CN107608367B - Multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method - Google Patents
Multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method Download PDFInfo
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Abstract
The invention relates to the technical field of unmanned aerial vehicle control, and provides a finite time track attitude cooperative control algorithm based on multivariable interference compensation, overcomes the defects of the traditional four-rotor unmanned aerial vehicle control method in the aspects of control precision, response speed and anti-interference, solves the problem of high-precision, rapid and stable tracking control of tracks and attitudes of a four-rotor unmanned aerial vehicle under the influence of comprehensive interference, and achieves the purposes of improving the control performance of the four-rotor unmanned aerial vehicle and enhancing the safety and reliability of a system. A multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method specifically comprises the following steps: a first part, trajectory controller-disturbance compensator design; the second part, attitude resolving; third, the attitude controller-disturbance compensator design. The invention is mainly applied to the control occasion of the unmanned aerial vehicle.
Description
Technical Field
The invention relates to the technical field of unmanned aerial vehicle control, in particular to the field of high-precision rapid trajectory and attitude cooperative control of a quad-rotor unmanned aerial vehicle. In particular to a multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method.
Background
Four rotor unmanned aerial vehicle have the axial symmetry on mechanical structure, and four even distributions of rotor are on four endpoints of cross structure, and this type unmanned aerial vehicle's power is provided by the lift that each rotor produced, only needs to change the rotation rate of four rotors, can realize actions such as rolling, every single move, driftage of unmanned aerial vehicle. The quad-rotor unmanned aerial vehicle has the advantages of small volume, light weight, good concealment, suitability for multi-platform and multi-space use, capability of flexibly and vertically taking off and landing on the ground and warships, and the like. The aircraft has a simple structure, ultra-strong maneuverability and a unique flight mode, shows great application value in the military and civil fields, and is widely applied to the fields of military reconnaissance, dangerous area detection, target capture, battlefield management, firepower support, electronic interference, communication relay and the like.
However, the quad-rotor unmanned aerial vehicle is a complex controlled object integrating multivariable, uncertain, nonlinear, fast time-varying, strong coupling, static instability and under-actuation, and the flight control technology of the quad-rotor unmanned aerial vehicle is always the key point and the difficulty point of the research in the field of aviation. At present, a traditional control method based on a classical theory, such as a PID control algorithm, is widely used in the field of flight control due to simple structure, easy realization and independence of a system mathematical model. However, when the control method based on the traditional theory is used for designing the four-rotor unmanned aerial vehicle, the defects are mainly reflected in the following aspects: (1) when a flight control system is designed based on a traditional control strategy, a multi-input multi-output unmanned aerial vehicle model is generally simplified into a plurality of single-input single-output models, then controller design is carried out on each channel, and the design strategy of artificial forced decoupling is easy to cause instability when the unmanned aerial vehicle carries out rapid maneuvering flight; (2) the conventional flight control system designed based on the Lyapunov theory can only realize asymptotic stable tracking control on a given reference instruction, and limits the ultimate flight capability of the unmanned aerial vehicle, and the conventional theory shows that the flight control system based on limited time can comprehensively improve the tracking precision, the convergence speed and the robustness of the system while ensuring the stability of the system; (3) the parameter adjustment of the controller designed based on the traditional control method depends heavily on the uncertainty of a system model and external interference, during actual flight control, due to the existence of unknown interference, the flight control performance is often difficult to obtain an expected control effect, and the parameter adjustment of the controller designed based on the strategy is time-consuming and labor-consuming.
