CN116300992A - L-based 1 Adaptive dynamic inverse variant aircraft control method - Google Patents

L-based 1 Adaptive dynamic inverse variant aircraft control method Download PDF

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CN116300992A
CN116300992A CN202211475942.6A CN202211475942A CN116300992A CN 116300992 A CN116300992 A CN 116300992A CN 202211475942 A CN202211475942 A CN 202211475942A CN 116300992 A CN116300992 A CN 116300992A
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林鹏
马青原
王业光
刘长秀
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Shenyang Aircraft Design Institute Yangzhou Collaborative Innovation Research Institute Co ltd
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
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    • G05D1/08Control of attitude, i.e. control of roll, pitch, or yaw
    • G05D1/0808Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G05D1/0816Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
    • G05D1/0825Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10Simultaneous control of position or course in three dimensions
    • G05D1/101Simultaneous control of position or course in three dimensions specially adapted for aircraft
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Abstract

The invention discloses a method based on L 1 A method for controlling a variant aircraft with self-adaptive dynamic inversion belongs to the field of flight control of variant aircrafts. The method comprises the following specific steps: establishing a six-degree-of-freedom nonlinear dynamics model of the variant aircraft; performing time scale separation on 12 state variables of the nonlinear dynamics model of the aircraft according to a singular perturbation theory; according to the differential equation of the angular velocity and attitude angle loop of the variant aircraft, respectively designing an angular velocity and attitude angle loop control law based on a nonlinear dynamic inverse method; based on dynamic inverse and linear feedback and L 1 The adaptive combining method designs the control law of the motor generator. The invention can improve the performance of the control system under the condition of uncertainty, improve the precision of tracking control and improve the robustness of the system, so that the variant aircraft can still keep stable flight under the conditions of input disturbance, pneumatic parameter uncertainty, parameter change and the like.

Description

L-based 1 Adaptive dynamic inverse variant aircraft control method
Technical Field
The invention belongs to the field of flight control of variant aircrafts, and particularly relates to a variable-speed aircraft based on L 1 A method for controlling a variant aircraft with adaptive dynamic inverse.
Background
A variant aircraft is an aircraft that can change its shape accordingly to the requirements of aircraft maneuver control or to changes in the flight environment and mission. In the new operational ideas and operational modes, military aviation and civil aviation in recent years put forward requirements for the aircraft to execute various flight tasks under different flight conditions, and the application value and importance of the variant aircraft in national defense military and civil aviation aspects are self-evident, so that the variant aircraft has become the leading edge and hot spot research content of the international aerospace world.
The variant aircraft is different from the fixed wing aircraft and is characterized by comprising a deformation mechanism, so that the main technical difficulties in the aspect of flight control are as follows: 1) The distributed driving characteristics of the deformation mechanism make modeling of the dynamics of the aircraft model difficult; 2) The change of the structural appearance of the aircraft can cause a series of problems such as structural parameter, aerodynamic characteristic change and the like, so that higher requirements are put on flight control. In the aspect of flight control of a variant aircraft, most researches are to conduct small disturbance linearization treatment on a nonlinear system, approximately convert the nonlinear system into a linear system, and then conduct control law design by adopting a common linear system control method, but neglecting a high-order nonlinear item in the linearization process can greatly influence the control precision; still further studies have simplified the six-degree-of-freedom kinetic model to three degrees of freedom, only studying the longitudinal control of the aircraft. Therefore, a nonlinear control scheme capable of accurately tracking and adapting to the structural parameter and aerodynamic characteristic changes of the aircraft is urgently needed to realize six-degree-of-freedom flight control of the variant aircraft.
Disclosure of Invention
(one) solving the technical problems
Aiming at the defects of the prior art, the invention provides a novel L-based optical fiber 1 Adaptive dynamic inverse variant aircraft controlThe method can realize accurate tracking and adapt to the structural parameter and aerodynamic characteristic change of the aircraft, and meets the robust requirement of the flight control of the variant aircraft.
(II) technical scheme
In order to achieve the technical purpose, the technical scheme of the invention comprises the following steps:
l-based 1 A method of adaptive dynamic reverse variant aircraft control comprising the steps of:
(1) Establishing a variant aircraft nonlinear dynamics model which can characterize dynamics in an aircraft variant process;
(2) Performing time scale separation on 12 state variables of the nonlinear dynamics model of the aircraft according to a singular perturbation theory;
(3) According to differential equations of the variant aircraft angular velocity loop, designing an angular velocity loop control law based on a nonlinear dynamic inverse method;
(4) According to a differential equation of the attitude angle loop of the variant aircraft, designing an attitude angle loop control law based on a nonlinear dynamic inverse method;
(5) Based on linear feedback nonlinear dynamic inverse sum L according to differential equation of variant aircraft maneuvering state quantity 1 The adaptive approach designs the motive generator control law.
Further, in step (1), the described variant aircraft nonlinear dynamics model comprises:
A. system of kinetic equations for aircraft centroid movement
Figure SMS_1
Figure SMS_2
Figure SMS_3
Wherein,,
Figure SMS_4
the flying acceleration, the attack angle acceleration and the sideslip angle acceleration of the aircraft are respectively, V, alpha, beta are respectively the flying speed, the attack angle and the sideslip angle of the aircraft, m is the mass of the aircraft, p, q and r are respectively the rolling, pitching and yaw angle speeds of the aircraft, F x ,F y ,F z The components of the combined external force applied by the aircraft under the body axis are respectively F ix ,F iy ,F iz The components of the additional force generated by the aircraft due to the change of the centroid position under the body axis are respectively calculated as follows:
Figure SMS_5
wherein T is engine thrust, D, Y and L are respectively resistance, lift force and side force born by the aircraft, g is gravity acceleration,
Figure SMS_6
respectively, aircraft roll angle and pitch angle, +.>
Figure SMS_7
Rolling angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; s is S x ,S y ,S z Representing the static moment under the aircraft fuselage axis, +.>
Figure SMS_8
Respectively the first derivative of the static moment over time,
Figure SMS_9
respectively the second derivative of the static moment over time.
