CN112319795A - Composite structure aircraft with tiltable rotor wing - Google Patents

Composite structure aircraft with tiltable rotor wing Download PDF

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CN112319795A
CN112319795A CN202011369672.1A CN202011369672A CN112319795A CN 112319795 A CN112319795 A CN 112319795A CN 202011369672 A CN202011369672 A CN 202011369672A CN 112319795 A CN112319795 A CN 112319795A
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CN112319795B (en
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雷瑶
王家鼎
冯志成
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Fuzhou University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/22—Compound rotorcraft, i.e. aircraft using in flight the features of both aeroplane and rotorcraft
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/32—Rotors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64C—AEROPLANES; HELICOPTERS
    • B64C27/00—Rotorcraft; Rotors peculiar thereto
    • B64C27/52—Tilting of rotor bodily relative to fuselage
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
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    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
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Abstract

The invention provides a composite structure aircraft with a tiltable rotor wing, wherein a fuselage of the aircraft comprises a main wing and an empennage for air cruise; the main wing is arranged at the middle section of the fuselage; the empennage is arranged at the tail part of the machine body; the aircraft is also provided with a rotor wing for providing power for the aircraft; the rotor wing comprises a first rotor wing group arranged at the fixed wing and a second rotor wing group arranged at the rear part of the fuselage; when the aircraft takes off or lands, the orientations of the rotors in the first rotor group and the second rotor group are vertical so as to provide lift force for the aircraft body, and when the aircraft is in an air cruise state, the orientations of the rotors in the second rotor group are adjusted to be horizontal so as to provide thrust for the aircraft; the invention better integrates the advantages of the fixed wing aircraft and the rotor aircraft, and improves the prior control system, so that the invention has higher reliability, anti-interference performance and control performance.

Description

Composite structure aircraft with tiltable rotor wing
Technical Field
The invention relates to the technical field of aircrafts, in particular to an aircraft with a composite structure and a tiltable rotor wing.
Background
Fixed wing unmanned vehicles and rotor unmanned vehicles have long played an important role in military and civilian applications as representative of conventional unmanned vehicle structures. However, their applications are always limited by flexibility, payload and endurance, which are associated with their own typical structure and power system. For example, the rotorcraft has short-distance take-off and landing capability, but has short endurance time. Although the fixed-wing unmanned aerial vehicle has long endurance time, the use is limited by a flight field, and the flexibility is poor.
Disclosure of Invention
The invention provides an aircraft with a tiltable rotor wing and a composite structure, which better integrates the advantages of a fixed wing aircraft and a rotor wing aircraft, and improves the existing control system to ensure that the aircraft has higher reliability, anti-interference performance and control performance.
The invention adopts the following technical scheme.
A composite structure aircraft with tiltable rotors, the aircraft body comprising main wings and empennage for air cruise; the main wing is arranged at the middle section of the fuselage; the empennage is arranged at the tail part of the machine body; the aircraft is also provided with a rotor wing for providing power for the aircraft; the rotor wing comprises a first rotor wing group arranged at the fixed wing and a second rotor wing group arranged at the rear part of the fuselage; when the aircraft takes off or lands, the orientation of each rotor in first rotor group, the second rotor group is vertical in order to provide lift to the fuselage, when the aircraft is in the air state of cruising, each rotor orientation in the second rotor group is adjusted to the horizontal direction, provides thrust for the aircraft.
The orientation of each rotor in the first rotor group is fixed to be vertical.
Each rotor wing in the first rotor wing group is fixed at the front part of the main wing; each rotor in the second rotor group is fixed at the root of the empennage.
The main wing and the empennage respectively comprise wing surface parts with variable angles, and the main wing forms an elevator by the wing surface parts with the variable angles; the empennage forms a rudder at the airfoil part with a variable angle; when the aircraft is in the air cruise state, each rotor in the first rotor group is in a shutdown state.
The tail part of the machine body is provided with a connecting rod mechanism connected with the second rotor wing group; the link mechanism can synchronously adjust the orientation of each rotor in the second rotor group, so that the rotors can be switched between the horizontal direction and the vertical direction.
The first rotor wing group and the second rotor wing group are both composed of two rotor wings driven by small rotors; the aircraft is an unmanned aerial vehicle, and the body of the unmanned aerial vehicle is provided with an automatic pilot, a sensing assembly and a remote control assembly for communicating with the ground station; the sensing assembly comprises a speed sensor, a global positioner, an inertial measurement unit and a pressure sensor; the autopilot measures aircraft operating conditions via the sensing assembly to optimize control of the aircraft.
The aircraft further comprises a linear model-based controller; the controller controls the flight of the aircraft based on a flight control law combining a Robust Servo Linear Quadratic Regulator (RSLQR) and an Extended State Observer (ESO).
The dynamics model in the flight control law is a non-linear dynamics model that is attached to the aircraft with a fuselage fixed frame BFFBy representing the inertially fixed frame EFF as OgxgygzgThe origin point is set at the starting point; establishing a coordinate system O of four auxiliary frames AFsixtiytizti(i ═ 1,2,3,4), based on considerations of tilt angle and roll angle, ztiThe shaft is along the propeller axis of the rotor; x is the number oftiThe axis being parallel to the longitudinal plane of the drone, perpendicular to ztiThe axis is vertical to the paper surface and faces outwards; y istiThe axis is determined by the right hand rule; the transformation matrix between the coordinate systems is set by the coordinate transformation principle between different coordinate systems as follows:
Figure BDA0002805694760000021
phi, theta, psi represent euler angles, c and s are the signs of the cosine and sine functions respectively, eta is a fixed roll angle for the propulsion system to improve its controllability, epsilon is the angle of inclination of the rotor;
the nonlinear dynamical model can be derived as a newton-euler formula, and the inertially fixed framework can be expressed as:
Figure BDA0002805694760000022
where m is the mass of the aircraft,
Figure BDA0002805694760000023
and
Figure BDA0002805694760000024
respectively representing resultant and resultant moment vectors, V, in inertially-fixed framesb＝[u,v,w]TIs the velocity vector, ωb＝[p,q,r]TAs an attitude angular rate vector, IbIs a rigid body inertia matrix, which can be expressed as follows:
Figure BDA0002805694760000031
the forces F and moments M represented in the fuselage-fixed frame are generated by the gyroscopic effect caused by the effects of gravity, the propulsion system, the aerodynamics and the rotor tilting, and can be represented as:
Figure BDA0002805694760000032
wherein all components and moments take the form shown below
The gravitational force in an inertially fixed frame can be expressed as:
Figure BDA0002805694760000033
the second rotor group is a propulsion system when the aircraft is cruising in the air, the propulsion vector of the propulsion system is expressed by using a rotation matrix between the auxiliary frame and the airframe fixed frame BFF, the thrust vector can be decomposed along the airframe fixed frame, and the following formula is obtained,
Figure BDA0002805694760000034
wherein, Ti aFor thrust vectors represented by auxiliary frames, TiIs the thrust value, δiFor motor throttling, gTi(. is an experimentally determined mathematical relationship; the torque vector produced by the propulsion system may be expressed as:
Figure BDA0002805694760000035
wherein
Figure BDA0002805694760000036
Moment vector generated for thrust vector, diIs the position vector, τ, from the gear to each rotor axisiIndicating rotor air resistanceThe moment of the force is generated by the force,
Figure BDA0002805694760000037
representing the moment vectors in the auxiliary frames AFs,
Figure BDA0002805694760000038
representing a moment vector in a fuselage fixed frame (BFF);
the rotor rotation of the rotor in the propulsion system produces a gyroscopic precessional moment effect. The expression of the moment vector is as follows:
Figure BDA0002805694760000039
wherein JriIs the moment of inertia, omega, of the propulsion assembly about its axisiRepresenting the angular velocity vector of the rotor in the Auxiliary Frames (AFs);
when a rudder factor is introduced in a flight model, the aerodynamic forces and moments of the aircraft are as follows:
Figure BDA0002805694760000041
wherein Q is dynamic pressure, α is angle of attack, β is sideslip angle, δα、δeAnd deltarThe deflection angles of the ailerons, the elevators and the rudders, respectively;
let ζ be [ x, y, z ]]TRepresenting the position vector of the airplane in the inertia fixed frame, the translational motion equation and the rotational motion equation can be expressed as follows according to the conversion relation between the coordinate systems:
Figure BDA0002805694760000042
based on the above, the 6-degree-of-freedom nonlinear dynamical equation of the flight model system can be described in the form of a first-order vector differential equation:
Figure BDA0002805694760000043
where x is the state variable u, v, w, p, q, r, phi, theta, psi, xg,yg,zgU is the vector of the input variables, including motor throttles δ 1, δ 2, δ 3 and δ 4 and control surface deflections δα、δe、δrThe transition mode when the aircraft is transitioning from airborne cruise to take-off and landing operations and the fixed-wing mode when the aircraft is airborne cruise are considered.