Aiming at the limitations, the invention firstly provides a multivariable interference compensation finite time trajectory attitude cooperative control method for the quad-rotor unmanned aerial vehicle in a multivariable control framework, and a flight control system designed based on the method can carry out online estimation and compensation on comprehensive interferences such as uncertain system model parameters, unmodeled dynamic conditions, external wind interference and the like, thereby obviously improving the capability of the quad-rotor unmanned aerial vehicle for coping with complex flight environments; in addition, the controller designed based on the method can realize the finite time cooperation of the track and the attitude of the quad-rotor unmanned aerial vehicle, ensure that a flight control system has higher control precision, faster convergence speed and stronger robustness, and effectively enhance the control performance of the system; more importantly, the selection of the controller parameters based on the method only depends on the nominal model of the system, and is irrelevant to the uncertainty of the system model and the external comprehensive interference, so that the parameter debugging of the control system is greatly simplified.
The invention relates to the technical field of flight control of quad-rotor unmanned aerial vehicles. Specifically, a multivariable interference compensation-based four-rotor unmanned aerial vehicle trajectory attitude cooperative control algorithm different from the traditional control mode is provided, and then the validity of the algorithm provided by the invention is verified through the comparative analysis of Simulink simulation and the traditional PID method.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a high-precision and quick track attitude cooperative control algorithm applied to a quad-rotor unmanned aerial vehicle. Particularly, the urgent need of safe, stable and reliable flight under the complex flight environment of the unmanned aerial vehicle is considered, under the condition that the model parameters of the unmanned aerial vehicle are uncertain, the dynamic state without modeling and the external interference influence are comprehensively considered, a finite time track attitude cooperative control algorithm based on multivariable interference compensation is provided, the defects of the traditional control method of the quad-rotor unmanned aerial vehicle in the aspects of control precision, response speed and interference resistance are overcome, the problem of high-precision, rapid and stable tracking control of tracks and attitudes of the quad-rotor unmanned aerial vehicle under the comprehensive interference influence is solved, and the purposes of improving the control performance of the quad-rotor unmanned aerial vehicle and enhancing the safety and reliability of the. The technical scheme adopted by the invention is that the multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method comprises the following specific steps:
first part, trajectory controller-disturbance compensator design: designing a multivariable track controller and an interference compensator with a finite time convergence characteristic aiming at an outer ring position subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the position subsystem and transmitting an interference estimation value to the track controller in real time, and the track controller ensures that high-precision rapid tracking of a reference track is realized within finite time and provides a feasible virtual control instruction for an attitude calculation module;
and in the second part, attitude calculation: based on the flight characteristics of the quad-rotor unmanned aerial vehicle, an analytic relation between a virtual control instruction and an expected attitude angle instruction is established, and the purpose of indirectly tracking a given reference trajectory is achieved while the follow-up inner-loop trajectory controller tracks the expected attitude;
third, attitude controller-disturbance compensator design: a multivariable attitude controller and an interference compensator with a finite time convergence characteristic are designed for an inner ring attitude subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the attitude subsystem and transmitting an interference estimation value to the attitude controller in real time, and the attitude controller ensures that high-precision rapid tracking of an expected attitude is realized within finite time.
The specific implementation process is as follows:
the method comprises the following steps of firstly, analyzing a four-rotor unmanned aerial vehicle model based on multiple time scales: according to the multi-time scale characteristic of the unmanned aerial vehicle, dividing the unmanned aerial vehicle model with six degrees of freedom into a position subsystem and an attitude subsystem:
location subsystem
Attitude subsystem