B. Kinetic equation of rotation about centroid
According to the knowledge of multi-rigid-body dynamics theory, unlike a conventional aircraft, the variant aircraft generates additional force and additional moment due to deformation, and the derived dynamic equation of the rotation of the variant aircraft around the mass center is as follows:
Figure SMS_10
wherein,,
Figure SMS_11
is the rotational inertia matrix of the airplane, I x 、I y 、I z For the moment of inertia of the aircraft, I xy 、I xz 、I yz Is the product of inertia. />
Figure SMS_12
Respectively a roll moment, a pitch moment and a yaw moment. />
Figure SMS_13
Respectively representing components of the flying acceleration on the machine body axis, b 1 ,b 2 ,b 3 The expressions of (2) are respectively:
Figure SMS_14
Figure SMS_15
Figure SMS_16
wherein u, v and w respectively represent components of the flying speed on the machine body axis, m i Representing the weight of the ith wing of the ith aircraft,
Figure SMS_17
Figure SMS_18
for the first order of the moment of inertia of the aircraft over time, < >>
Figure SMS_19
Is the first order derivative of the product of inertia over time, S ix ,S iy ,S iz Respectively representing the static moment of the ith wing of the aircraft, < ->
Figure SMS_20
Representing the first order derivative of the static moment of the ith wing of the aircraft over time, respectively,/->
Figure SMS_21
Representing the second derivative of the static moment of the ith wing of the aircraft over time, respectively.
C. Kinematic equation of centroid movement
Figure SMS_22
Figure SMS_23
Figure SMS_24
Where x, y, z are the positions of the aircraft in the ground coordinate system and ψ is the yaw angle of the aircraft.
D. Kinematic equations of rotation about centroid
The projection of the aircraft rotation angular velocity on the engine body axis system can be written from the formation process of the engine body axis system as follows:
Figure SMS_25
Figure SMS_26
Figure SMS_27
the kinematic equation of the airplane around the mass center can be obtained by solving:
Figure SMS_28
Figure SMS_29
Figure SMS_30
further, the specific process of step (2) is as follows:
the 12 state variables of the nonlinear dynamics model of the aircraft are subjected to time scale division according to the singular perturbation theory:
(1) fast state: roll angle speed p, pitch angle speed q, yaw angle speed r;
(2) slow state: angle of attack α, sideslip angle β, track roll angle μ;
(3) very slow state: speed V, track pitch angle γ, track yaw angle χ;
(4) slowest state: x, y, z.
Further, the specific process of step (3) is as follows:
neglecting the additional forces and additional moments caused by the aircraft variants, the differential equation of the angular velocity loop is expressed in the form of a nonlinear system as follows:
Figure SMS_31
Figure SMS_32
is->
Figure SMS_33
Expression of the part of the control surface independent of the control surface,/->
Figure SMS_34
A matrix for controlling the control surface; />
Figure SMS_35
A vector of 8 aircraft states is defined:>
Figure SMS_36
Figure SMS_37
is defined as a control vector consisting of 3 control plane deflection angles
Figure SMS_38
Figure SMS_39
Is the output of the controller and is also the input of the aircraft object.
The ideal closed loop dynamics of the angular velocity loop is set as follows:
Figure SMS_40
Figure SMS_41
Figure SMS_42
wherein: p is p c ,q c ,r c As command signals generated by the attitude control system, they are also steady state values for the fast state and will be input to the slow state of the aircraft, generating the desired angular rate signal in the aircraft dynamics
Figure SMS_43
Is the angular velocity loop bandwidth.
From this, it can be calculated to obtain the desired angular acceleration
Figure SMS_44
Control input->
Figure SMS_45
Should have the form:
Figure SMS_46
wherein:
Figure SMS_47
is a 3 x 3 matrix, due to its right inverse +.>
Figure SMS_48
There is only a set of suitable rudder deflection combination inputs that need to be found so that the loop produces the desired angular acceleration. Calculated rudder deflection [ delta ] a δ e δ r ] T I.e. the output of the angular velocity control system.
Further, the specific process of step (4) is as follows:
neglecting the additional force and the additional moment caused by the aircraft variant, neglecting the direct force generated by the deflection of the control surface, the aircraft equation corresponding to the attitude angle loop can be written as follows:
Figure SMS_49
wherein:
Figure SMS_50
Figure SMS_51
is->
Figure SMS_52
Expression of the p, q, r independent part of the expression, + the expression of the p, q, r independent part of the expression,>
Figure SMS_53
and p, q, r. In order to make the aircraft output state track the attitude angle expected value alpha well ccc ,/>
Figure SMS_54
Will be +.>
Figure SMS_55
Instead, the desired dynamics have the form:
Figure SMS_56
Figure SMS_57
Figure SMS_58
Figure SMS_59
the three channels are wide for the attitude angle loop.
Definition of the definition
Figure SMS_60
Middle [ pqr] T =[p c q c r c ] T ,/>
Figure SMS_61
The output of the attitude control system can thus be solved as:
Figure SMS_62
further, the specific process of step (5) is as follows:
neglecting the additional forces and additional moments caused by aircraft variants, mu can first be solved directly c The method comprises the following steps of:
Figure SMS_63
Figure SMS_64
is the expected dynamics of track yaw acceleration;
then at mu c In the known case, it will be possible to obtain a composition containing only the variable alpha c Is a nonlinear equation of (2):
Figure SMS_65
newton iteration method for solving nonlinear equation can be used for solving attack angle command alpha c Finally, the thrust command T can be calculated c
Figure SMS_66
Wherein,,
Figure SMS_67
the aircraft acceleration and the aircraft track yaw angle acceleration and the track pitch angle acceleration are respectively,
Figure SMS_68
in the expected value of the maneuver generator->
Figure SMS_69
Will be summed by linear feedback and L 1 The self-adaptive control method comprises the following steps:
taking the velocity channel as an example, the velocity tracking error e is noted V (t)=V(t)-V r (t) wherein V r (t) redefining a velocity error vector for the velocity command signal:
Figure SMS_70
according to the definition above, the following error dynamic system equation is further available:
Figure SMS_71
wherein:
Figure SMS_72
a system matrix and an input matrix, respectively.