The linear controller performs control distribution based on channel throttling and balancing calculation, and specifically comprises a vertical channel deltaHPitch channel deltaθTumble passage deltaφYaw channel deltaψ，
The relationship between the virtual control inputs of the four channels and the actual throttling of the propeller is established as follows:
Figure BDA0002805694760000051
wherein deltaHi,δθi,δφi,δψi(i ═ 1,2,3,4) are vertical channels δ, respectivelyHPitch channel deltaθTumble passage deltaφYaw channel deltaψThe weight of the throttle valve of (a);
when the aircraft is in a state of equilibrium,
Figure BDA0002805694760000056
based on the nonlinear dynamical equation in equation 11, the following disturbance equilibrium equation can be obtained:
Figure BDA0002805694760000052
wherein Δ (·) ═ (-) - (·)op"op" represents an operating point;
from the above description, the trimming conditions for the four channels can be expressed as:
Figure BDA0002805694760000053
when the aircraft is set to work in a rotorcraft mode, the efficiency of the pneumatic effect device and the gyroscopic effect device is negligibly low; when the aircraft is set to operate in helicopter mode, epsilon, theta and phi are equal to zero; assuming that the smaller higher order terms are considered negligible, one can get:
Figure BDA0002805694760000054
wherein
Figure BDA0002805694760000055
If two rotors are arranged in the first rotor group and are respectively driven by the first motor and the second motor, and the first motor and the second motor firstly reach the maximum capacity due to the asymmetry of the geometric parameters of the first rotor group and the second rotor group, the weight coefficient of each channel can be obtained based on the first motor, and the calculation result is as follows:
Figure BDA0002805694760000061
finally, the control distribution relationship between the channel input and the actual throttle valve can be obtained by substituting equation 17 into equation 13.
When the aircraft works in a rotorcraft mode, if a state vector needs to be introduced for attitude control and altitude control, the nonlinear dynamical equation in the formula 11 is segmented to obtain
Figure BDA0002805694760000062
And an input vector
Figure BDA0002805694760000063
The flight model system can be expressed as
Figure BDA0002805694760000064
The flight model system is linearized at the equilibrium operating point, expanded by a taylor series and truncated in the first order term. Thus, the linearized flight model system is shown in the following equation:
Figure BDA0002805694760000065
wherein,
Figure BDA0002805694760000066
the linearized system equations for the aircraft model system may be further expressed based on equation 19 as
Figure BDA0002805694760000067
Wherein y iscIs the output vector, CcIs the corresponding transition matrix;
the control method based on the robust servo linear quadratic regulator RSLQR is obtained by introducing a state deviation into a system on the basis of the control method of the linear quadratic regulator LQR, wherein the state deviation can be adjusted to zero, so that a system state variable can accurately track an input command;
if the deviation is assumed to be e-rc-ycWhere r is a control command, the aircraft state equation may be defined as:
Figure BDA0002805694760000068
wherein
Figure BDA0002805694760000069
The cost function of the robust servo linear quadratic regulator RSLQR control is given by:
Figure BDA0002805694760000071
wherein Q and R are weight matrices; a control system of the controller selects a matrix R as an identity matrix and a matrix Q as a diagonal matrix; the values in the matrix Q are scaled using the bulison Bryson law; finally, the gain matrix for the robust servo linear quadratic regulator RSLQR control can be expressed as:
Kc＝[ki,kp]＝R-1BTp (formula 23)
Wherein k isi、kpAre different block matrices having the same dimensions e and
Figure BDA0002805694760000074
P(＝pT> 0) is the solution of the following algebraic ricatt equation:
PA+ATP-PBR-1BTp + Q ═ 0 (formula 24)
The optimal control input for the robust servo linear quadratic regulator RSLQR control is shown in equation 25 below,
Figure BDA0002805694760000072
the RSLQR control adds an integral element in a state feedback control loop to improve the system performance and the anti-interference capability;
the flight control law based on the RSLQR control can improve the dynamic performance and the steady-state performance of the control system; when designing the RSLQR control of the controller, firstly, extracting an angular velocity model and a vertical velocity model; then, designing an RSLQR controller for the angular speed and the speed ring or the inner ring;
the attitude and height loop control of the controller adopts a PI control method to improve the control precision;
in the roll channel of the controller, the PI gain of the control structure
Figure BDA0002805694760000075
And
Figure BDA0002805694760000076
the optimal damping ratio between the inner ring and the outer ring and the bandwidth matching relation are determined; they can be obtained by a PI parameter setting toolbox in MATLAB;
the controller uses an Extended State Observer (ESO) to estimate the state and the unknown total interference, and then compensates the initial control quantity of the RSLQR to obtain the final control input so as to improve the capacity of resisting disturbance and uncertain factors,
by the perturbation condition expressed by equation 18, the following second order nonlinear system can be obtained:
Figure BDA0002805694760000073
where x1 represents a state variable for attitude or altitude, f (-) is the total disturbance of the system including model uncertainty and external disturbances,
Figure BDA0002805694760000081
representing the control input, b is the magnification; the total disturbance experienced by the controller system is then expanded to a new state variable x3And let
Figure BDA0002805694760000082
The new system can be expressed as follows:
Figure BDA0002805694760000083
for the system with the controller expanded, there are the following extended state observers:
Figure BDA0002805694760000084
wherein Z is [ Z ]1,z2,z3]TIs the extended state vector X ═ X1,x2,x3]TEstimate of (1), beta1,β2,β3Is the observer gain, a nonlinear function fal (e, α)iδ) can be expressed as:
Figure BDA0002805694760000085
wherein alpha is1、α2And δ is a parameter of a nonlinear function fal (·), α represents a nonlinear shape, and α is taken1＝0.5、α2δ determines the width of the linear interval around the origin, 0.25; observer parameter betaiDetermines the state xiThe tracking speed of (2); increase beta appropriately1And beta2Can effectively inhibit beta3Excessive observer oscillations. The three parameters are adjusted in a coordinated manner, so that the expansion state x is observed in real time by adjusting the parameters3；
After obtaining an estimate z of the total disturbance3Then, the output is output to the RSLQR controller
Figure BDA0002805694760000086
The real-time control quantity can be obtained by the disturbance compensation of (1):
Figure BDA0002805694760000087
by substituting equation 30 into equation 25, the nonlinear control system becomes a linear integral series system, which is called dynamic compensation linearization, expressed as
Figure BDA0002805694760000088
Compared with the prior art, the invention better integrates the advantages of a fixed wing aircraft and a rotor aircraft, and improves the existing control system, so that the control system has higher reliability, anti-interference performance and control performance.
