CN111176311A - Sliding mode delay estimation control method for attitude of quad-rotor unmanned aerial vehicle and storage medium - Google Patents

Sliding mode delay estimation control method for attitude of quad-rotor unmanned aerial vehicle and storage medium Download PDF

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CN111176311A
CN111176311A CN202010003769.4A CN202010003769A CN111176311A CN 111176311 A CN111176311 A CN 111176311A CN 202010003769 A CN202010003769 A CN 202010003769A CN 111176311 A CN111176311 A CN 111176311A
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unmanned aerial
aerial vehicle
rotor unmanned
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attitude
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窦景欣
范逸群
马伟平
杨建军
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Putian University
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Putian University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • 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
    • G05D1/0808—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft

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Abstract

The method relates to a sliding mode delay estimation control method and a storage medium for the attitude of a quad-rotor unmanned aerial vehicle, and the method comprises the following steps: establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion; establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle; and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting a control quantity. The attitude is represented based on the error quaternion, an attitude dynamics model of the quad-rotor unmanned aerial vehicle is established, a global progressive convergence observer is used for observing the state quantity of the system, the observer has the characteristics of simple parameter setting, insensitivity to noise interference, better robustness to system parameter perturbation and the like, and the attitude of the quad-rotor unmanned aerial vehicle is controlled based on the sliding mode delay estimation controller, so that the attitude control of the quad-rotor unmanned aerial vehicle has better control performance and effectiveness.

Description

Sliding mode delay estimation control method for attitude of quad-rotor unmanned aerial vehicle and storage medium
Technical Field
The invention relates to the technical field of quad-rotor unmanned aerial vehicles, in particular to a sliding mode delay estimation control method and a storage medium for attitude of a quad-rotor unmanned aerial vehicle.
Background
The quad-rotor unmanned aerial vehicle has the characteristics of vertical take-off and landing, fixed-point hovering, strong maneuverability, flexible operation and the like, and is widely applied to military and civil fields of search and rescue, battlefield investigation, fire scene reconnaissance, traffic control and the like. The attitude mathematical model of the existing four-rotor unmanned aerial vehicle attitude controller is usually established under the condition that the change rate of the limited attitude angle is equal to the angular velocity around the body axis, namely, the default transformation relation matrix from the body axis angular velocity to the euler angle is an identity matrix, but the default condition is reasonable only when the aircraft is hovered or flies at a small angle. However, when the quad-rotor unmanned aerial vehicle is applied to the fields of military and the like, the aircraft may be required to perform large-angle maneuvering flight, namely when the conversion relation matrix is not an identity matrix, the problem of singular value of the conversion matrix expressed based on the euler angle is solved, and meanwhile, the problem of uncertain interference of the quad-rotor unmanned aerial vehicle in the flight process is solved under the condition of not depending on the control system full-state feedback and the system accurate model.
Disclosure of Invention
Therefore, a sliding-mode delay estimation control method and a storage medium for the attitude of the quad-rotor unmanned aerial vehicle are needed to be provided, so that the problem that a conversion matrix based on Euler angle representation in an attitude dynamics model of the existing quad-rotor unmanned aerial vehicle has singular values is solved, and the problem that the quad-rotor unmanned aerial vehicle suffers from uncertain interference in the flight process under the condition of not depending on control system full-state feedback and system accurate model is solved.
In order to achieve the above object, the inventor provides a sliding mode delay estimation control method for attitude of a quad-rotor unmanned aerial vehicle, comprising the following steps:
establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion;
establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting the attitude control quantity of the quad-rotor unmanned aerial vehicle.