The control inputs of the error system are:
Figure SMS_73
further available are speed channel outer loop control command signals:
Figure SMS_74
solving for feedback gain k using LQ (linear quadratic) method V The following main control system speed channel control law can be obtained:
Figure SMS_75
adding in
Figure SMS_76
In the case of an auxiliary control system, the control input comprises two parts,:
u V (t)=u V,b (t)+u V,a (t)
i.e. the main control system control input u V,b (t) and control input u of the auxiliary control system V,a (t). Substituting the control law u of the main control system V,b (t) after introducing both the uncertainty of the input gain and the input disturbance, obtaining the following error dynamics system:
Figure SMS_77
wherein A is m,V =A V -b V k V ,
Figure SMS_78
To characterize the unknown real number of the input gain; />
Figure SMS_79
For time-varying parameter vectors->
Figure SMS_80
Representing an input disturbance related to a system state; />
Figure SMS_81
Representing an exogenous input disturbance.
From the above error dynamics system can be obtained
Figure SMS_82
The control law of the auxiliary control system is as follows:
Figure SMS_83
wherein r is V (s) and
Figure SMS_84
respectively the reference signals r V Laplace transform of (t)
Figure SMS_85
k gv 、/>
Figure SMS_86
For feedback gain, D V (s) is a transfer function of strict true component, ">
Figure SMS_87
Respectively represent pair->
Figure SMS_88
Is determined by the estimation of (a);
establishment of
Figure SMS_89
Is the adaptive law of (1):
Figure SMS_90
Figure SMS_91
Figure SMS_92
Figure SMS_93
representing an estimation error of the system state +.>
Figure SMS_94
Is self-adaptive law, P V Is algebraic Lyapunov equation->
Figure SMS_95
Solution of Q V For any symmetric positive definite matrix, proj is the projection operator.
For the track angle control channel, including the track inclination angle channel and the track yaw angle channel, the track error of the track angle and the corresponding error value vector can be defined similarly, and the error power system of the track angle can be derived, so that the control signal of the track angle channel can be further obtained.
The beneficial effects brought by adopting the technical scheme are that:
(1) The nonlinear dynamic inverse control method based on the six-degree-of-freedom dynamic model of the variant aircraft is adopted, any high-order nonlinear item in the model is not ignored, and the control precision is ensured;
(2) The invention adopts linear feedback dynamic inverse sum L in the flight path control system 1 The self-adaptive combination method can well inhibit the influence caused by system uncertainty and input disturbance, and can keep the accuracy of tracking control and the robustness of the system under the condition of parameter uncertainty.
(3) The invention is easily portable into the control system design of other variant aircraft.
Drawings
FIG. 1 shows a variant aircraft L according to the invention 1 A self-adaptive dynamic inverse control scheme schematic diagram;
FIG. 2 is a block diagram of a variant aircraft angular velocity control system according to the present invention;
FIG. 3 is a block diagram of a variant aircraft attitude control system of the present invention;
FIG. 4 is a block diagram of a variant aircraft track control system of the present invention;
FIG. 5 is a graph of tracking error of a variant aircraft in the presence of input disturbances in a simulation example; (a) is the tracking error of the speed when the input disturbance exists, (b) is the tracking error of the track pitch angle when the input disturbance exists, and (c) is the tracking error of the track yaw angle when the input disturbance exists;
FIG. 6 is a graph of tracking error of a variant aircraft as the profile changes in a simulation example; (a) is a tracking error of a speed at the time of profile change, (b) is a tracking error of a track pitch angle at the time of profile change, and (c) is a tracking error of a track yaw angle at the time of profile change;
fig. 7 shows the tracking error of a variant aircraft in the simulation example when the input disturbance and the profile change are present simultaneously, (a) the tracking error of the speed when the input disturbance and the profile change are present simultaneously, (b) the tracking error of the track pitch angle when the input disturbance and the profile change are present simultaneously, and (c) the tracking error of the track yaw angle when the input disturbance and the profile change are present simultaneously.
Detailed Description
The technical scheme of the present invention will be described in detail below with reference to the accompanying drawings.
The invention designs a nonlinear dynamic inverse sum L based on linear feedback 1 In order to achieve the technical purpose, the technical scheme of the flight control system of the self-adaptive method comprises the following steps:
step 1: establishing a variant aircraft nonlinear dynamics model which can characterize dynamics in an aircraft variant process;
step 2: performing time scale separation on 12 state variables of the nonlinear dynamics model of the aircraft according to a singular perturbation theory;
step 3: according to a differential equation of the attitude angle loop of the variant aircraft, designing an attitude angle loop control law based on a nonlinear dynamic inverse method;
step 4: according to a differential equation of the attitude angle loop of the variant aircraft, designing an attitude angle loop control law based on a nonlinear dynamic inverse method;
step 5: according to variant aircraft maneuversDifferential equation of state quantity based on linear feedback nonlinear dynamic inverse sum L 1 The self-adaptive method designs a control law of the maneuvering generator;
a variant aircraft flight control scheme of the invention is shown in figure 1.