The invention adopts a structure combining the fixed wing, the tiltable rotor wing and the non-tiltable rotor wing, and the vertical lifting can be realized under the condition of no runway; when the aircraft is vertically lifted, the two pairs of rotors run simultaneously, and when the aircraft is cruising, only one pair of rotors located at the root of the empennage runs. By combining the rotor wing and the fixed wing, the endurance time of the aircraft is increased, and the engineering application prospect of the aircraft is widened. Meanwhile, the invention provides an improved flight control law combining the optimal control of the robust servo linear secondary regulator and the extended state observer, and the control performance and the engineering reliability are improved.
In engineering practice, the PID control is still widely used, however, the performance of the PID method control is not ideal, and the problems of actuator saturation and uncertain interference which often occur in actual flight tests cannot be solved. How to design a better linear controller to solve these practical problems, and improving the control performance is the focus of the present invention. The invention provides an improved flight control law based on combination of RSLQR and ESO to control the flight of a novel unmanned aerial vehicle. Similar to PID control, the controller designed by the invention is a linear control method, and has the characteristics of low cost and easy realization. The problems of actuator saturation and uncertain disturbance are solved, and the control performance in actual flight is improved. Therefore, the proposed flight control laws have broad prospects in the engineering application of tiltrotor aircraft.
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The invention is described in further detail below with reference to the following figures and detailed description:
FIG. 1 is a schematic structural view of the aircraft of the present invention;
FIG. 1a is a schematic view of the rotor orientation adjustment of a second rotor set of the aircraft of the present invention;
FIG. 2 is a schematic representation of a reference coordinate system corresponding to the aircraft structure of the present invention;
FIG. 3 is a control schematic diagram of the robust servo-based linear quadratic regulator of the present invention;
FIG. 4 is a schematic roll angle control of the present invention;
FIG. 5 is a Robust Servo Linear Quadratic Regulator (RSLQR) control schematic based on an Extended State Observer (ESO);
FIG. 6 is a schematic representation of the working principle of the aircraft according to the invention;
in the figure: 1-a first rotor set; 2-a fuselage; 3-main wing; 4-tail fin; 5-a second rotor set; 6-a linkage mechanism; 7-elevator; 8-rudder;
Detailed Description
As shown in the figures, a tiltrotor composite structure aircraft, the fuselage of which comprises a main wing and a tail wing for air cruise; the main wing is arranged at the middle section of the fuselage; the empennage is arranged at the tail part of the machine body; the aircraft is also provided with a rotor wing for providing power for the aircraft; the rotor wing comprises a first rotor wing group arranged at the fixed wing and a second rotor wing group arranged at the rear part of the fuselage; when the aircraft takes off or lands, the orientation of each rotor in first rotor group, the second rotor group is vertical in order to provide lift to the fuselage, when the aircraft is in the air state of cruising, each rotor orientation in the second rotor group is adjusted to the horizontal direction, provides thrust for the aircraft.
The orientation of each rotor in the first rotor group is fixed to be vertical.
Each rotor wing in the first rotor wing group is fixed at the front part of the main wing; each rotor in the second rotor group is fixed at the root of the empennage.
The main wing and the empennage respectively comprise wing surface parts with variable angles, and the main wing forms an elevator by the wing surface parts with the variable angles; the empennage forms a rudder at the airfoil part with a variable angle; when the aircraft is in the air cruise state, each rotor in the first rotor group is in a shutdown state.
The tail part of the machine body is provided with a connecting rod mechanism connected with the second rotor wing group; the link mechanism can synchronously adjust the orientation of each rotor in the second rotor group, so that the rotors can be switched between the horizontal direction and the vertical direction.
The first rotor wing group and the second rotor wing group are both composed of two rotor wings driven by small rotors; the aircraft is an unmanned aerial vehicle, and the body of the unmanned aerial vehicle is provided with an automatic pilot, a sensing assembly and a remote control assembly for communicating with the ground station; the sensing assembly comprises a speed sensor, a global positioner, an inertial measurement unit and a pressure sensor; the autopilot measures aircraft operating conditions via the sensing assembly to optimize control of the aircraft.
The aircraft further comprises a linear model-based controller; the controller controls the flight of the aircraft based on a flight control law combining a Robust Servo Linear Quadratic Regulator (RSLQR) and an Extended State Observer (ESO).