Wherein xi is [ x, y, z ═ z]T∈R3Indicating the location of the drone; v ═ vx,vy,vz]TRepresenting the speed of the unmanned aerial vehicle in the directions of coordinate axes x, y and z; g represents the gravitational acceleration; e.g. of the typez＝[0,0,1]T；τfRepresenting the total lift of the unmanned aerial vehicle; m represents the mass of the drone; theta is phi, theta, psi]Representing an attitude angle vector of the unmanned aerial vehicle, wherein phi represents a pitch angle, theta represents a roll angle, and psi represents a yaw angle; w ═ ωx,ωy,ωz]TRepresenting an attitude angular velocity vector; i ═ diag [ I ═ Ix,Iy,Iz]Representing an aircraft inertia matrix; τ ═ τ [ τ ]1,τ2,τ3]TRepresents a control torque; delta1And Δ2Separate representation of position subsystems andexternal interference suffered by the attitude subsystem; the matrix W is defined as follows
The orthogonal rotation matrix R is defined as follows
The second step, four rotor unmanned aerial vehicle trajectory control ware-interference compensator design: introducing virtual control variables for a position subsystem (1)
To ensure control signals taufContinuously, the location subsystem (1) is extended, defining the following augmentation variables:
defining quad-rotor unmanned aerial vehicle trajectory tracking error
Wherein x1ref＝[xref,yref,zref]A reference trajectory of the drone is represented,
denotes x1refI times the differential signal. The augmented dynamic system based on the tracking error is expressed as
Aiming at a four-rotor unmanned aerial vehicle trajectory error augmentation system (6), the design control law is as shown in (7)
Wherein
In formula (7)
Equivalent to an interference compensator for realizing the comprehensive interference in the pair formula (6)
Real-time online estimation. In the formula (7), the parameter λ is selectedi(i ═ 1,2,3,4) so that polynomial s4+λ4s3+λ3s2+λ2s+λ1Is a Hurwitz polynomial, the gain k of the interference compensator1And k2Satisfy the requirement of
Wherein L isoComprehensive interference heald for position representative subsystem
Upper bound of (d), controller parameter ρi(i ═ 1.., 4.) is calculated by equation (9)
Thirdly, resolving the four-rotor unmanned aerial vehicle attitude: resolving through the attitude to obtain the analytic relation between the flight trajectory and the flight attitude of the quad-rotor unmanned aerial vehicle, and obtaining the total lift of the quad-rotor unmanned aerial vehicle at the same time, wherein the specific calculation process is as follows:
wherein τ'fi(i-1, 2,3) represents a virtual control vector τ'fThe ith element of (1), sφ＝sinφ,sθ＝sinθ,
cφ＝cosφ,cosθ＝cosθ,
φrefAnd thetarefAn expected attitude angle command obtained through attitude calculation;
fourthly, designing a four-rotor unmanned aerial vehicle attitude controller-interference compensator: introducing intermediate variables for the attitude subsystem (2)
x5＝Θ,x6＝WΩ (13)
Defining attitude tracking errors
Wherein Θ isref＝[φref,θref,ψref]Representing the expected attitude of the unmanned aerial vehicle, the dynamic system based on the attitude tracking error is expressed as:
attitude error dynamic system (15) for quad-rotor unmanned aerial vehicle, control torque is designed as shown in (16)
Wherein
The system is an interference compensator of the attitude subsystem and is used for realizing real-time online estimation of comprehensive interference of the attitude subsystem. In formula (16), λ5And λ6At an arbitrary normal value, the interference compensator gain k3And k4Satisfy the requirement of
Wherein L isiRepresenting the upper bound of the attitude subsystem synthetic disturbance Δ', the controller parameter ρ5＝ρ/(2-ρ),ρ6ρ, where ρ ∈ (0, 1). The actual control torque of the quad-rotor unmanned aerial vehicle can be calculated through (15) as follows: tau is IW-1τ'。
Verifying effectiveness, namely performing integrated design on a track attitude cooperative control system of the quad-rotor unmanned aerial vehicle in Matlab/Simulink, and performing a simulation experiment, wherein the simulation implementation process is as follows:
(1) parameter setting
1) Reference trajectory of quad-rotor unmanned aerial vehicle: p is a radical ofref(t)＝pr0+a3pt3+a4pt4+a5pt5Wherein p isref(t) denotes a given reference trajectory in p ∈ { x, y, z } direction, pr0Representing the initial position, coefficient a3p,a4p,a5pBy the formula
Is calculated to obtain wherein
pfAnd tfRespectively representing the position of the terminal and the time of response, and taking t in simulation f20, x, y, z direction terminal position xf＝20,yf＝5,z f10, heading reference trajectory ψref＝0。
2) Physical parameters of the quad-rotor unmanned aerial vehicle: mass m of aircraft is 0.625kg, inertia parameter Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2；
3) Setting parameters of the cooperative controller: trajectory controller-disturbance compensator parameter lambda1＝6,λ2＝15,λ3＝15,λ4＝6ρ＝0.75,L o10; attitude controller-disturbance compensator parameter lambda5＝15,λ6＝20ρ＝0.7,Li＝10；
In the simulation test verification process, the sampling time is set to be a fixed step length of 1 millisecond, and the position ring external interference uses a time-varying function delta1＝50(1+cos(t)+sin(t))diag(Ix,Iy,Iz) Simulation is carried out, and the external interference delta of the attitude ring20.5(1+ cos (t) + sin (t)), and furthermore, the model was assumed in the simulation to have an inertial parameter uncertainty of 20%.