In this embodiment, the above step 1 is implemented by adopting the following preferred scheme:
A. system of kinetic equations for aircraft centroid movement
Figure SMS_96
Figure SMS_97
Figure SMS_98
Wherein,,
Figure SMS_99
the flying acceleration, the attack angle acceleration and the sideslip angle acceleration of the aircraft are respectively, V, alpha, beta are respectively the flying speed, the attack angle and the sideslip angle of the aircraft, m is the mass of the aircraft, p, q and r are respectively the rolling, pitching and yaw angle speeds of the aircraft, F x ,F y ,F z The components of the combined external force applied by the aircraft under the body axis are respectively F ix ,F iy ,F iz The components of the additional force generated by the aircraft due to the change of the centroid position under the body axis are respectively calculated as follows:
Figure SMS_100
wherein T is engine thrust, D, Y and L are respectively resistance, lift force and side force born by the aircraft, g is gravity acceleration,
Figure SMS_101
respectively the roll angle and pitch of the aircraftAngle (S)/(S)>
Figure SMS_102
Rolling angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; s is S x ,S y ,S z Representing the static moment under the aircraft fuselage axis, +.>
Figure SMS_103
Respectively the first order derivative of the static moment over time, < >>
Figure SMS_104
Respectively the second derivative of the static moment over time.
B. Kinetic equation of rotation about centroid
According to the knowledge of multi-rigid-body dynamics theory, unlike a conventional aircraft, the variant aircraft generates additional force and additional moment due to deformation, and the derived dynamic equation of the rotation of the variant aircraft around the mass center is as follows:
Figure SMS_105
wherein,,
Figure SMS_106
is the rotational inertia matrix of the airplane, I x 、I y 、I z For the moment of inertia of the aircraft, I xy 、I xz 、I yz Is the product of inertia. />
Figure SMS_107
Respectively a roll moment, a pitch moment and a yaw moment. />
Figure SMS_108
Respectively representing components of the flying acceleration on the machine body axis, b 1 ,b 2 ,b 3 The expressions of (2) are respectively:
Figure SMS_109
Figure SMS_110
Figure SMS_111
wherein u, v and w respectively represent components of the flying speed on the machine body axis, m i Representing the weight of the ith wing of the ith aircraft,
Figure SMS_112
Figure SMS_113
for the first order of the moment of inertia of the aircraft over time, < >>
Figure SMS_114
Is the first order derivative of the product of inertia over time, S ix ,S iy ,S iz Respectively representing the static moment of the ith wing of the aircraft, < ->
Figure SMS_115
Representing the first order derivative of the static moment of the ith wing of the aircraft over time, respectively,/->
Figure SMS_116
Representing the second derivative of the static moment of the ith wing of the aircraft over time, respectively.
C. Kinematic equation of centroid movement
Figure SMS_117
Figure SMS_118
Figure SMS_119
Where x, y, z are the positions of the aircraft in the ground coordinate system and ψ is the yaw angle of the aircraft.
D. Kinematic equations of rotation about centroid
The projection of the aircraft rotation angular velocity on the engine body axis system can be written from the formation process of the engine body axis system as follows:
Figure SMS_120
Figure SMS_121
Figure SMS_122
the kinematic equation of the airplane around the mass center can be obtained by solving:
Figure SMS_123
Figure SMS_124
Figure SMS_125
the forces and moments experienced by the variant aircraft are calculated as follows:
aerodynamic forces including side force Y, drag force D and lift force L, aerodynamic moments including roll moment
Figure SMS_126
Pitching moment->
Figure SMS_127
And yaw moment->
Figure SMS_128
The aerodynamic force and moment module calculates aerodynamic coefficient on the stable shaft by using feedback data (such as Mach number, altitude, attack angle, sideslip angle, aircraft gravity center position, angular speed and other flight parameters and control surface position, landing gear and flap position provided by the hydraulic system) from the inside of the flight simulation system, and finally calculates aerodynamic force and moment on the engine body shaft and outputs the aerodynamic force and moment to the six-degree-of-freedom motion model module of the aircraft. Aerodynamic force is calculated mainly according to aerodynamic pressure and aerodynamic coefficient on the stable axis. The aerodynamic coefficient calculation formulas are respectively as follows:
Figure SMS_129
the calculation formulas of lift force, resistance and side force are respectively as follows:
Figure SMS_130
the aerodynamic moment is calculated mainly according to aerodynamic pressure and aerodynamic moment coefficient on the stable shaft, wherein the pitching moment coefficient, the rolling moment coefficient and the yaw moment coefficient are calculated according to the following formula:
Figure SMS_131
the calculation formulas of the pitching moment, the rolling moment and the yawing moment are respectively as follows:
Figure SMS_132
wherein ρ is the air density, S is the wing area, b is the wing span, and c is the average aerodynamic chord length of the wing. C (C) L 、C D 、C Y 、C m 、C l 、C n Respectively being the lift coefficient, drag coefficient, side force coefficient, pitch moment coefficient, roll moment coefficient and yaw moment coefficient of the variant aircraft, eta being a measure of the deformation of the variant aircraft,
Figure SMS_133
Figure SMS_134
respectively, the corresponding aerodynamic coefficients that vary with the shape of the aircraft. The variant aircraft was then dynamically modeled. Based on the aerodynamic derivatives obtained above, a six-degree-of-freedom nonlinear multi-body dynamics model of the variant aircraft was derived.
In this embodiment, the above step 2 is implemented by adopting the following preferred scheme:
since the six-degree-of-freedom nonlinear dynamics model of the variant aircraft is a dynamics system of 12 state variables, the 12 state variables are respectively speed V, angle of attack α, angle of sideslip β, roll angle speed p, pitch angle speed q, yaw angle speed r, track roll angle μ, track pitch angle γ, track yaw angle χ and coordinates x, y, z of the projection of the centroid position on the horizontal plane. The response speeds of the 12 states for the manipulation command are different, and if the nonlinear dynamic inversion method is adopted to complete the input/output linearization of the speed control channel and the track angle (including the track deflection angle and the track dip angle) control channel, the six-degree-of-freedom nonlinear dynamic equation of the aircraft is required to be divided into 4 subsystems according to the different response speeds of the state variables. The method can be classified into time scales according to the singular perturbation theory:
(1) fast state: roll angle speed p, pitch angle speed q, yaw angle speed r;
(2) slow state: angle of attack α, sideslip angle β, track roll angle μ;
(3) very slow state: speed V, track pitch angle γ, track yaw angle χ;
(4) slowest state: x, y, z.