The dynamics model in the flight control law is a non-linear dynamics model, which uses a fixed frame BFF of the fuselage to be attached to the gravity center position CoG of the aircraft to establish a coordinate system, and the method is to represent an inertia fixed frame EFF as OgxgygzgThe origin point is set at the starting point; establishing a coordinate system O of four auxiliary frames AFsixtiytizti(i ═ 1,2,3,4), based on considerations of tilt angle and roll angle, ztiThe shaft is along the propeller axis of the rotor; x is the number oftiThe axis being parallel to the longitudinal plane of the drone, perpendicular to ztiThe axis is vertical to the paper surface and faces outwards; y istiThe axis is determined by the right hand rule; the transformation matrix between the coordinate systems is set by the coordinate transformation principle between different coordinate systems as follows:
Figure BDA0002805694760000101
phi, theta, psi represent euler angles, c and s are the signs of the cosine and sine functions respectively, eta is a fixed roll angle for the propulsion system to improve its controllability, epsilon is the angle of inclination of the rotor;
the nonlinear dynamical model can be derived as a newton-euler formula, and the inertially fixed framework can be expressed as:
Figure BDA0002805694760000111
where m is the aircraft mass，
Figure BDA0002805694760000112
And
Figure BDA0002805694760000113
respectively representing resultant and resultant moment vectors, V, in inertially-fixed framesb＝[u,v,w]TIs the velocity vector, ωb＝[p,q,r]TAs an attitude angular rate vector, IbIs a rigid body inertia matrix, which can be expressed as follows:
Figure BDA0002805694760000114
the forces F and moments M represented in the fuselage-fixed frame are generated by the gyroscopic effect caused by the effects of gravity, the propulsion system, the aerodynamics and the rotor tilting, and can be represented as:
Figure BDA0002805694760000115
wherein all components and moments take the form shown below
The gravitational force in an inertially fixed frame can be expressed as:
Figure BDA0002805694760000116
the second rotor group is a propulsion system when the aircraft is cruising in the air, the propulsion vector of the propulsion system is expressed by using a rotation matrix between the auxiliary frame and the airframe fixed frame BFF, the thrust vector can be decomposed along the airframe fixed frame, and the following formula is obtained,
Figure BDA0002805694760000117
wherein, Ti aFor thrust vectors represented by auxiliary frames, TiIs the thrust value, δiFor motor throttling, gTi(. is an experimentally determined mathematical relationship; the torque vector produced by the propulsion system may be expressed as:
Figure BDA0002805694760000118
wherein
Figure BDA0002805694760000119
Moment vector generated for thrust vector, diIs the position vector, τ, from the gear to each rotor axisiThe moment caused by the air resistance of the rotor is shown,
Figure BDA00028056947600001110
representing the moment vectors in the auxiliary frames AFs,
Figure BDA00028056947600001111
representing a moment vector in a fuselage fixed frame (BFF);
the rotor rotation of the rotor in the propulsion system produces a gyroscopic precessional moment effect. The expression of the moment vector is as follows:
Figure BDA0002805694760000121
wherein JriIs the moment of inertia, omega, of the propulsion assembly about its axisiRepresenting the angular velocity vector of the rotor in the Auxiliary Frames (AFs);
when a rudder factor is introduced in a flight model, the aerodynamic forces and moments of the aircraft are as follows:
Figure BDA0002805694760000122
wherein Q is dynamic pressure, α is angle of attack, β is sideslip angle, δα、δeAnd deltarYaw angles of ailerons, elevators and rudders, respectively；
Let ζ be [ x, y, z ]]TRepresenting the position vector of the airplane in the inertia fixed frame, the translational motion equation and the rotational motion equation can be expressed as follows according to the conversion relation between the coordinate systems:
Figure BDA0002805694760000123
based on the above, the 6-degree-of-freedom nonlinear dynamical equation of the flight model system can be described in the form of a first-order vector differential equation:
Figure BDA0002805694760000124
where x is the state variable u, v, w, p, q, r, phi, theta, psi, xg,yg,zgU is the vector of the input variables, including motor throttles δ 1, δ 2, δ 3 and δ 4 and control surface deflections δα、δe、δrThe transition mode when the aircraft is transitioning from airborne cruise to take-off and landing operations and the fixed-wing mode when the aircraft is airborne cruise are considered.
The linear controller performs control distribution based on channel throttling and balancing calculation, and specifically comprises a vertical channel deltaHPitch channel deltaθTumble passage deltaφYaw channel deltaψ，
The relationship between the virtual control inputs of the four channels and the actual throttling of the propeller is established as follows:
Figure BDA0002805694760000131
wherein deltaHi,δθi,δφi,δψi(i ═ 1,2,3,4) are vertical channels δ, respectivelyHPitch channel deltaθTumble passage deltaφYaw channel deltaψThe weight of the throttle valve of (a);
when the aircraft is in equilibriumIn the state of the electric power generating device,
Figure BDA0002805694760000132
based on the nonlinear dynamical equation in equation 11, the following disturbance equilibrium equation can be obtained:
Figure BDA0002805694760000133
wherein Δ (·) ═ (-) - (·)op"op" represents an operating point;
from the above description, the trimming conditions for the four channels can be expressed as:
Figure BDA0002805694760000134
when the aircraft is set to work in a rotorcraft mode, the efficiency of the pneumatic effect device and the gyroscopic effect device is negligibly low; when the aircraft is set to operate in helicopter mode, epsilon, theta and phi are equal to zero; assuming that the smaller higher order terms are considered negligible, one can get:
Figure BDA0002805694760000136
wherein
Figure BDA0002805694760000135
If two rotors are arranged in the first rotor group and are respectively driven by the first motor and the second motor, and the first motor and the second motor firstly reach the maximum capacity due to the asymmetry of the geometric parameters of the first rotor group and the second rotor group, the weight coefficient of each channel can be obtained based on the first motor, and the calculation result is as follows:
Figure BDA0002805694760000141
finally, the control distribution relationship between the channel input and the actual throttle valve can be obtained by substituting equation 17 into equation 13.
When the aircraft works in a rotorcraft mode, if a state vector needs to be introduced for attitude control and altitude control, the nonlinear dynamical equation in the formula 11 is segmented to obtain
Figure BDA0002805694760000142
And an input vector
Figure BDA0002805694760000143
The flight model system can be expressed as
Figure BDA0002805694760000144
The flight model system is linearized at the equilibrium operating point, expanded by a taylor series and truncated in the first order term. Thus, the linearized flight model system is shown in the following equation:
Figure BDA0002805694760000145
wherein,
Figure BDA0002805694760000146
the linearized system equations for the aircraft model system may be further expressed based on equation 19 as
Figure BDA0002805694760000147
Wherein y iscIs the output vector, CcIs the corresponding transition matrix;
the control method based on the robust servo linear quadratic regulator RSLQR is obtained by introducing a state deviation into a system on the basis of the control method of the linear quadratic regulator LQR, wherein the state deviation can be adjusted to zero, so that a system state variable can accurately track an input command;
if the deviation is assumed to be e-rc-ycWhere r is a control command, the aircraft state equation may be defined as:
Figure BDA0002805694760000148
wherein
Figure BDA0002805694760000149
The cost function of the robust servo linear quadratic regulator RSLQR control is given by:
Figure BDA0002805694760000151
