utilizes the input limitation condition of the aircraft; in addition, the uncertainty of the system is estimated by adopting the high-gain extended state observer, the design idea of identifying nonlinearity by using a neural network and a fuzzy system and observing interference by using an interference observer is simple, the defects that the neural network and the fuzzy system are only effective on some tight sets do not need to be considered, and the anti-interference performance and the robustness of the system are stronger.
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 flowchart of an anti-interference backstepping control method for a hypersonic flight vehicle considering input limitation, which is provided by 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:
an anti-interference backstepping control method of a hypersonic aircraft considering input limitation comprises the following steps:
step 1: the method comprises the steps of considering parameter uncertainty, unmodeled dynamic state and external disturbance in a mathematical model of the unpowered reentry process of the hypersonic aircraft 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 control method; specifically, mathematical models of the attitude loop and the angular rate loop are written into a form suitable for designing an anti-interference backstepping control method.
The mathematical model of the unpowered reentry process of the hypersonic aircraft can be written as shown in the following formula (a):
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 and the yawYaw rate and pitch rate; m is the mass of the aircraft wing; g is the acceleration of gravity; s is the reference area of the aircraft wing; i isx、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,
v is the velocity of the hypersonic aircraft, b is the span length, c is the mean aerodynamic chord length,
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);
wherein: delta is the control input to the system, deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δmin∈ (0, ∞) are 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):
wherein x is1＝[x11,x12,x13]T＝[α,β,μ]T，x2＝[x21,x22,x23]T＝[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):
f1(x1)＝[fαfβfμ]T,f2(x1,x2)＝[fpfqfr]T
wherein: cD,α、
CL,α、
CY,β、
Cl,β、
Cl,p、Cl,q、Cm,β、
Cm,p、Cm,q、Cn,α、
Cn,rIs the aerodynamic derivative.
Equations (a.3) and (a.4) are respectively called an attitude loop and an angular rate loop, the attitude loop and the angular rate loop can form a cascade system, and the attitude loop is used as an outer loop of the cascade system and is used for controlling the high-ultrasoundThe attitude angle of the fast aircraft and the deviation of an aircraft control system are eliminated, and the angular rate loop is used as an inner ring of a cascade system and is used for quickly compensating or inhibiting the influence of external disturbance, and simultaneously ensuring that the output of the inner ring quickly tracks the output signal x of an outer ring controller with high precision2dFor convenience of controller design, equations (a.3) and (a.4) are abbreviated as the forms shown in equations (a.6) and (a.7):
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 preset 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 inequality constraints. 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 x1d＝[x1d,1,x1d,2,x1d,3]TIs a state variable x1Reference input of, x2d＝[x2d,1,x2d,2,x2d,3]TIs a state variable x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
-ρij(t)<eij(t)<ρij(t)，(i＝1,2；j＝1,2,3) (b.1)
t ∈ [0, ∞), rhoij(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:
wherein: k is a radical ofij,c>0，
ρij,0>0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
When the inequality (b.1) is satisfied, the trace error curve is limited to- ρij(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-pij(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 ρij,0. Thus by selecting the appropriate performance functionTo limit the steady-state and transient performance of the tracking error.
And step 3: designing a High-gain Extended State Observer (High-gain Extended State Observer-HGESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting proper Observer gain, 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;
wherein: a is11、a12、a21、a22Design satisfies s2+a11s+a12＝(s+ωo1)2、s2+a21s+a22＝(s+ωo2)2Wherein ω o1、ωo2For high gain extended state observer bandwidth, z11＝[z11,1,z11,2,z11,3]TIs attitude loop output x1Estimate of, mui∈ (0,1) (i ═ 1,2) is the parameter to be designed, z12＝[z12,1,z12,2,z12,3]TIs the total disturbance h of the attitude loop1Estimated value of eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs the angular rate loop output x2Estimate of z22＝[z22,1,z22,2,z22,3]TIs the total disturbance h of the angular rate loop2Estimated value of eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
And 4, step 4: estimating the output of the attitude loop and the angular rate loop obtained in the step 3Designing a disturbance compensation control method aiming at the mathematical models of the attitude loop and the angular rate loop in the step 1 and based on a frame of a backstepping method, so that the tracking error e of the system is limited in input (a.2)1、e2Can converge into a predetermined region (b.1).