The fast state, slow state, very slow state and slowest state in the 4 groups of states form 4 dynamic subsystems, namely an angular speed control system, a gesture control system, a track control system and a position control system, so as to form a large system of a flight control system. Different bandwidths are selected among all subsystems in a large system according to the principle of time scale separation, so that all dynamic subsystems are ensured to operate in different time domains. And for each subsystem, the nonlinear dynamic inverse calculation method is adopted to complete input/output linearization, and finally linearization of the speed control channel and the track angle control channel can be realized.
In this embodiment, the above step 3 is implemented by adopting the following preferred scheme:
neglecting the additional forces and additional moments caused by the aircraft variants, the differential equation of the angular velocity loop is expressed in the form of a nonlinear system as follows:
Figure SMS_135
Figure SMS_136
is->
Figure SMS_137
Expression of the part of the control surface independent of the control surface,/->
Figure SMS_138
A matrix for controlling the control surface; />
Figure SMS_139
A vector of 8 aircraft states is defined:>
Figure SMS_140
Figure SMS_141
is defined as a control vector consisting of 3 control plane deflection angles
Figure SMS_142
Figure SMS_143
Is the output of the controller and is also the input of the aircraft object.
The ideal closed loop dynamics of the angular velocity loop is set as follows:
Figure SMS_144
Figure SMS_145
Figure SMS_146
wherein: p is p c ,q c ,r c As command signals generated by the attitude control system, they are also steady state values for the fast state and will be input to the slow state of the aircraft, generating the desired angular rate signal in the aircraft dynamics
Figure SMS_147
The angular velocity loop bandwidth was taken to be 10rad/s.
From this, it can be calculated to obtain the desired angular acceleration
Figure SMS_148
Control input->
Figure SMS_149
Should have the form:
Figure SMS_150
wherein:
Figure SMS_151
is a 3 x 3 matrix, due to its right inverse +.>
Figure SMS_152
There is only a set of suitable rudder deflection combination inputs that need to be found so that the loop produces the desired angular acceleration. Calculated rudder deflection [ delta ] a δ e δ r ] T I.e. the output of the angular velocity control system.
A block diagram of the angular velocity control system is shown in fig. 2.
In this embodiment, the above step 4 is implemented by adopting the following preferred scheme:
neglecting the additional force and the additional moment caused by the aircraft variant, neglecting the direct force generated by the deflection of the control surface, the aircraft equation corresponding to the attitude angle loop can be written as follows:
Figure SMS_153
wherein:
Figure SMS_154
Figure SMS_155
is->
Figure SMS_156
Expression of the p, q, r independent part of the expression, + the expression of the p, q, r independent part of the expression,>
Figure SMS_157
and p, q, r. In order to make the aircraft output state track the attitude angle expected value alpha well ccc ,/>
Figure SMS_158
Will be +.>
Figure SMS_159
Instead, the desired dynamics have the form:
Figure SMS_160
Figure SMS_161
Figure SMS_162
Figure SMS_163
the three channels are wide for the attitude angle loop.
Definition of the definition
Figure SMS_164
Middle [ pqr] T =[p c q c r c ] T ,/>
Figure SMS_165
The output of the attitude control system can thus be solved as:
Figure SMS_166
a block diagram of the attitude control system is shown in fig. 3.
In this embodiment, the above step 5 is implemented by adopting the following preferred scheme:
neglecting the additional forces and additional moments caused by aircraft variants, mu can first be solved directly c The method comprises the following steps of:
Figure SMS_167
Figure SMS_168
is the expected dynamics of track yaw acceleration;
then at mu c In the known case, it will be possible to obtain a composition containing only the variable alpha c Is a nonlinear equation of (2):
Figure SMS_169
newton iteration method for solving nonlinear equation can be used for solving attack angle command alpha c Finally, the thrust command T can be calculated c
Figure SMS_170
Wherein,,
Figure SMS_171
the aircraft acceleration and the aircraft track yaw angle acceleration and the track pitch angle acceleration are respectively,
Figure SMS_172
in the expected value of the maneuver generator->
Figure SMS_173
Will be summed by linear feedback and L 1 The self-adaptive control method comprises the following steps:
taking the velocity channel as an example, the velocity tracking error e is noted V (t)=V(t)-V r (t) wherein V r (t) redefining a velocity error vector for the velocity command signal:
Figure SMS_174
according to the definition above, the following error dynamic system equation is further available:
Figure SMS_175
wherein:
Figure SMS_176
a system matrix and an input matrix, respectively.
The control inputs of the error system are:
Figure SMS_177
further available are speed channel outer loop control command signals:
Figure SMS_178
solving for feedback gain k using LQ (linear quadratic) method V The following main control system speed channel control law can be obtained:
Figure SMS_179
adding in
Figure SMS_180
In the case of an auxiliary control system, the control input comprises two parts,:
u V (t)=u V,b (t)+u V,a (t)
i.e. the main control system control input u V,b (t) and control input u of the auxiliary control system V,a (t). Substituting the control law u of the main control system V,b (t) after introducing both the uncertainty of the input gain and the input disturbance, obtaining the following error dynamics system:
Figure SMS_181
wherein A is m,V =A V -b V k V ,
Figure SMS_182
To characterize the unknown real number of the input gain; />
Figure SMS_183
For time-varying parameter vectors->
Figure SMS_184
Representing an input disturbance related to a system state; />
Figure SMS_185
Representing an exogenous input disturbance.
L 1 The goal of the adaptive control design is to ensure that the system output tracks effectively a given command signal. The design is based on the following 3 assumptions:
a. unknown parameter θ V (t) and sigma V (t) consistently bounded;
b. the change rate of the parameters along with time is consistent and bounded;
c. the upper and lower bounds of the uncertainty input gain are known. It should be noted that θ, as a representation of the input disturbance to the real physical system V (t) and sigma V (t) the nature of the corresponding time rate of change is ensured; for input gains, although accurate upper and lower bound information is not available, larger limits may be set for it in the design to improve the ability of the system to cope with gain uncertainty.