wherein Q and R are weight matrices; a control system of the controller selects a matrix R as an identity matrix and a matrix Q as a diagonal matrix; the values in the matrix Q are scaled using the bulison Bryson law; finally, the gain matrix for the robust servo linear quadratic regulator RSLQR control can be expressed as:
Kc＝[ki,kp]＝R-1BTp (formula 23)
Wherein k isi、kpAre different block matrices having the same dimensions e and
Figure BDA0002805694760000152
P(＝pT> 0) is the solution of the following algebraic ricatt equation:
PA+ATP-PBR-1BTp + Q ═ 0 (formula 24)
The optimal control input for the robust servo linear quadratic regulator RSLQR control is shown in equation 25 below,
Figure BDA0002805694760000153
the RSLQR control adds an integral element in a state feedback control loop to improve the system performance and the anti-interference capability;
the flight control law based on the RSLQR control can improve the dynamic performance and the steady-state performance of the control system; when designing the RSLQR control of the controller, firstly, extracting an angular velocity model and a vertical velocity model; then, designing an RSLQR controller for the angular speed and the speed ring or the inner ring;
the attitude and height loop control of the controller adopts a PI control method to improve the control precision;
in the roll channel of the controller, the PI gain of the control structure
Figure BDA0002805694760000154
And
Figure BDA0002805694760000155
the optimal damping ratio between the inner ring and the outer ring and the bandwidth matching relation are determined; they can be obtained by a PI parameter setting toolbox in MATLAB;
the controller uses an Extended State Observer (ESO) to estimate the state and the unknown total interference, and then compensates the initial control quantity of the RSLQR to obtain the final control input so as to improve the capacity of resisting disturbance and uncertain factors,
by the perturbation condition expressed by equation 18, the following second order nonlinear system can be obtained:
Figure BDA0002805694760000156
where x1 represents a state variable for attitude or altitude, f (-) is the total disturbance of the system including model uncertainty and external disturbances,
Figure BDA0002805694760000161
representing the control input, b is the magnification; the total disturbance experienced by the controller system is then expanded to a new state variable x3And let
Figure BDA0002805694760000162
The new system can be expressed as follows:
Figure BDA0002805694760000163
for the system with the controller expanded, there are the following extended state observers:
Figure BDA0002805694760000164
wherein Z is [ Z ]1,z2,z3]TIs the extended state vector X ═ X1,x2,x3]TEstimate of (1), beta1,β2,β3Is the observer gain, a nonlinear function fal (e, α)iδ) can be expressed as:
Figure BDA0002805694760000165
wherein alpha is1、α2And δ is a parameter of a nonlinear function fal (·), α represents a nonlinear shape, and α is taken1＝0.5、α2δ determines the width of the linear interval around the origin, 0.25; observer parameter betaiDetermines the state xiThe tracking speed of (2); increase beta appropriately1And beta2Can effectively inhibit beta3Excessive observer oscillations. The three parameters are adjusted in a coordinated manner, so that the expansion state x is observed in real time by adjusting the parameters3；
After obtaining an estimate z of the total disturbance3Then, the output is output to the RSLQR controller
Figure BDA0002805694760000168
The real-time control quantity can be obtained by the disturbance compensation of (1):
Figure BDA0002805694760000166
by substituting equation 30 into equation 25, the nonlinear control system becomes a linear integral series system, which is called dynamic compensation linearization, expressed as
Figure BDA0002805694760000167
Example 1:
in this example only one pair of tiltable rotors is used to meet the thrust requirement, which means fewer mechanisms, lower cost, lower power consumption and longer flight time. As shown in fig. 1, propulsion system rotors 3 and 4 may be tilted from a vertical position (e 0) to a horizontal position (e 90) or vice versa via a four-bar linkage. When the aircraft enters a fixed wing aircraft mode, the rotors 1 and 2 stop working; at the same time, rotors 3 and 4 power the aircraft. The present invention uses a smaller rotor than a conventional aircraft to meet the low thrust-to-weight ratio requirements during cruise flight, thereby reducing aircraft weight and improving cruise efficiency.
Example 2:
in aircraft modeling work, this example has a fuselage-fixed frame (BFF) attached to the aircraft's center of gravity position (CoG). The inertially fixed frame (EFF) is denoted OgxgygzgThe origin is set at the starting point. Unlike other similar works, a coordinate system O of four Auxiliary Frames (AFs) is establishedixtiytizti( i 1,2,3,4) taking into account the inclination angle and the roll angle, ztiThe shaft is along the propeller axis. x is the number oftiThe axis being parallel to the longitudinal plane of the drone, perpendicular to ztiThe axis is perpendicular to the paper and out. y istiThe axes are determined by the right hand rule. The reference coordinate system is shown in figure 2. According to the principle of coordinate transformation, a transformation matrix between coordinate systems is given:
Figure BDA0002805694760000171
phi, theta, psi represent euler angles, c and s are the signs of the cosine and sine functions, respectively, eta is a fixed roll angle for the propulsion system to improve its controllability, and epsilon is the angle of inclination of the rotor.
The nonlinear dynamic model of the composite structure aircraft can be derived as a Newton-Euler formula, and the inertia fixed frame can be expressed as:
Figure BDA0002805694760000181
where m is the mass of the aircraft,
Figure BDA0002805694760000182
and
Figure BDA0002805694760000183
respectively representing resultant and resultant moment vectors, V, in inertially-fixed framesb＝[u,v,w]TIs the velocity vector, ωb＝[p,q,r]TAs an attitude angular rate vector, IbIs a rigid body inertia matrix, which can be expressed as follows:
Figure BDA0002805694760000184
the forces and moments represented in the fuselage fixed frame are generated by the gyroscopic effect caused by gravity, the propulsion system, the aerodynamics and the rotor tilting action, which can be represented as:
Figure BDA0002805694760000185
wherein all components and moments are represented in the following form.
1. Gravity force
The gravitational force in an inertially fixed frame can be expressed as:
Figure BDA0002805694760000186
2. propulsion system
(ii) a propulsion vector
With the rotation matrix between the auxiliary frame and the fuselage fixed frame (BFF), the thrust vector can be decomposed along the fuselage fixed frame:
Figure BDA0002805694760000187
wherein, Ti aFor thrust vectors represented by auxiliary frames, TiIs the thrust value, δiFor motor throttling, gTi(. cndot.) is an experimentally determined mathematical relationship.
Moment vector-
The torque vector produced by the propulsion system may be expressed as:
Figure BDA0002805694760000191
wherein
Figure BDA0002805694760000192
Moment vector generated for thrust vector, diIs the position vector, τ, from the gear to each rotor axisiThe moment caused by the air resistance of the rotor is shown,
Figure BDA0002805694760000193
representing the moment vectors in the auxiliary frames AFs,
Figure BDA0002805694760000194
representing the moment vector in the fuselage fixed frame (BFF).
And thirdly, gyro moment.
Rotating the rotor produces a gyroscopic precessional moment effect. The expression of the moment vector is as follows:
Figure BDA0002805694760000195
wherein JriIs the moment of inertia, omega, of the propulsion assembly about its axisiRepresenting the angular velocity vector of the rotor in the Auxiliary Frames (AFs).
Air power and moment
The aerodynamic forces and moments of a tiltably-rotatable rotor composite structure aircraft, considering the rudder, are as follows:
Figure BDA0002805694760000201
wherein Q is dynamic pressure, α is angle of attack, β is sideslip angle, δα、δeAnd deltarThe deflection angles of the ailerons, elevators and rudder, respectively.