Further optimization, the method for establishing a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion specifically comprises the following steps:
confirm four rotor unmanned aerial vehicle's mathematical model
Figure BDA0002354450350000021
Omega is the in-vivo coordinate EBRelative to the inertial coordinate EIAngular velocity of, and
Figure BDA0002354450350000022
j is the moment of inertia matrix of quad-rotor unmanned aerial vehicle, and
Figure BDA0002354450350000023
u is the control moment of quad-rotor unmanned aerial vehicle, and
Figure BDA0002354450350000024
d is a combined external moment MTIn addition to the control torque U,
Figure BDA0002354450350000025
bounded and derivatives exist, S (-) is a symmetric matrix;
obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure BDA0002354450350000026
The conversion matrix R is described based on unit quaternion instead of Euler angle to obtain the conversion matrix based on unit quaternion
Figure BDA0002354450350000027
Is simplified to
Figure BDA0002354450350000028
Unit quaternion of
Figure BDA0002354450350000029
q0Is a scalar portion of the unit quaternion,
Figure BDA00023544503500000210
is a vector part of unit quaternion, and the unit quaternion q satisfies
Figure BDA00023544503500000211
I3Is a 3 × 3 identity matrix;
relational equation between angular velocity omega and body coordinate established based on unit quaternion
Figure BDA00023544503500000212
Expected body coordinate system E according to quad-rotor unmanned aerial vehicleBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure BDA00023544503500000213
Satisfy the requirement of
Figure BDA00023544503500000214
i is 0,1,2,3, and the transformation matrix from the expected body coordinate to the inertial coordinate is obtained as RdE SO (3) is obtained according to the quaternion of the expected unit
Figure BDA0002354450350000031
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure BDA0002354450350000032
Wherein the content of the first and second substances,
Figure BDA0002354450350000033
Figure BDA0002354450350000034
determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as the expected body coordinate according to the real-time body coordinate
Figure BDA0002354450350000035
Wherein the content of the first and second substances,
Figure BDA0002354450350000036
qve＝qodqv-q0qvd+S(qv)qvd，
Figure BDA0002354450350000037
according to conversion matrices R and RdA conversion error matrix of
Figure BDA0002354450350000038
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure BDA0002354450350000039
Figure BDA00023544503500000310
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure BDA00023544503500000311
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure BDA00023544503500000312
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure BDA00023544503500000313
Wherein the content of the first and second substances,
Figure BDA00023544503500000314
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure BDA00023544503500000315
Figure BDA00023544503500000316
Further optimization, the establishment of the global progressive convergence observer based on the state quantity output by the dynamics model of the attitude of the quad-rotor unmanned aerial vehicle specifically comprises the following steps:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure BDA00023544503500000317
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure BDA00023544503500000318
Figure BDA00023544503500000319
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure BDA0002354450350000041
i＝1,2；αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure BDA0002354450350000042
Wherein the content of the first and second substances,
Figure BDA0002354450350000043
further optimization, the establishing of the sliding mode delay estimation controller based on the observation state quantity of the global asymptotic convergence observer and the outputting of the control quantity specifically comprise the following steps:
measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure BDA0002354450350000044
According to the sliding mode function s ═ z2+Ksz1Estimating the uncertainty according to a delay estimation algorithm
Figure BDA0002354450350000045
Calculating sliding mode delay estimation controller
Figure BDA0002354450350000046
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure BDA0002354450350000047
Further optimization, the method also comprises the following steps:
replacing sign function sgn () with tan h (), rewriting the sliding mode delay estimation controller obtained by calculation to obtain a new sliding mode delay estimation controller
Figure BDA0002354450350000048
Wherein the content of the first and second substances,
Figure BDA0002354450350000049
mu is positiveThe gain of the power amplifier is increased,
Figure BDA00023544503500000410
is positively determinate of a switch matrix, an
Figure BDA00023544503500000411
Positive definite switch matrix
Figure BDA00023544503500000412
Is adaptive to
Figure BDA00023544503500000413
i＝1,2,3，
Figure BDA00023544503500000414
α is a positive gain and ε is an adaptive gain.
The inventor also provides another technical scheme that: a storage medium storing a computer program which, when executed by a processor, performs the steps of:
establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion;
establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting a control quantity.