For the error dynamics system proposed previously, consider the following state estimator:
Figure SMS_186
wherein the adaptive estimation
Figure SMS_187
And->
Figure SMS_188
The method is obtained by the following adaptive law:
Figure SMS_189
Figure SMS_190
Figure SMS_191
wherein,,
Figure SMS_192
representing an estimation error of the system state +.>
Figure SMS_193
Is self-adaptive law, P V Is algebraic Lyapunov equation->
Figure SMS_194
Solution (Q) V Positive definite matrix for arbitrary symmetry), proj is the projection operator.
From the above error dynamics system can be obtained
Figure SMS_195
The control law of the auxiliary control system is as follows:
Figure SMS_196
wherein r is V (s) and
Figure SMS_197
respectively the reference signals r V Laplace transform of (t)
Figure SMS_198
k gv 、/>
Figure SMS_199
For feedback gain, D V (s) is a strict true-fraction transfer function, and thus the following strict-fraction and stable transfer function can be obtained:
Figure SMS_200
and has C V (0) Taking r into account that the design goal of the control system in this problem is to track the speed command =1 V (t) =0, and the control law can be simplified accordingly as follows:
Figure SMS_201
for the track angle control channel (comprising a track inclination angle channel and a track yaw angle channel), the track error of the track angle and the corresponding error value vector can be defined similarly, so that the error power system of the track angle can be derived, and further, the control signal of the track angle channel can be obtained.
The track control system is shown in block diagram form in fig. 4.
The simulation scene is set as follows: the initial conditions for the simulation were trim cruise state (h=5000 m, v=200 m/s) followed by command signal tracking, which is described as follows:
at the time t=0s, giving a +10m/s speed step instruction, and generating a reference track through a filter to serve as a target for variant aircraft model tracking; at the time t=20s, giving a track tilt angle step instruction of +0.15rad, generating a reference track through a filter, and taking the reference track as a target for variant aircraft model tracking; at time t=40s, a step command of +0.2rad of track yaw angle is given, and a reference track is generated via a filter as a target for variant aircraft model tracking.
Meanwhile, simulation is executed under the condition that input disturbance and airplane appearance change exist, and simulation experiment conditions and numbers are shown in the following table:
table: simulation test condition setting
Figure SMS_202
Test case i will investigate the effect of input disturbances on the control effect of the aircraft. The added input disturbance is generated through a signal with a reference value of 0 and conforming to continuous normal distribution, and the disturbance is directly overlapped to a control input signal generated by a controller; the disturbance signals superimposed to the accelerator push rod value and each pneumatic control surface randomly fluctuate by 10% up and down on the basis of the original control signals, namely sigma PLA ∈[-0.1,0.1],
Figure SMS_203
Test case II simulates the variant process of a variant aircraft by changing the aircraft span, average aerodynamic chord length, moment of inertia and related aerodynamic parameters during simulation (the aircraft mass parameters and the change range and change law of the aerodynamic parameters are obtained by the related literature data).
And the test case III is combined with the test cases I and II to test the control effect of the control system under the condition that input disturbance and parameter uncertainty exist simultaneously.
As can be seen from FIGS. 5-7, L is added 1 After the self-adaptive dynamic inverse control system, the aircraft model can still track the reference track of the speed and track angle command signals well in the modification process, the tracking error of each output quantity can be stably converged, the error in the whole simulation process is within the allowable range of engineering, and the system is kept in a stable working state. From the simulation results, L 1 The self-adaptive dynamic inverse controller can enable the flight control system to have higher tracking control precision and capability of coping with flight parameter changes, so that stability of the variant aircraft in the deformation process is ensured.
The embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by the embodiments, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.

Claims (7)

1. L-based 1 A method of adaptive dynamic reverse variant aircraft control, comprising the steps of:
(1) Establishing a variant aircraft nonlinear dynamics model which can characterize dynamics in an aircraft variant process;
(2) Performing time scale separation on 12 state variables of the nonlinear dynamics model of the aircraft according to a singular perturbation theory;
(3) According to differential equations of the variant aircraft angular velocity loop, designing an angular velocity loop control law based on a nonlinear dynamic inverse method;
(4) According to a differential equation of the attitude angle loop of the variant aircraft, designing an attitude angle loop control law based on a nonlinear dynamic inverse method;
(5) Based on linear feedback nonlinear dynamic inverse sum L according to differential equation of variant aircraft maneuvering state quantity 1 The adaptive approach designs the motive generator control law.