In addition, let ζ be [ x, y, z ]]TRepresenting the position vector of the aircraft in an inertially fixed frame. According to the conversion relationship between the coordinate systems, the translational motion equation and the rotational motion equation can be expressed as:
Figure BDA0002805694760000202
based on the above analysis, the 6-degree-of-freedom nonlinear dynamical equation of the system can be described in the form of a first-order vector differential equation:
Figure BDA0002805694760000203
where x is the state variable u, v, w, p, q, r, phi, theta, psi, xg,yg,zgU is the vector of the input variables, typically including motor throttles δ 1, δ 2, δ 3, and δ 4 and control surface deflections δα、δe、δrThey are considered in the transition mode and the fixed-wing mode.
Example 3:
in this embodiment, the following method is adopted when designing the controller:
control distribution strategy based on channel throttling and balancing calculation
The invention provides a control distribution method based on channel throttling and trim calculation for a composite structure aircraft with a tiltable rotor wing. First, the relationship between the virtual control inputs of the four channels and the actual throttling of the propeller is established as follows:
Figure BDA0002805694760000211
wherein deltaHi,δθi,δφi,δψi(i ═ 1,2,3,4) are vertical channels δ, respectivelyHPitch channel deltaθTumble passage deltaφYaw channel deltaψThe weight of the throttle valve.
When the aircraft is in equilibrium, i.e.
Figure BDA0002805694760000212
Based on the nonlinear dynamical equation (11), the following disturbance equilibrium equation is easily obtained:
Figure BDA0002805694760000213
wherein Δ (·) ═ (-) - (·)opAnd "op" represents an operation point.
From the above description, the trimming conditions for the four channels can be expressed as:
Figure BDA0002805694760000214
before solving the equation, the following assumptions need to be made. (1) In rotorcraft mode, the efficiency of the pneumatic and gyroscopic effectors is very low and therefore negligible. (2) Suppose in helicopter mode, ε, θ, and φ are equal to zero. (3) Ignoring the smaller higher order terms, one can get:
Figure BDA0002805694760000215
wherein
Figure BDA0002805694760000216
Due to the geometric asymmetry, the first and second motors reach maximum capacity first. Therefore, a weight coefficient for each channel can be obtained based on the first motor, and the calculation result is as follows:
Figure BDA0002805694760000221
finally, the control distribution relationship between the channel input and the actual throttle valve can be obtained by substituting equation (17) for equation (13).
② linearized model
For designing attitude and altitude controllers in rotorcraft mode, the nonlinear model (11) is segmented taking into account the state vectors to obtain
Figure BDA0002805694760000222
And an input vector
Figure BDA0002805694760000223
This creates a new system model:
Figure BDA0002805694760000224
since the controller is designed based on a linear model, the system (18) is linearized near the equilibrium operating point, expanded by a taylor series and truncated in the first order term. Thus, the linearized model is as follows:
Figure BDA0002805694760000225
wherein,
Figure BDA0002805694760000226
and controlling a Robust Servo Linear Quadratic Regulator (RSLQR).
Based on the model (19), the linearized system equation for the aircraft is given by:
Figure BDA0002805694760000227
wherein y iscIs the output vector, CcIs the corresponding transition matrix.
The Robust Servo Linear Quadratic Regulator (RSLQR) control method is developed by introducing state deviation into a system as a new variable on the basis of the Linear Quadratic Regulator (LQR) control method. In this way, the offset can be adjusted to zero so that the system state variables can accurately track the input commands. If the deviation is assumed to be e-rc-ycWhere r is a control instruction. The new state equation can be defined as:
Figure BDA0002805694760000231
wherein
Figure BDA0002805694760000232
The cost function of the robust servo linear quadratic regulator RSLQR control based on the new system is given by the following formula:
Figure BDA0002805694760000233
where Q and R are weight matrices. Weighting matrices are selected to characterize the performance of the control design, but techniques for applying these selected matrices are not yet mature. For engineering application convenience, according to the requirements of a control system, a matrix R is selected as an identity matrix, and a matrix Q is selected as a diagonal matrix. The values in the matrix Q are scaled using the bulison Bryson law. Finally, the gain matrix for the robust servo linear quadratic regulator RSLQR control can be expressed as:
Kc＝[ki,kp]＝R-1BTp (formula 23)
Wherein k isi、kpAre different block matrices having the same dimensions e and
Figure BDA0002805694760000234
P(＝pT> 0) is the solution of the following algebraic ricatt equation:
PA+ATP-PBR-1BTp + Q ═ 0 (formula 24)
The optimal control input for the robust servo linear quadratic regulator RSLQR control is shown in equation (25), and a schematic diagram of the robust servo linear quadratic regulator RSLQR state feedback control is shown in fig. 3:
Figure BDA0002805694760000235
as can be seen, the RSLQR control improves system performance and immunity to interference because it adds an integrating element to the state feedback control loop. Thus, a flight control law based on RSLQR control may improve the dynamic and steady-state performance of the control system. First, we can extract an angular velocity model and a vertical velocity model. The RSLQR controller is then designed for angular velocity and velocity rings (also referred to as inner rings). In addition, in order to meet the requirement of higher control precision, a mature and reliable PI control method is adopted for attitude and height loop control. Taking the roll channel as an example, the control structure is shown in FIG. 4, in which the PI gain
Figure BDA0002805694760000241
And
Figure BDA0002805694760000242
is determined by the optimal damping ratio and bandwidth matching relationship between the inner and outer rings. They can be obtained by PI parameter setting tool box in MATLABAnd (5) obtaining the product.
Robust servo linear quadratic regulator RSLQR control based on Extended State Observer (ESO)
Controllers based on the RSLQR control design do not work well under uncertain and noisy conditions because it is not possible to obtain a true state at all times. And then, the final control input is obtained by compensating the initial control quantity of the RSLQR, so that the capacity of resisting disturbance and uncertain factors can be effectively improved.
Taking into account the disturbance conditions of the system (18), the following second order nonlinear system can be obtained:
Figure BDA0002805694760000243
where x1 represents a state variable for attitude or altitude, f (-) is the total disturbance of the system including model uncertainty and external disturbances,
Figure BDA0002805694760000244
representing the control input, and b is the magnification. The total perturbation is then expanded into a new state variable x3And let
Figure BDA0002805694760000245
The new system can be expressed as follows:
Figure BDA0002805694760000246
for the extended system, the following extended state observer was designed:
Figure BDA0002805694760000247
wherein Z is [ Z ]1,z2,z3]TIs the extended state vector X ═ X1,x2,x3]TEstimate of (1), beta1,β2,β3Is the observer gain, a nonlinear function fal (e, α)iδ) can be expressed as:
Figure BDA0002805694760000248
wherein alpha is1、α2And δ is a parameter of a non-linear function fal (·), α representing a non-linear shape, typically α1＝0.5、α2δ is 0.25, which determines the width of the linear interval around the origin. If too large, large amplitude disturbance signals cannot be tracked. In contrast, high-frequency oscillation easily occurs near the origin. Observer parameter betaiDetermines the state xiThe tracking speed of (2). Furthermore, these parameters are mutually restrictive. Increase beta appropriately1And beta2Can effectively inhibit beta3Excessive observer oscillations. The three parameters are therefore adjusted in a coordinated manner, and by continuously adjusting these parameters, the observer can observe the state, in particular the extended state x, in real time3. The control structure is shown in fig. 5.