Further optimization, when the computer program is executed by the processor to perform the step of establishing a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion, the following steps are specifically performed:
confirm four rotor unmanned aerial vehicle's mathematical model
Figure BDA0002354450350000051
Omega is the in-vivo coordinate EBRelative to the inertial coordinate EIAngular velocity of, and
Figure BDA0002354450350000052
j is four rotor unmanned aerial vehicleA rotational inertia matrix of
Figure BDA0002354450350000053
U is the control moment of quad-rotor unmanned aerial vehicle, and
Figure BDA0002354450350000054
d is a combined external moment MTIn addition to the control torque U,
Figure BDA0002354450350000055
bounded and derivatives exist, S (-) is a symmetric matrix;
obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure BDA0002354450350000056
Phi is a rolling attitude angle of the quad-rotor unmanned aerial vehicle, theta is a pitching attitude angle of the quad-rotor unmanned aerial vehicle, and psi is a yawing attitude angle of the quad-rotor unmanned aerial vehicle;
the conversion matrix R is described based on unit quaternion instead of Euler angle to obtain the conversion matrix based on unit quaternion
Figure BDA0002354450350000057
Is simplified to
Figure BDA0002354450350000058
Unit quaternion of
Figure BDA0002354450350000059
q0Is a scalar portion of the unit quaternion,
Figure BDA00023544503500000510
is a vector part of unit quaternion, and the unit quaternion q satisfies
Figure BDA00023544503500000511
I3Is a 3 × 3 identity matrix;
relational equation between angular velocity omega and body coordinate established based on unit quaternion
Figure BDA00023544503500000512
Expected body coordinate system E according to quad-rotor unmanned aerial vehicleBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure BDA00023544503500000513
Satisfy the requirement of
Figure BDA00023544503500000514
i is 0,1,2,3, and the transformation matrix from the expected body coordinate to the inertial coordinate is obtained as RdE SO (3) is obtained according to the quaternion of the expected unit
Figure BDA0002354450350000061
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure BDA0002354450350000062
Wherein the content of the first and second substances,
Figure BDA0002354450350000063
Figure BDA0002354450350000064
obtaining expected body coordinates according to the relatively real-time body coordinates, and determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as
Figure BDA0002354450350000065
Wherein the content of the first and second substances,
Figure BDA0002354450350000066
qve＝qodqv-q0qvd+S(qv)qvd，
Figure BDA0002354450350000067
according to conversion matrices R and RdA conversion error matrix of
Figure BDA0002354450350000068
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure BDA0002354450350000069
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure BDA00023544503500000610
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure BDA00023544503500000611
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure BDA00023544503500000612
Wherein the content of the first and second substances,
Figure BDA00023544503500000613
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure BDA00023544503500000614
Figure BDA00023544503500000615
Further optimization, when the computer program is executed by the processor to perform the step of "establishing a global progressive convergence observer based on the state quantity output by the dynamical model of the attitude of the quad-rotor unmanned aerial vehicle", the following steps are specifically performed:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure BDA00023544503500000616
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure BDA0002354450350000071
Figure BDA0002354450350000072
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure BDA0002354450350000073
i＝1,2；αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure BDA0002354450350000074
Wherein the content of the first and second substances,
Figure BDA0002354450350000075
further optimization, when the computer program is executed by the processor, the step of establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer and outputting the control quantity is executed, and the following steps are specifically executed:
measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure BDA0002354450350000076
According to the sliding mode function s ═ z2+Ksz1Estimating the uncertainty according to a delay estimation algorithm
Figure BDA0002354450350000077
Calculating sliding mode delay estimation controller
Figure BDA0002354450350000078
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure BDA0002354450350000079
Further preferably, the computer program when executed by the processor further performs the steps of:
replacing sign function sgn () with tan h (), rewriting the sliding mode delay estimation controller obtained by calculation to obtain a new sliding mode delay estimation controller
Figure BDA00023544503500000710
Wherein the content of the first and second substances,
Figure BDA00023544503500000711
mu is a positive gain, and mu is a positive gain,
Figure BDA00023544503500000712
is positively determinate of a switch matrix, an
Figure BDA00023544503500000713
Positive definite switch matrix
Figure BDA00023544503500000714
Is adaptive to
Figure BDA00023544503500000715
i＝1,2,3，
Figure BDA00023544503500000716
α is a positive gain and ε is an adaptive gain.
Compared with the prior art, the technical scheme has the advantages that the attitude is expressed based on the error quaternion, the attitude dynamics model of the quad-rotor unmanned aerial vehicle is established, and the problem that singular values can appear in a conversion matrix expressed based on an Euler angle is solved; in order to be independent of the full-state feedback of the system, the state quantity of the system is observed by utilizing the global progressive convergence observer, the observer has the characteristics of simple parameter setting, insensitivity to noise interference, better robustness to system parameter perturbation and the like, and the attitude of the quad-rotor unmanned aerial vehicle is controlled based on the sliding-mode delay estimation controller, so that the attitude control of the quad-rotor unmanned aerial vehicle has better control performance and effectiveness.
Drawings
Fig. 1 is a schematic flow chart of a sliding-mode delay estimation control method for attitude of a quad-rotor unmanned aerial vehicle according to an embodiment;
fig. 2 is a topological diagram of a sliding-mode delay estimation control method for attitude of a quad-rotor unmanned aerial vehicle according to an embodiment;
fig. 3 is a schematic structural diagram of a storage medium according to an embodiment.
Description of reference numerals:
310. a storage medium.
Detailed Description
To explain technical contents, structural features, and objects and effects of the technical solutions in detail, the following detailed description is given with reference to the accompanying drawings in conjunction with the embodiments.