The invention has the characteristics and beneficial effects that:
comparing the algorithm provided by the invention with the traditional PID control algorithm, the simulation results obtained by the two control methods are shown in FIGS. 2-8. Wherein, fig. 2-5 are the result of the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation proposed by the invention, fig. 6-7 are the result obtained based on the conventional PID, and fig. 8 is the comparison curve of the two control algorithms on the accuracy and convergence speed of the trajectory attitude cooperative control.
When the algorithm provided by the invention is used for tracking the expected attitude command, the maximum tracking error is about 10-6Radian and tracking precision are obviously superior to those of a PID control algorithm.
Description of the drawings:
figure 1 is a diagram of a trajectory and attitude coordinated control system of a quad-rotor unmanned aerial vehicle based on multivariate disturbance compensation.
FIG. 2 illustrates a disturbance compensation-trajectory attitude co-tracking curve.
Fig. 3 shows a disturbance compensation-control input profile.
Fig. 4 interference compensation-position loop (outer loop) interference estimation curve.
Fig. 5 interference compensation-attitude loop (inner loop) interference estimation curve.
FIG. 6 is a conventional PID-trajectory pose co-tracking curve.
FIG. 7 is a conventional PID-control input profile.
FIG. 8 interference compensation-conventional PID trajectory attitude coordinated tracking error comparison.
Detailed Description
The general technical scheme of the trajectory and attitude cooperative control algorithm of the four-rotor unmanned aerial vehicle based on multivariate interference compensation is shown in figure 1, and the whole system mainly comprises three parts: the method comprises the following specific technical scheme that the method comprises the following steps of track controller-interference compensator design, attitude calculation and attitude controller-interference compensator design:
first part, trajectory controller-disturbance compensator design: a multivariable track controller and an interference compensator with a finite time convergence characteristic are designed for an outer ring position subsystem based on a homogeneous theory, wherein the interference compensator is used for achieving online observation of external interference of the position subsystem and transmitting an interference estimation value to the track controller in real time, and the track controller ensures that high-precision rapid tracking of a reference track is achieved within finite time and provides a feasible virtual control instruction for an attitude calculation module.
And in the second part, attitude calculation: based on the flight characteristics of the quad-rotor unmanned aerial vehicle, an analytic relation between an outer ring virtual control instruction and an inner ring expected attitude angle instruction is established, and the purpose of indirectly tracking a given reference trajectory is achieved while a subsequent inner ring trajectory controller tracks an expected attitude.
Third, attitude controller-disturbance compensator design: a multivariable attitude controller and an interference compensator with a finite time convergence characteristic are designed for an inner ring attitude subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the attitude subsystem and transmitting an interference estimation value to the attitude controller in real time, and the attitude controller ensures that high-precision rapid tracking of an expected attitude is realized within finite time.
And finally, in order to verify the effectiveness of the algorithm provided by the invention, an MATLAB/Simulink simulation system for the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle is set up, and the simulation result is compared with the traditional PID control method, so that the advantages of the algorithm provided by the invention on the tracking precision and the convergence speed are verified.