After obtaining an estimate z of the total disturbance3Then, the output is output to the RSLQR controller
Figure BDA0002805694760000251
The real-time control quantity can be obtained by the disturbance compensation of (1):
Figure BDA0002805694760000252
by substituting equation (30) into the system (25), the nonlinear control system becomes a linear-integral series system, which is called dynamic compensation linearization [31]:
Figure BDA0002805694760000253

Claims (10)

1. the utility model provides a composite construction aircraft of tilting rotor which characterized in that: the fuselage of the aircraft comprises a main wing and an empennage for air cruising; the main wing is arranged at the middle section of the fuselage; the empennage is arranged at the tail part of the machine body; the aircraft is also provided with a rotor wing for providing power for the aircraft; the rotor wing comprises a first rotor wing group arranged at the fixed wing and a second rotor wing group arranged at the rear part of the fuselage; when the aircraft takes off or lands, the orientation of each rotor in first rotor group, the second rotor group is vertical in order to provide lift to the fuselage, when the aircraft is in the air state of cruising, each rotor orientation in the second rotor group is adjusted to the horizontal direction, provides thrust for the aircraft.
2. A tiltrotor composite structure aircraft according to claim 1, wherein: the orientation of each rotor in the first rotor group is fixed to be vertical.
3. A tiltrotor composite structure aircraft according to claim 2, wherein: each rotor wing in the first rotor wing group is fixed at the front part of the main wing; each rotor in the second rotor group is fixed at the root of the empennage.
4. A tiltrotor composite structure aircraft according to claim 2, wherein: the main wing and the empennage respectively comprise wing surface parts with variable angles, and the main wing forms an elevator by the wing surface parts with the variable angles; the empennage forms a rudder at the airfoil part with a variable angle; when the aircraft is in the air cruise state, each rotor in the first rotor group is in a shutdown state.
5. A tiltrotor composite structure aircraft according to claim 1, wherein: the tail part of the machine body is provided with a connecting rod mechanism connected with the second rotor wing group; the link mechanism can synchronously adjust the orientation of each rotor in the second rotor group, so that the rotors can be switched between the horizontal direction and the vertical direction.
6. A tiltrotor composite structure aircraft according to claim 1, wherein: the first rotor wing group and the second rotor wing group are both composed of two rotor wings driven by small rotors; the aircraft is an unmanned aerial vehicle, and the body of the unmanned aerial vehicle is provided with an automatic pilot, a sensing assembly and a remote control assembly for communicating with the ground station; the sensing assembly comprises a speed sensor, a global positioner, an inertial measurement unit and a pressure sensor; the autopilot measures aircraft operating conditions via the sensing assembly to optimize control of the aircraft.
7. A tiltrotor composite structural aircraft according to claim 4, wherein: the aircraft further comprises a linear model-based controller; the controller controls the flight of the aircraft based on a flight control law combining a Robust Servo Linear Quadratic Regulator (RSLQR) and an Extended State Observer (ESO).
8. A tiltrotor composite structure aircraft according to claim 7, wherein: the dynamics model in the flight control law is a non-linear dynamics model, which uses a fixed frame BFF of the fuselage to be attached to the gravity center position CoG of the aircraft to establish a coordinate system, and the method is to represent an inertia fixed frame EFF as OgxgygzgThe origin point is set at the starting point; establishing a coordinate system O of four auxiliary frames AFsixtiytizti(i ═ 1,2,3,4), based on considerations of tilt angle and roll angle, ztiThe shaft is along the propeller axis of the rotor; x is the number oftiThe axis being parallel to the longitudinal plane of the drone, perpendicular to ztiThe axis is vertical to the paper surface and faces outwards; y istiThe axis is determined by the right hand rule; the transformation matrix between the coordinate systems is set by the coordinate transformation principle between different coordinate systems as follows:
Figure FDA0002805694750000021
phi, theta, psi represent euler angles, c and s are the signs of the cosine and sine functions respectively, eta is a fixed roll angle for the propulsion system to improve its controllability, epsilon is the angle of inclination of the rotor;
the nonlinear dynamical model can be derived as a newton-euler formula, and the inertially fixed framework can be expressed as:
Figure FDA0002805694750000022
where m is the mass of the aircraft,
Figure FDA0002805694750000023
and
Figure FDA0002805694750000024
respectively representing resultant and resultant moment vectors, V, in inertially-fixed framesb＝[u,v,w]TIs the velocity vector, ωb＝[p,q,r]TAs an attitude angular rate vector, IbIs a rigid body inertia matrix, which can be expressed as follows:
Figure FDA0002805694750000025
the forces F and moments M represented in the fuselage-fixed frame are generated by the gyroscopic effect caused by the effects of gravity, the propulsion system, the aerodynamics and the rotor tilting, and can be represented as:
Figure FDA0002805694750000026
wherein all components and moments take the form shown below
The gravitational force in an inertially fixed frame can be expressed as:
Figure FDA0002805694750000027
the second rotor group is a propulsion system when the aircraft is cruising in the air, the propulsion vector of the propulsion system is expressed by using a rotation matrix between the auxiliary frame and the airframe fixed frame BFF, the thrust vector can be decomposed along the airframe fixed frame, and the following formula is obtained,
Figure FDA0002805694750000031
wherein, Ti aFor thrust vectors represented by auxiliary frames, TiIs the thrust value, δiFor motor throttling, gTi(. is an experimentally determined mathematical relationship; the torque vector produced by the propulsion system may be expressed as:
Figure FDA0002805694750000032
wherein
Figure FDA0002805694750000033
Moment vector generated for thrust vector, diIs the position vector, τ, from the gear to each rotor axisiThe moment caused by the air resistance of the rotor is shown,
Figure FDA0002805694750000034
representing the moment vectors in the auxiliary frames AFs,
Figure FDA0002805694750000035
representing a moment vector in a fuselage fixed frame (BFF);
the rotor rotation of the rotor in the propulsion system produces a gyroscopic precessional moment effect. The expression of the moment vector is as follows:
Figure FDA0002805694750000036
wherein JriIs the moment of inertia, omega, of the propulsion assembly about its axisiRepresenting the angular velocity vector of the rotor in the Auxiliary Frames (AFs);
when a rudder factor is introduced in a flight model, the aerodynamic forces and moments of the aircraft are as follows:
Figure FDA0002805694750000037
wherein Q is dynamic pressure, α is angle of attack, β is sideslip angle, δα、δeAnd deltarThe deflection angles of the ailerons, the elevators and the rudders, respectively;
let ζ be [ x, y, z ]]TRepresenting the position vector of the airplane in the inertia fixed frame, the translational motion equation and the rotational motion equation can be expressed as follows according to the conversion relation between the coordinate systems:
Figure FDA0002805694750000041
based on the above, the 6-degree-of-freedom nonlinear dynamical equation of the flight model system can be described in the form of a first-order vector differential equation:
Figure FDA0002805694750000042
where x is the state variable u, v, w, p, q, r, phi, theta, psi, xg,yg,zgU is the vector of the input variables, including motor throttles δ 1, δ 2, δ 3 and δ 4 and control surface deflections δα、δe、δrThe transition mode when the aircraft is transitioning from airborne cruise to take-off and landing operations and the fixed-wing mode when the aircraft is airborne cruise are considered.