Referring to fig. 1-2, the present embodiment provides a sliding mode delay estimation control method for attitude of a quad-rotor unmanned aerial vehicle, including the following steps:
step S110: establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion; consider that four rotor unmanned aerial vehicle are in state of hovering, perhaps low-speed flight state, consider closing external moment M that four rotor unmanned aerial vehicle received simultaneouslyTBy controlling torqueU, Coriolis moment McAnd other uncertainty factor moment delta, determining a mathematical model of the quad-rotor unmanned aerial vehicle
Figure BDA0002354450350000091
Omega is the in-vivo coordinate EBRelative to the inertial coordinate EIAngular velocity of, and
Figure BDA0002354450350000092
j is the moment of inertia matrix of quad-rotor unmanned aerial vehicle, and
Figure BDA0002354450350000093
u is the control moment of quad-rotor unmanned aerial vehicle, and
Figure BDA0002354450350000094
d is a combined external moment MTIn addition to the control moment U, including the Coriolis moment McAn unmodeled part, an external disturbance, etc.,
Figure BDA0002354450350000095
bounded and derivatives exist, S (-) is a symmetric matrix; the general form of the symmetric matrix S (-) is:
Figure BDA0002354450350000096
wherein the content of the first and second substances,
Figure BDA0002354450350000097
singular value problems may arise when the transformation matrix R is represented based on euler angles. Here, the conversion matrix R is represented as a conversion matrix from the body coordinates to the inertial coordinates. Obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure BDA0002354450350000098
Phi is a rolling attitude angle of the quad-rotor unmanned aerial vehicle, theta is a pitching attitude angle of the quad-rotor unmanned aerial vehicle, and psi is a yawing attitude angle of the quad-rotor unmanned aerial vehicle; to avoid the problem of singular values, euler is replaced based on unit quaternionThe angle describes a conversion matrix R to obtain a conversion matrix based on unit quaternion
Figure BDA0002354450350000099
Is simplified to
Figure BDA00023544503500000910
Unit quaternion of
Figure BDA00023544503500000911
q0Is a scalar portion of the unit quaternion,
Figure BDA00023544503500000912
is a vector part of unit quaternion, and the unit quaternion q satisfies
Figure BDA00023544503500000913
I3Is a 3 × 3 identity matrix;
expressing the attitude dynamics equation of the quad-rotor unmanned aerial vehicle by using unit quaternion, namely establishing a relational equation between the unit quaternion and the angular velocity omega under the body coordinate
Figure BDA00023544503500000914
Wherein the content of the first and second substances,
Figure BDA00023544503500000915
in order to ensure the attitude control of the quad-rotor unmanned aerial vehicle by designing a proper control quantity tau, an expected body coordinate system E of the quad-rotor unmanned aerial vehicle is adoptedBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure BDA0002354450350000101
Satisfy the requirement of
Figure BDA0002354450350000102
i is 0,1,2,3, and the expected machine is obtainedThe transformation matrix from the body coordinate to the inertial coordinate is RdE SO (3) is obtained according to the quaternion of the expected unit
Figure BDA0002354450350000103
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure BDA0002354450350000104
Wherein the content of the first and second substances,
Figure BDA0002354450350000105
Figure BDA0002354450350000106
obtaining expected body coordinates according to the relatively real-time body coordinates, and determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as
Figure BDA0002354450350000107
Wherein the content of the first and second substances,
Figure BDA0002354450350000108
qve＝qodqv-q0qvd+S(qv)qvdand the error quaternion satisfies the condition:
Figure BDA0002354450350000109
according to conversion matrices R and RdA conversion error matrix of
Figure BDA00023544503500001010
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure BDA00023544503500001011
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure BDA00023544503500001012
From the tracking error quaternion and the transformation matrices R and RdThe error matrix of the conversion between, can be known as
Figure BDA00023544503500001013
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure BDA00023544503500001014
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure BDA00023544503500001015
Wherein the content of the first and second substances,
Figure BDA00023544503500001016
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure BDA00023544503500001017
Figure BDA00023544503500001018
According to the conditions satisfied by the error quaternion and the error quaternion qeAnd angular velocity omegaeCan obtain the relation equation of
Figure BDA00023544503500001019
According to the determined mathematical model of the quad-rotor unmanned aerial vehicle and the angular velocity omega under the body coordinatese＝ω-ReωdAnd establishing a kinetic equation of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion.
Step S120: establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
the method specifically comprises the following steps:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure BDA0002354450350000111
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure BDA0002354450350000112
Figure BDA0002354450350000113
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure BDA0002354450350000114
i＝1,2；αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure BDA0002354450350000115
Wherein the content of the first and second substances,
Figure BDA0002354450350000116
based on the Lyapunov stability theorem and the Barbalt theorem analysis, the observation error of the global progressive convergence observer and the tracking error of the closed-loop system are progressively converged.