The invention provides a trajectory and attitude cooperative control algorithm of a four-rotor unmanned aerial vehicle based on multivariate interference compensation by taking a finite time control theory based on homogeneity as a main research means, and the specific implementation process is as follows.
In a first step, a quad-rotor drone model analysis based on multiple time scales. According to the multi-time scale characteristic of the unmanned aerial vehicle, dividing the unmanned aerial vehicle model with six degrees of freedom into a position subsystem and an attitude subsystem:
location subsystem
Attitude subsystem
Wherein xi is [ x, y, z ═ z]T∈R3Indicating the location of the drone; v ═ vx,vy,vz]TRepresenting the speed of the unmanned aerial vehicle in the directions of coordinate axes x, y and z; g represents the gravitational acceleration; e.g. of the typez＝[0,0,1]T；τfRepresenting the total lift of the unmanned aerial vehicle; m represents the mass of the drone; theta is phi, theta, psi]Representing the attitude of the unmanned aerial vehicle, wherein phi represents a pitch angle, theta represents a roll angle, and psi represents a yaw angle; w ═ ωx,ωy,ωz]TRepresenting an attitude angular velocity; i ═ diag [ I ═ Ix,Iy,Iz]Representing an aircraft inertia matrix; τ ═ τ [ τ ]1,τ2,τ3]TPresentation controlTorque is produced; delta1And Δ2Respectively representing external interference suffered by the position subsystem and the attitude subsystem; the matrix W is defined as follows
The orthogonal rotation matrix R is defined as follows
And step two, designing a four-rotor unmanned aerial vehicle trajectory controller-interference compensator. Introducing virtual control variables for the position subsystem (17)
To ensure control signals taufContinuously, the position subsystem (17) is extended, defining the following augmentation variables:
defining quad-rotor unmanned aerial vehicle trajectory tracking error
Wherein x1ref＝[xref,yref,zref]A reference trajectory of the drone is represented,
denotes x1refThe i-th order differential signal is expressed as the augmented dynamic system based on the track tracking error
Aiming at a four-rotor unmanned aerial vehicle trajectory error augmentation system (22), the design control law is shown as (23)
Wherein
In formula (23)
Corresponding to an interference compensator for realizing the comprehensive interference in the pair formula (22)
Is estimated in real time on-line, in equation (23), the parameter λ is selectedi(i is 1,2,3,4) such that the polynomial s4+λ4s3+λ3s2+λ2s+λ1Is a Hurwitz polynomial, the gain k of the interference compensator1And k2Satisfy the requirement of
Wherein L isoRepresenting location subsystem synthetic interference
Upper bound of (d), controller parameter ρi(i ═ 1.., 4.) is calculated by equation (25)
Thirdly, resolving the four-rotor unmanned aerial vehicle attitude: resolving through the attitude to obtain an analytic relation between the flight trajectory and the flight attitude of the quad-rotor unmanned aerial vehicle, and simultaneously obtaining the total lift of the quad-rotor unmanned aerial vehicle, wherein the specific calculation process is as follows.
Wherein τ'fi(i-1, 2,3) represents a virtual control vector τ'fThe ith element of (1), sφ＝sinφ,sθ＝sinθ,
cφ＝cosφ,cosθ＝cosθ,
φrefAnd thetarefIs a desired attitude angle command obtained by attitude calculation.