9. A tiltrotor composite aircraft according to claim 8, wherein the aircraft is of a particular configurationCharacterized in that: the linear controller performs control distribution based on channel throttling and balancing calculation, and specifically comprises a vertical channel deltaHPitch channel deltaθTumble passage deltaφYaw channel deltaψThe relationship between the virtual control inputs of the four channels and the actual throttling of the propeller is established as follows:
Figure FDA0002805694750000043
wherein deltaHi,δθi,δφi,δψi(i ═ 1,2,3,4) are vertical channels δ, respectivelyHPitch channel deltaθTumble passage deltaφYaw channel deltaψThe weight of the throttle valve of (a);
when the aircraft is in a state of equilibrium,
Figure FDA0002805694750000044
based on the nonlinear dynamical equation in equation 11, the following disturbance equilibrium equation can be obtained:
Figure FDA0002805694750000045
wherein Δ (·) ═ (-) - (·)op"op" represents an operating point;
from the above description, the trimming conditions for the four channels can be expressed as:
Figure FDA0002805694750000051
when the aircraft is set to work in a rotorcraft mode, the efficiency of the pneumatic effect device and the gyroscopic effect device is negligibly low; when the aircraft is set to operate in helicopter mode, epsilon, theta and phi are equal to zero; assuming that the smaller higher order terms are considered negligible, one can get:
Figure FDA0002805694750000052
wherein
Figure FDA0002805694750000053
If two rotors are arranged in the first rotor group and are respectively driven by the first motor and the second motor, and the first motor and the second motor firstly reach the maximum capacity due to the asymmetry of the geometric parameters of the first rotor group and the second rotor group, the weight coefficient of each channel can be obtained based on the first motor, and the calculation result is as follows:
Figure FDA0002805694750000054
finally, the control distribution relationship between the channel input and the actual throttle valve can be obtained by substituting equation 17 into equation 13.
10. A tiltrotor composite structure aircraft according to claim 8, wherein: when the aircraft works in a rotorcraft mode, if a state vector needs to be introduced for attitude control and altitude control, the nonlinear dynamical equation in the formula 11 is segmented to obtain
Figure FDA0002805694750000055
And an input vector
Figure FDA0002805694750000056
The flight model system can be expressed as
Figure FDA0002805694750000057
The flight model system is linearized at the equilibrium operating point, expanded by a taylor series and truncated in the first order term. Thus, the linearized flight model system is shown in the following equation:
Figure FDA0002805694750000058
wherein,
Figure FDA0002805694750000061
the linearized system equations for the aircraft model system may be further expressed based on equation 19 as
Figure FDA0002805694750000062
Wherein y iscIs the output vector, CcIs the corresponding transition matrix;
the control method based on the robust servo linear quadratic regulator RSLQR is obtained by introducing a state deviation into a system on the basis of the control method of the linear quadratic regulator LQR, wherein the state deviation can be adjusted to zero, so that a system state variable can accurately track an input command;
if the deviation is assumed to be e-rc-ycWhere r is a control command, the aircraft state equation may be defined as:
Figure FDA0002805694750000063
wherein
Figure FDA0002805694750000064
The cost function of the robust servo linear quadratic regulator RSLQR control is given by:
Figure FDA0002805694750000065
wherein Q and R are weight matrices; a control system of the controller selects a matrix R as an identity matrix and a matrix Q as a diagonal matrix; the values in the matrix Q are scaled using the bulison Bryson law; finally, the gain matrix for the robust servo linear quadratic regulator RSLQR control can be expressed as:
Kc＝[ki,kp]＝R-1BTp (formula 23)
Wherein k isi、kpAre different block matrices having the same dimensions e and
Figure FDA0002805694750000066
P(＝pT> 0) is the solution of the following algebraic ricatt equation:
PA+ATP-PBR-1BTp + Q ═ 0 (formula 24)
The optimal control input for the robust servo linear quadratic regulator RSLQR control is shown in equation 25 below,
Figure FDA0002805694750000067
the RSLQR control adds an integral element in a state feedback control loop to improve the system performance and the anti-interference capability;
the flight control law based on the RSLQR control can improve the dynamic performance and the steady-state performance of the control system; when designing the RSLQR control of the controller, firstly, extracting an angular velocity model and a vertical velocity model; then, designing an RSLQR controller for the angular speed and the speed ring or the inner ring;
the attitude and height loop control of the controller adopts a PI control method to improve the control precision;
in the roll channel of the controller, the PI gain of the control structure
Figure FDA0002805694750000071
And
Figure FDA0002805694750000072
the optimal damping ratio between the inner ring and the outer ring and the bandwidth matching relation are determined; they can be obtained by a PI parameter setting toolbox in MATLAB;
the controller uses an Extended State Observer (ESO) to estimate the state and the unknown total interference, and then compensates the initial control quantity of the RSLQR to obtain the final control input so as to improve the capacity of resisting disturbance and uncertain factors,
by the perturbation condition expressed by equation 18, the following second order nonlinear system can be obtained:
Figure FDA0002805694750000073
where x1 represents a state variable for attitude or altitude, f (-) is the total disturbance of the system including model uncertainty and external disturbances,
Figure FDA0002805694750000077
representing the control input, b is the magnification; the total disturbance experienced by the controller system is then expanded to a new state variable x3And let
Figure FDA0002805694750000074
The new system can be expressed as follows:
Figure FDA0002805694750000075
for the system with the controller expanded, there are the following extended state observers:
Figure FDA0002805694750000076
wherein Z is [ Z ]1,z2,z3]TIs the extended state vector X ═ X1,x2,x3]TEstimate of (1), beta1,β2,β3Is the observer gain, a nonlinear function fal (e, α)iδ) can be expressed as:
Figure FDA0002805694750000081
wherein alpha is1、α2And δ is a parameter of a nonlinear function fal (·), α represents a nonlinear shape, and α is taken1＝0.5、α2δ determines the width of the linear interval around the origin, 0.25; observer parameter betaiDetermines the state xiThe tracking speed of (2); increase beta appropriately1And beta2Can effectively inhibit beta3Excessive observer oscillations. The three parameters are adjusted in a coordinated manner, so that the expansion state x is observed in real time by adjusting the parameters3；
After obtaining an estimate z of the total disturbance3Then, the output is output to the RSLQR controller
Figure FDA0002805694750000082
The real-time control quantity can be obtained by the disturbance compensation of (1):
Figure FDA0002805694750000083
by substituting equation 30 into equation 25, the nonlinear control system becomes a linear integral series system, which is called dynamic compensation linearization, expressed as
Figure FDA0002805694750000084
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