Step S130: and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting a control quantity.
Setting the state quantity q without measuring the angular velocity of the state quantityveIs expected value of
Figure BDA0002354450350000117
And set itThe first and second derivatives exist and are bounded; setting the tracking error amount of the system to
Figure BDA0002354450350000118
Measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure BDA0002354450350000119
According to the sliding mode function s ═ z2+Ksz1Wherein, K iss＝diag(ks1,ks2,ks3) For positive control gain, the uncertainty is estimated according to a delay estimation algorithm, so that
Figure BDA00023544503500001110
Calculating sliding mode delay estimation controller
Figure BDA00023544503500001111
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure BDA0002354450350000121
Error of time delay estimation algorithm
Figure BDA0002354450350000122
Is sufficiently small to be able to be adjusted by adjusting the parameter Ksand β, the tracking error can converge to near zero.
In order to reduce buffeting, a sign function sgn () is replaced by tanh (), the sliding mode delay estimation controller obtained through calculation is rewritten, and a new sliding mode delay estimation controller is obtained
Figure BDA0002354450350000123
Wherein the content of the first and second substances,
Figure BDA0002354450350000124
mu is a positive gain, and mu is a positive gain,
Figure BDA0002354450350000125
is positively determinate of a switch matrix, an
Figure BDA0002354450350000126
Positive definite switch matrix
Figure BDA0002354450350000127
Is adaptive to
Figure BDA0002354450350000128
i＝1,2,3，
Figure BDA0002354450350000129
α is a positive gain and ε is an adaptive gain.
Referring to fig. 3, in another embodiment, a storage medium 310, the storage medium 310 storing a computer program, the computer program when executed by a processor performing the steps of:
establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion;
establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting a control quantity.
When the computer program is executed by the processor to perform the step of establishing a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion, the following steps are specifically performed:
confirm four rotor unmanned aerial vehicle's mathematical model
Figure BDA00023544503500001210
Omega is a sit-on bodyMark EBRelative to the inertial coordinate EIAngular velocity of, and
Figure BDA00023544503500001211
j is the moment of inertia matrix of quad-rotor unmanned aerial vehicle, and
Figure BDA00023544503500001212
u is the control moment of quad-rotor unmanned aerial vehicle, and
Figure BDA00023544503500001213
d is a combined external moment MTIn addition to the control torque U,
Figure BDA00023544503500001214
bounded and derivatives exist, S (-) is a symmetric matrix;
obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure BDA0002354450350000131
The conversion matrix R is described based on unit quaternion instead of Euler angle to obtain the conversion matrix based on unit quaternion
Figure BDA0002354450350000132
Is simplified to
Figure BDA0002354450350000133
Unit quaternion of
Figure BDA0002354450350000134
q0Is a scalar portion of the unit quaternion,
Figure BDA0002354450350000135
is a vector part of unit quaternion, and the unit quaternion q satisfies
Figure BDA0002354450350000136
I3Is a 3 × 3 identity matrix;
based onRelation equation between unit quaternion establishment and angular velocity omega under body coordinate
Figure BDA0002354450350000137
Expected body coordinate system E according to quad-rotor unmanned aerial vehicleBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure BDA0002354450350000138
Satisfy the requirement of
Figure BDA0002354450350000139
i is 0,1,2,3, and the transformation matrix from the expected body coordinate to the inertial coordinate is obtained as RdE SO (3) is obtained according to the quaternion of the expected unit
Figure BDA00023544503500001310
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure BDA00023544503500001311
Wherein the content of the first and second substances,
Figure BDA00023544503500001312
Figure BDA00023544503500001313
obtaining expected body coordinates according to the relatively real-time body coordinates, and determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as
Figure BDA00023544503500001314
Wherein the content of the first and second substances,
Figure BDA00023544503500001315
qve＝qodqv-q0qvd+S(qv)qvd，
Figure BDA00023544503500001316
according to conversion matrices R and RdA conversion error matrix of
Figure BDA00023544503500001317
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure BDA00023544503500001318
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure BDA0002354450350000141
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure BDA0002354450350000142
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure BDA0002354450350000143
Wherein the content of the first and second substances,
Figure BDA0002354450350000144
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure BDA0002354450350000145
Figure BDA0002354450350000146
Further optimization, when the computer program is executed by the processor to perform the step of "establishing a global progressive convergence observer based on the state quantity output by the dynamical model of the attitude of the quad-rotor unmanned aerial vehicle", the following steps are specifically performed:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure BDA0002354450350000147