2. L-based according to claim 1 1 A method of adaptive dynamic inverse variant aircraft control, characterized in that in step (1) the described variant aircraft nonlinear dynamics model comprises:
A. system of kinetic equations for aircraft centroid movement
Figure QLYQS_1
Figure QLYQS_2
Figure QLYQS_3
Wherein,,
Figure QLYQS_4
the flying acceleration, the attack angle acceleration and the sideslip angle acceleration of the aircraft are respectively, V, alpha, beta are respectively the flying speed, the attack angle and the sideslip angle of the aircraft, m is the mass of the aircraft, p, q and r are respectively the rolling, pitching and yaw angle speeds of the aircraft, F x ,F y ,F z The components of the combined external force applied by the aircraft under the body axis are respectively F ix ,F iy ,F iz The components of the additional force generated by the aircraft due to the change of the centroid position under the body axis are respectively calculated as follows:
Figure QLYQS_5
wherein T is engine thrust, D, Y and L are respectively resistance, lift force and side force born by the aircraft, g is gravitational acceleration, phi and theta are respectively rolling angle and pitch angle of the aircraft,
Figure QLYQS_6
rolling angular acceleration, pitch angular acceleration, and yaw angular acceleration, respectively; s is S x ,S y ,S z Representing the static moment under the aircraft fuselage axis, +.>
Figure QLYQS_7
Respectively the first order derivative of the static moment over time, < >>
Figure QLYQS_8
Respectively the second derivative of the static moment along with time;
B. kinetic equation of rotation about centroid
According to the knowledge of multi-rigid-body dynamics theory, unlike a conventional aircraft, the variant aircraft generates additional force and additional moment due to deformation, and the derived dynamic equation of the rotation of the variant aircraft around the mass center is as follows:
Figure QLYQS_9
wherein,,
Figure QLYQS_10
is the rotational inertia matrix of the airplane, I x 、I y 、I z For the moment of inertia of the aircraft, I xy 、I xz 、I yz Is the product of inertia; />
Figure QLYQS_11
M and N are respectively rolling moment, pitching moment and yawing moment; />
Figure QLYQS_12
Respectively representing components of the flying acceleration on the machine body axis, b 1 ,b 2 ,b 3 The expressions of (2) are respectively:
Figure QLYQS_13
Figure QLYQS_14
Figure QLYQS_15
wherein u, v and w respectively represent components of the flying speed on the machine body axis, m i Representing the weight of the ith wing of the ith aircraft,
Figure QLYQS_16
Figure QLYQS_17
for the first order of the moment of inertia of the aircraft over time, < >>
Figure QLYQS_18
Is the first order derivative of the product of inertia over time, S ix ,S iy ,S iz Respectively representing the static moment of the ith wing of the aircraft, < ->
Figure QLYQS_19
Representing the first order derivative of the static moment of the ith wing of the aircraft over time, respectively,/->
Figure QLYQS_20
Respectively representing the second derivative of the static moment of the ith wing of the airplane along with time;
C. kinematic equation of centroid movement
Figure QLYQS_21
Figure QLYQS_22
Figure QLYQS_23
Wherein x, y and z are the positions of the aircraft under a ground coordinate system, and ψ is the yaw angle of the aircraft;
D. kinematic equations of rotation about centroid
The projection of the aircraft rotation angular velocity on the engine body axis system can be written from the formation process of the engine body axis system as follows:
Figure QLYQS_24
Figure QLYQS_25
Figure QLYQS_26
the kinematic equation of the airplane around the mass center can be obtained by solving:
Figure QLYQS_27
Figure QLYQS_28
Figure QLYQS_29
3. l-based according to claim 1 1 The adaptive dynamic inverse variant aircraft control method is characterized in that the specific process of the step (2) is as follows:
the 12 state variables of the nonlinear dynamics model of the aircraft are subjected to time scale division according to the singular perturbation theory:
(1) fast state: roll angle speed p, pitch angle speed q, yaw angle speed r;
(2) slow state: angle of attack α, sideslip angle β, track roll angle μ;
(3) very slow state: speed V, track pitch angle γ, track yaw angle χ;
(4) slowest state: x, y, z.
4. L-based according to claim 1 1 The adaptive dynamic inverse variant aircraft control method is characterized in that the specific process of the step (3) is as follows:
neglecting the additional forces and additional moments caused by the aircraft variants, the differential equation of the angular velocity loop is expressed in the form of a nonlinear system as follows:
Figure QLYQS_30
Figure QLYQS_31
is->
Figure QLYQS_32
Expression of the part of the control surface independent of the control surface,/->
Figure QLYQS_33
A matrix for controlling the control surface; />
Figure QLYQS_34
A vector of 8 aircraft states is defined:>
Figure QLYQS_35
Figure QLYQS_36
is defined as a control vector consisting of 3 control plane deflection angles
Figure QLYQS_37
Figure QLYQS_38
Is the output of the controller and is also the input of the aircraft object;
the ideal closed loop dynamics of the angular velocity loop is set as follows:
Figure QLYQS_39
Figure QLYQS_40
Figure QLYQS_41
wherein: p is p c ,q c ,r c As command signals generated by the attitude control system, they are also steady state values for the fast state and will be input to the slow state of the aircraft, generating the desired angular rate signal in the aircraft dynamics
Figure QLYQS_42
Bandwidth for the angular velocity loop;
from this, it can be calculated to obtain the desired angular acceleration
Figure QLYQS_43
Control input->
Figure QLYQS_44
Should have the form:
Figure QLYQS_45
wherein:
Figure QLYQS_46
is a 3 x 3 matrix, due to its right inverse +.>
Figure QLYQS_47
Only a group of proper rudder deflection combination inputs need to be found, so that the loop generates expected angular acceleration; calculated rudder deflection [ delta ] a δ e δ r ] T I.e. the output of the angular velocity control system.