Firstly, controller design is carried out on an attitude loop, and a preset performance function rho is selected1j(t) is as shown in formula (b.2), and ρ1jThe initial value of (t) satisfies rho1j(0)>|x1j(0)-x1d,j(0) (j ═ 1,2,3) to achieve performance constraints on attitude loop tracking errors; meanwhile, the following virtual control law can be designed
Wherein: k is a radical of1jIs the gain of the attitude loop virtual control law.
In order to realize the compensation of the total disturbance of the attitude loop, the final control law of the attitude loop is designed into the following form:
x2d＝-z12+α1(d.2)
α therein1＝[α11,α12,α13]T。
Designing a controller for a diagonal rate loop, and selecting a preset performance function rho2j(t) is as shown in formula (b.2), and ρ2jThe initial value of (t) satisfies rho2j(0)>|x2j(0)-x2d,j(0) (j ═ 1,2,3) to achieve performance constraints on the angular rate loop tracking error; meanwhile, the following virtual control law can be designed
Wherein: k is a radical of2jIs the gain of the attitude loop virtual control law.
Final control law δ of the system for compensation of total disturbance of the diagonal rate loopcIs designed asThe following forms:
δc＝-z22+α2(d.4)
α therein2＝[α21,α22,α23]T. The system actual control law δ can be obtained by substituting the formula (d.4) into the formula (a.2).
Aiming at the unpowered reentry process of the hypersonic aircraft with limited input, the embodiment of the invention adopts a preset performance control function to constrain the tracking errors of a system attitude loop and an angular rate loop, so that the tracking error of the system can be converged into a preset region; and considering the internal uncertainty and the external disturbance of the aircraft together as a total disturbance, designing a high-gain extended state observer to realize the estimation of the total disturbance, and designing a disturbance compensation control method based on a frame of a backstepping method to realize the tracking control of an attitude loop and an angular rate loop. The introduction of a preset performance control algorithm improves the dynamic performance and the steady-state performance of the whole control system, the total disturbance of the system is estimated by adopting the high-gain 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 the interference, the defect that the neural network and the fuzzy system are only effective on some tight sets is not considered, and the anti-interference performance and the robustness of the system are stronger.
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 (7)
1. An anti-interference backstepping control method of a hypersonic aircraft considering input limitation is characterized by comprising the following steps:
step 1: the parameter uncertainty, unmodeled dynamic state and external disturbance of the hypersonic aircraft unpowered reentry process mathematical model 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 designed by an anti-interference backstepping control method;
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: designing a High-gain Extended State Observer (High-gain Extended State Observer-HGESO) according to the mathematical models of the attitude loop and the angular rate loop in the step 1, selecting proper Observer gain, and acquiring an output estimation value and a total disturbance estimation value of each loop;
and 4, step 4: and (3) designing a disturbance compensation control method aiming at the mathematical models of the attitude loop and the angular rate loop in the step (1) based on a frame of a backstepping method according to the output estimation value and the total disturbance estimation value obtained in the step (3), so that the tracking error of the system can be converged into a preset area under the condition of limited input.
2. The anti-interference backstepping control method of the hypersonic aircraft considering input limitation, as claimed in claim 1, wherein the expressions of the mathematical models of the attitude loop and the angular rate loop suitable for the design form of the anti-interference backstepping control method in step 1 are as follows (1) and (2):
wherein: x is the number of1＝[x11,x12,x13]T＝[α,β,μ]T，x2＝[x21,x22,x23]T＝[p,q,r]T，δ＝[δeδaδr]Tα, β, μ are aircraft, respectivelyAngle of attack, sideslip angle, and roll angle of; p, q and r are respectively a rolling angular velocity, a yaw angular velocity and a pitch angular velocity; h is1(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:
wherein: deltac＝[δec,δac,δrc]TIs the control input signal to be designed, δmax∈(0,∞)、δmin∈ (0, ∞) are the upper and lower bounds, respectively, for which the rudder surface deflection angle is known.