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure BDA0002354450350000148
Figure BDA0002354450350000149
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure BDA00023544503500001410
i＝1,2；αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure BDA00023544503500001411
Wherein the content of the first and second substances,
Figure BDA00023544503500001412
when the computer program is operated by the processor, the steps of establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer and outputting the attitude control quantity of the quad-rotor unmanned aerial vehicle are executed, and the following steps are specifically executed:
measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure BDA00023544503500001413
According to the sliding mode function s ═ z2+Ksz1Estimating the uncertainty according to a delay estimation algorithm
Figure BDA0002354450350000151
Calculating sliding mode delay estimation controller
Figure BDA0002354450350000152
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure BDA0002354450350000153
Wherein the computer program when executed by the processor further performs the steps of:
replacing sign function sgn () with tan h (), rewriting the sliding mode delay estimation controller obtained by calculation to obtain a new sliding mode delay estimation controller
Figure BDA0002354450350000154
Wherein the content of the first and second substances,
Figure BDA0002354450350000155
mu is a positive gain, and mu is a positive gain,
Figure BDA0002354450350000156
is positively determinate of a switch matrix, an
Figure BDA0002354450350000157
Positive definite switch matrix
Figure BDA00023544503500001510
Is adaptive to
Figure BDA0002354450350000158
i＝1,2,3，
Figure BDA0002354450350000159
α is a positive gain and ε is an adaptive gain.
It should be noted that, although the above embodiments have been described herein, the invention is not limited thereto. Therefore, based on the innovative concepts of the present invention, the technical solutions of the present invention can be directly or indirectly applied to other related technical fields by making changes and modifications to the embodiments described herein, or by using equivalent structures or equivalent processes performed in the content of the present specification and the attached drawings, which are included in the scope of the present invention.

Claims (10)

1. A sliding mode delay estimation control method for the attitude of a quad-rotor unmanned aerial vehicle is characterized by comprising the following steps:
establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion;
establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting the attitude control quantity of the quad-rotor unmanned aerial vehicle.
2. The sliding-mode delay estimation control method for the attitude of the quad-rotor unmanned aerial vehicle according to claim 1, wherein the step of establishing a dynamical model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion specifically comprises the following steps:
confirm four rotor unmanned aerial vehicle's mathematical model
Figure FDA0002354450340000011
Omega is the coordinate E of the bodyBRelative to the inertial coordinate EIAngular velocity of, and
Figure FDA0002354450340000012
j is the moment of inertia matrix of quad-rotor unmanned aerial vehicle, and
Figure FDA0002354450340000013
u is the control moment of quad-rotor unmanned aerial vehicle, and
Figure FDA0002354450340000014
d is a combined external moment MTIn addition to the control torque U,
Figure FDA0002354450340000015
bounded and derivatives exist, S (-) is a symmetric matrix;
obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure FDA0002354450340000016
Phi is a rolling attitude angle of the quad-rotor unmanned aerial vehicle, theta is a pitching attitude angle of the quad-rotor unmanned aerial vehicle, and psi is a yawing attitude angle of the quad-rotor unmanned aerial vehicle;
the conversion matrix R is described based on unit quaternion instead of Euler angle to obtain the conversion matrix based on unit quaternion
Figure FDA0002354450340000017
Is simplified to
Figure FDA0002354450340000018
Unit quaternion of
Figure FDA0002354450340000019
q0Is a scalar portion of the unit quaternion,
Figure FDA00023544503400000110
is a vector part of unit quaternion, and the unit quaternion q satisfies
Figure FDA0002354450340000021
I3Is a 3 × 3 identity matrix;
relational equation between angular velocity omega and body coordinate established based on unit quaternion
Figure FDA0002354450340000022
Expected body coordinate system E according to quad-rotor unmanned aerial vehicleBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure FDA0002354450340000023
Satisfy the requirement of
Figure FDA0002354450340000024
Obtaining a transformation matrix from the expected body coordinate to the inertial coordinate as RdE SO (3) is obtained according to the quaternion of the expected unit
Figure FDA0002354450340000025
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure FDA0002354450340000026
Wherein the content of the first and second substances,
Figure FDA0002354450340000027
Figure FDA0002354450340000028
determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as