5. L-based according to claim 1 1 The adaptive dynamic inverse variant aircraft control method is characterized in that the specific process of the step (4) is as follows:
neglecting the additional force and the additional moment caused by the aircraft variant, neglecting the direct force generated by the deflection of the control surface, the aircraft equation corresponding to the attitude angle loop can be written as follows:
Figure QLYQS_48
wherein:
Figure QLYQS_49
Figure QLYQS_50
is->
Figure QLYQS_51
The expression of the part which is irrelevant to p, q and r in the expression,
Figure QLYQS_52
a coefficient matrix related to p, q and r; in order to make the aircraft output state track the attitude angle expected value alpha well ccc
Figure QLYQS_53
Will be expected by them in a gesture control systemValue->
Figure QLYQS_54
Instead, the desired dynamics have the form:
Figure QLYQS_55
Figure QLYQS_56
Figure QLYQS_57
Figure QLYQS_58
the three paths of the loop are of a three-way bandwidth for the attitude angle;
definition of the definition
Figure QLYQS_59
Middle [ pqr] T =[p c q c r c ] T ,/>
Figure QLYQS_60
The output of the attitude control system can thus be solved as:
Figure QLYQS_61
6. l-based according to claim 1 1 The adaptive dynamic inverse variant aircraft control method is characterized in that the specific process of the step (5) is as follows:
neglecting the additional forces and additional moments caused by aircraft variants, mu can first be solved directly c The method comprises the following steps of:
Figure QLYQS_62
Figure QLYQS_63
is the expected dynamics of track yaw acceleration;
then at mu c In the known case, it will be possible to obtain a composition containing only the variable alpha c Is a nonlinear equation of (2):
Figure QLYQS_64
newton iteration method for solving nonlinear equation can be used for solving attack angle command alpha c Finally, the thrust command T can be calculated c
Figure QLYQS_65
Wherein,,
Figure QLYQS_66
the aircraft acceleration and the aircraft track yaw angle acceleration and the aircraft track pitch angle acceleration are respectively +.>
Figure QLYQS_67
In the expected value of the maneuver generator->
Figure QLYQS_68
Will be summed by linear feedback and L 1 The self-adaptive control method comprises the following steps:
recording speed tracking error e V (t)=V(t)-V r (t) wherein V r (t) redefining a velocity error vector for the velocity command signal:
Figure QLYQS_69
according to the definition above, the following error dynamic system equation is further available:
Figure QLYQS_70
wherein:
Figure QLYQS_71
respectively a system matrix and an input matrix;
the control inputs of the error system are:
Figure QLYQS_72
further available are speed channel outer loop control command signals:
Figure QLYQS_73
solving the feedback gain k by LQ method V The following main control system speed channel control law can be obtained:
Figure QLYQS_74
adding in
Figure QLYQS_75
In the case of an auxiliary control system, the control input comprises two parts,:
u V (t)=u V,b (t)+u V,a (t)
i.e. the main control system control input u V,b (t) and control input u of the auxiliary control system V,a (t); substituting the control law u of the main control system V,b (t) after introducing both the uncertainty of the input gain and the input disturbance, obtaining the following error dynamics system:
Figure QLYQS_76
wherein A is m,V =A V -b V k V ,
Figure QLYQS_77
To characterize the unknown real number of the input gain; />
Figure QLYQS_78
As a time-varying parameter vector,
Figure QLYQS_79
representing an input disturbance related to a system state; />
Figure QLYQS_80
Representing an exogenous input disturbance;
from the above error dynamics system can be obtained
Figure QLYQS_81
The control law of the auxiliary control system is as follows:
Figure QLYQS_82
wherein r is V (s) and
Figure QLYQS_83
respectively the reference signals r V Laplace transform of (t)
Figure QLYQS_84
For feedback gain, D V (s) is a transfer function of strict true component, ">
Figure QLYQS_85
Respectively represent the pair omega V ,/>
Figure QLYQS_86
σ V An estimate of (t);
establishment of
Figure QLYQS_87
Is the adaptive law of (1):
Figure QLYQS_88
Figure QLYQS_89
Figure QLYQS_90
Figure QLYQS_91
representing an estimation error of the system state +.>
Figure QLYQS_92
Is self-adaptive law, P V Is algebraic Lyapunov equation->
Figure QLYQS_93
Solution of Q V For any symmetric positive definite matrix, proj is projection operator;
for the track angle control channel, including the track inclination angle channel and the track yaw angle channel, the track error of the track angle and the corresponding error value vector can be defined similarly, and the error power system of the track angle can be derived, so that the control signal of the track angle channel can be further obtained.
7. L-based according to claim 2 1 The method for controlling the adaptive dynamic reverse variant aircraft is characterized in that the calculation modes of the forces and the moments born by the variant aircraft are as follows:
aerodynamic forces including side force Y, drag force D and lift force L, aerodynamic moments including roll moment
Figure QLYQS_94
Pitching moment M and yawing moment N;
the aerodynamic force and moment module calculates aerodynamic coefficients on a stable shaft by using feedback data from the inside of the flight simulation system, and finally calculates aerodynamic force and moment on a machine body shaft and outputs the aerodynamic force and moment to the six-degree-of-freedom motion model module of the aircraft; aerodynamic force is calculated mainly according to aerodynamic pressure and aerodynamic coefficient on a stable shaft; the aerodynamic coefficient calculation formulas are respectively as follows:
Figure QLYQS_95
the calculation formulas of lift force, resistance and side force are respectively as follows:
Figure QLYQS_96
the aerodynamic moment is calculated mainly according to aerodynamic pressure and aerodynamic moment coefficient on the stable shaft, wherein the pitching moment coefficient, the rolling moment coefficient and the yaw moment coefficient are calculated according to the following formula:
Figure QLYQS_97
the calculation formulas of the pitching moment, the rolling moment and the yawing moment are respectively as follows:
Figure QLYQS_98
wherein ρ is air density, S is wing area, b is wing span length, c is average aerodynamic chord length of the wing; c (C) L 、C D 、C Y 、C m 、C l 、C n Respectively being the lift coefficient, drag coefficient, side force coefficient, pitch moment coefficient, roll moment coefficient and yaw moment coefficient of the variant aircraft, eta being a measure of the deformation of the variant aircraft,
Figure QLYQS_99
Figure QLYQS_100
respectively C L 、C D 、C Y 、C m 、C l 、C n The corresponding aerodynamic coefficients in the expression vary with the shape of the aircraft.
CN202211475942.6A 2022-11-23 2022-11-23 L-based 1 Adaptive dynamic inverse variant aircraft control method Pending CN116300992A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118112513A (en) * 2024-04-30 2024-05-31 山东科技大学 Radar signal-to-noise ratio calculation method for detecting unmanned aerial vehicle target
CN118131649A (en) * 2024-05-10 2024-06-04 西北工业大学宁波研究院 Intelligent deformation decision method for variable-length aircraft under pneumatic uncertainty

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN118112513A (en) * 2024-04-30 2024-05-31 山东科技大学 Radar signal-to-noise ratio calculation method for detecting unmanned aerial vehicle target
CN118112513B (en) * 2024-04-30 2024-07-19 山东科技大学 Radar signal-to-noise ratio calculation method for detecting unmanned aerial vehicle target
CN118131649A (en) * 2024-05-10 2024-06-04 西北工业大学宁波研究院 Intelligent deformation decision method for variable-length aircraft under pneumatic uncertainty

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