3. The anti-interference backstepping control method for the hypersonic aircraft considering input limitation, as claimed in claim 1, wherein 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.
4. The anti-interference backstepping control method for hypersonic flight vehicle considering input limitation as claimed in claim 1, wherein in the 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 x1d＝[x1d,1,x1d,2,x1d,3]TIs a state variable x1Reference input of, x2d＝[x2d,1,x2d,2,x2d,3]TIs a change of stateQuantity x2According to the preset performance control method, the specified tracking error needs to satisfy the following constraint:
-ρij(t)<eij(t)<ρij(t)，(i＝1,2；j＝1,2,3) (4)
t ∈ [0, ∞), rhoij(t) is a smooth, bounded, positive and strictly decreasing performance function, the performance function ρij(t) is designed in the form of:
wherein: k is a radical ofij,c>0，
ρij,0>0, and rho is selectedij,0So that-pij,0<eij(0)<ρij,0。
5. The anti-interference backstepping control method for the hypersonic aircraft considering input limitation as claimed in claim 1, wherein in the step 3, a high-gain extended state observer as shown in formulas (6) and (7) is designed:
wherein: a is11、a12、a21、a22Design satisfies s2+a11s+a12＝(s+ωo1)2、s2+a21s+a22＝(s+ωo2)2Wherein ω iso1、ωo2For high gain extended state observer bandwidth, z11＝[z11,1,z11,2,z11,3]TIs the posture returnsOutput x1Estimate of, mui∈ (0,1) (i ═ 1,2) is the parameter to be designed, z12＝[z12,1,z12,2,z12,3]TIs the total disturbance h of the attitude loop1Estimated value of eE1＝[eE1,1,eE1,2,eE1,3]TIs the estimation error of the attitude loop, z21＝[z21,1,z21,2,z21,3]TIs the angular rate loop output x2Estimate of z22＝[z22,1,z22,2,z22,3]TIs the total disturbance h of the angular rate loop2Estimated value of eE2＝[eE2,1,eE2,2,eE2,3]TIs the estimation error of the angular rate loop.
6. The anti-interference backstepping control method for the hypersonic flight vehicle considering the input limitation as claimed in claim 1, wherein in the step 4, the controller design process is as follows:
firstly, controller design is carried out on an attitude loop, and a preset performance function rho is selected1j(t) is represented by the formula (5) and ρ1jThe initial value of (t) satisfies rho1j(0)>|x1j(0)-x1d,j(0) (j ═ 1,2,3) to achieve performance constraints on attitude loop tracking errors; meanwhile, the following virtual control law is designed
Wherein: k is a radical of1jIs the gain of the attitude loop virtual control law;
in order to realize the compensation of the total disturbance of the attitude loop, the final control law of the attitude loop is designed into the following form:
x2d＝-z12+α1(9)
α therein1＝[α11,α12,α13]T；
The controller design is carried out on the angular rate loop, and a preset value is selectedPerformance function ρ2j(t) is represented by the formula (5) and ρ2jThe initial value of (t) satisfies rho2j(0)>|x2j(0)-x2d,j(0) (j ═ 1,2,3) to achieve performance constraints on the angular rate loop tracking error; meanwhile, the following virtual control law is designed
Wherein: k is a radical of2jIs the gain of the attitude loop virtual control law;
final control law δ of the system for compensation of total disturbance of the diagonal rate loopcThe design is as follows:
δc＝-z22+α2(11)
α therein2＝[α21,α22,α23]T(ii) a The system actual control law δ can be obtained by substituting equation (11) into equation (3).
7. An anti-interference backstepping control system of a hypersonic aircraft considering input limitation, characterized in that the control method of any of claims 1-6 is adopted.
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| CN111831002A (en) * | 2020-07-10 | 2020-10-27 | 中国人民解放军海军工程大学 | Hypersonic aircraft attitude control method based on preset performance |
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