Figure FDA0002354450340000029
Wherein the content of the first and second substances,
Figure FDA00023544503400000210
qve＝qodqv-q0qvd+S(qv)qvd，
Figure FDA00023544503400000211
according to conversion matrices R and RdA conversion error matrix of
Figure FDA00023544503400000212
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure FDA00023544503400000213
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure FDA00023544503400000214
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure FDA00023544503400000215
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure FDA00023544503400000216
Wherein the content of the first and second substances,
Figure FDA00023544503400000217
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure FDA00023544503400000218
Figure FDA00023544503400000219
3. The sliding-mode delay estimation control method for the attitude of the quad-rotor unmanned aerial vehicle according to claim 2, wherein the step of establishing the global asymptotic convergence observer based on the state quantity output by the dynamical model of the attitude of the quad-rotor unmanned aerial vehicle specifically comprises the following steps:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure FDA0002354450340000031
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure FDA0002354450340000032
Figure FDA0002354450340000033
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure FDA0002354450340000034
αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure FDA0002354450340000035
Wherein the content of the first and second substances,
Figure FDA0002354450340000036
4. the sliding-mode delay estimation control method for the attitude of the quad-rotor unmanned aerial vehicle according to claim 3, wherein the step of establishing the sliding-mode delay estimation controller and outputting the attitude control quantity of the quad-rotor unmanned aerial vehicle based on the observation state quantity of the global progressive convergence observer specifically comprises the following steps:
measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure FDA0002354450340000037
According to the sliding mode function s ═ z2+Ksz1Estimating the uncertainty according to a delay estimation algorithm
Figure FDA0002354450340000038
Calculating sliding mode delay estimation controller
Figure FDA0002354450340000039
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure FDA00023544503400000310
5. The sliding-mode delay estimation control method for the attitude of the quad-rotor unmanned aerial vehicle according to claim 4, further comprising the following steps:
replacing sign function sgn () with tan h (), rewriting the sliding mode delay estimation controller obtained by calculation to obtain a new sliding mode delay estimation controller
Figure FDA0002354450340000041
Wherein the content of the first and second substances,
Figure FDA0002354450340000042
mu is a positive gain, and mu is a positive gain,
Figure FDA0002354450340000043
is positively determinate of a switch matrix, an
Figure FDA0002354450340000044
Positive definite switch matrix
Figure FDA0002354450340000045
Is adaptive to
Figure FDA0002354450340000046
Figure FDA0002354450340000047
α is a positive gain and ε is an adaptive gain.
6. A storage medium storing a computer program, the computer program when executed by a processor performing the steps of:
establishing a dynamic model of the attitude of the quad-rotor unmanned aerial vehicle based on the error quaternion;
establishing a global progressive convergence observer based on the state quantity output by the dynamic model of the attitude of the quad-rotor unmanned aerial vehicle;
and establishing a sliding mode delay estimation controller based on the observation state quantity of the global progressive convergence observer, and outputting a control quantity.
7. The storage medium of claim 6, wherein the computer program when executed by the processor performs the step of "building a dynamical model of quad-rotor drone attitude based on error quaternion", by performing the steps of:
confirm four rotor unmanned aerial vehicle's mathematical model
Figure FDA0002354450340000048
Omega is the in-vivo coordinate EBRelative to the inertial coordinate EIAngular velocity of, and
Figure FDA0002354450340000049
j is the moment of inertia matrix of quad-rotor unmanned aerial vehicle, and
Figure FDA00023544503400000410
u is the control moment of quad-rotor unmanned aerial vehicle, and
Figure FDA00023544503400000411
d is a combined external moment MTIn addition to the control torque U,
Figure FDA00023544503400000412
bounded and derivatives exist, S (-) is a symmetric matrix;
obtaining a conversion matrix according to Euler angle parameterization and XYZ axis rotation sequence
Figure FDA00023544503400000413
The conversion matrix R is described based on unit quaternion instead of Euler angle to obtain the conversion matrix based on unit quaternion
Figure FDA00023544503400000414
Is simplified to
Figure FDA0002354450340000051
Unit quaternion of
Figure FDA0002354450340000052
q0Is a scalar portion of the unit quaternion,
Figure FDA0002354450340000053
vector portion being unit quaternion, unitA bit quaternion q satisfying
Figure FDA0002354450340000054
I3Is a 3 × 3 identity matrix;
relational equation between angular velocity omega and body coordinate established based on unit quaternion
Figure FDA0002354450340000055
Expected body coordinate system E according to quad-rotor unmanned aerial vehicleBd＝(xBd,yBd,zBd) Quadrotor drone with respect to inertial coordinate EIAt desired body coordinates EBdDesired angular velocity ofdThe desired unit quaternion is
Figure FDA0002354450340000056
Satisfy the requirement of
Figure FDA0002354450340000057
Obtaining a transformation matrix from the expected body coordinate to the inertial coordinate as RdE SO (3) is obtained according to the quaternion of the expected unit
Figure FDA0002354450340000058
Establishing expected angular velocity omega under expected body coordinates according to expected quaterniondEquation of relationship (c)
Figure FDA0002354450340000059
Wherein the content of the first and second substances,
Figure FDA00023544503400000510
Figure FDA00023544503400000511
obtaining expected body coordinates according to the relatively real-time body coordinates, and determining the tracking error quaternion of the quad-rotor unmanned aerial vehicle as
Figure FDA00023544503400000512
Wherein the content of the first and second substances,
Figure FDA00023544503400000513
qve＝qodqv-q0qvd+S(qv)qvd，
Figure FDA00023544503400000514
according to conversion matrices R and RdA conversion error matrix of
Figure FDA00023544503400000515
Establishing an expected quaternion qdWith the desired body coordinates EBDesired angular velocity ωdEquation of relationship (c)
Figure FDA00023544503400000516
Determining a four-rotor unmanned aerial vehicle attitude control target as
Figure FDA00023544503400000517
According to the angular velocity in the body coordinates relative to the desired body coordinates of
Figure FDA00023544503400000518
I.e. omegae＝ω-ReωdEstablishing an error quaternion qeAnd angular velocity omegaeEquation of relationship (c)
Figure FDA00023544503400000519
Wherein the content of the first and second substances,
Figure FDA00023544503400000520
based on error quaternion, establish four rotor unmanned aerial vehicle attitude's kinetic equation
Figure FDA00023544503400000521
Figure FDA0002354450340000061
8. The storage medium according to claim 7, wherein the computer program, when executed by the processor, when executing the step "establishing a global asymptotic convergence observer based on a state quantity output by a dynamical model of a quad-rotor drone attitude", specifically executes the following steps:
state quantity q output by dynamics model of four-rotor unmanned aerial vehicle attitudeve，ωeRespectively is
Figure FDA0002354450340000062
Determining the observation error of a global progressive convergence observer as χ1＝δ1-qve，χ2＝δ2-ωe；
According to the observation error, a global progressive convergence observer is established as
Figure FDA0002354450340000063
Figure FDA0002354450340000064
n is the degree of freedom, LiA matrix is positively determined for a diagonal, an
Figure FDA0002354450340000065
αiIs a pending positive number less than 1, i is 1, 2;
calculating the derivation of the observation error to obtain the state equation of the observation error
Figure FDA0002354450340000066
Wherein the content of the first and second substances,
Figure FDA0002354450340000067
9. the storage medium according to claim 8, wherein when the computer program is executed by the processor, when the step "establishing a sliding-mode delay estimation controller based on the observed state quantity of the global asymptotic convergence observer, and outputting the control quantity" is executed, the following steps are specifically executed:
measuring state delta of global progressive convergence observer1And delta2State quantity q output by dynamic model for replacing four-rotor unmanned aerial vehicle attitude respectivelyveAnd ωe；
Establishing a new tracking error quantity of
Figure FDA0002354450340000068
According to the sliding mode function s ═ z2+Ksz1Estimating the uncertainty according to a delay estimation algorithm
Figure FDA0002354450340000069
Calculating sliding mode delay estimation controller
Figure FDA00023544503400000610
β is a normal number, and L is sampling time;
substituting a sliding mode function and a sliding mode delay estimation controller into a dynamics model of the attitude of the quad-rotor unmanned aerial vehicle to obtain a closed-loop system equation
Figure FDA00023544503400000611
10. The storage medium of claim 9, wherein the computer program, when executed by the processor, further performs the steps of:
replacing sign function sgn () with tanh (), rewriting the sliding mode delay estimation controller obtained by calculation to obtain new sliding mode delay estimation controlDevice for making articles
Figure FDA0002354450340000071
Wherein the content of the first and second substances,
Figure FDA0002354450340000072
mu is a positive gain, and mu is a positive gain,
Figure FDA0002354450340000073
is positively determinate of a switch matrix, an
Figure FDA0002354450340000074
Positive definite switch matrix
Figure FDA0002354450340000075
Is adaptive to
Figure FDA0002354450340000076
Figure FDA0002354450340000077
α is a positive gain and ε is an adaptive gain.
CN202010003769.4A 2020-01-03 2020-01-03 Sliding mode delay estimation control method for attitude of quad-rotor unmanned aerial vehicle and storage medium Pending CN111176311A (en)

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