And fourthly, designing a four-rotor unmanned aerial vehicle attitude controller-interference compensator. Introducing intermediate variables for the pose subsystem (18)
x5＝Θ,x6＝WΩ (29)
Defining attitude tracking errors
Wherein Θ isref＝[φref,θref,ψref]Representing the desired pose of the drone, a dynamic system based on pose tracking errors can be expressed as
For attitude error dynamic system (31) of quad-rotor unmanned aerial vehicle, design control torque is as shown in (32)
Wherein
The system is an interference compensator of the attitude subsystem and is used for realizing real-time online estimation of comprehensive interference of the attitude subsystem. In formula (32), λ5And λ6At an arbitrary normal value, the interference compensator gain k3And k4Satisfy the requirement of
Wherein L isiRepresenting the upper bound of the attitude subsystem synthetic disturbance Δ', the controller parameter ρ5＝ρ/(2-ρ),ρ6ρ, where ρ ∈ (0, 1). The actual control torque of the quadrotor unmanned aerial vehicle can be calculated through the method (31) as follows: tau is IW-1τ'。
In order to verify the effectiveness of the trajectory attitude cooperative control algorithm of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation, the trajectory attitude cooperative control system of the quad-rotor unmanned aerial vehicle is integrated and designed in Matlab/Simulink, and a simulation experiment is carried out, wherein the main simulation process comprises the following steps:
(1) parameter setting
1) Reference trajectory of quad-rotor unmanned aerial vehicle: p is a radical ofref(t)＝pr0+a3pt3+a4pt4+a5pt5Wherein p isref(t) denotes a given reference trajectory in p ∈ { x, y, z } direction, pr0Representing the initial position, coefficient a3p,a4p,a5pBy the formula
Is calculated to obtain wherein
pfAnd tfRespectively representing the position of the terminal and the time of response, and taking t in simulation f20, x, y, z direction terminal position xf＝20,yf＝5,z f10, heading reference trajectory ψref＝0。
2) Physical parameters of the quad-rotor unmanned aerial vehicle: mass m of aircraft is 0.625kg, inertia parameter Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2。
3) Setting parameters of the cooperative controller: trajectory controller-disturbance compensator parameter lambda1＝6,λ2＝15,λ3＝15,λ4＝6ρ＝0.75,L o10; attitude controller-disturbance compensator parameter lambda5＝15,λ6＝20ρ＝0.7,Li＝10。
In the simulation test verification process, the sampling time is set to be a fixed step length of 1 millisecond, and the position ring external interference uses a time-varying function delta1＝50(1+cos(t)+sin(t))diag(Ix,Iy,Iz) Simulation is carried out, and the external interference delta of the attitude ring20.5(1+ cos (t) + sin (t)), and furthermore, the model was assumed in the simulation to have an inertial parameter uncertainty of 20%.
(2) Analysis of results
Under the given conditions, the algorithm provided by the invention is compared with the traditional PID control algorithm, and the simulation results obtained by the two control methods are shown in FIGS. 2-8. Wherein, fig. 2-5 are the result of the trajectory attitude cooperative control of the quad-rotor unmanned aerial vehicle based on multivariate interference compensation proposed by the invention, fig. 6-7 are the result obtained based on the conventional PID, and fig. 8 is the comparison curve of the two control algorithms on the accuracy and convergence speed of the trajectory attitude cooperative control.
And (3) analyzing the result of multivariate disturbance compensation trajectory attitude cooperative control: fig. 2 shows that in the proposed trajectory-attitude cooperative control framework (as in fig. 1) of a quad-rotor unmanned aerial vehicle, cooperative tracking control over a given reference trajectory and a desired attitude can be well achieved by using the trajectory-attitude cooperative control algorithm based on multivariate interference compensation proposed by the present invention. Fig. 3 shows the corresponding control torque and total control lift force required for realizing the cooperative control of flight trajectory attitude, from which it can be found that the control curve obtained based on the algorithm of the present invention has smooth change and is easy to realize in engineering. In addition, the algorithm can realize the track and attitude cooperative control of the quad-rotor unmanned aerial vehicle in a limited time, and can perform online observation on the comprehensive interference of the unmanned aerial vehicle, such as external interference, model uncertainty and the like, and the change curves of the position ring and attitude ring interference compensators on the comprehensive interference estimation of the position subsystem and the attitude subsystem of the quad-rotor unmanned aerial vehicle are respectively shown in fig. 4 and 5.
Analyzing the result of the multivariate interference compensation orbit and the traditional PID orbit attitude cooperative control: fig. 6 and 7 respectively show a trajectory-attitude cooperative tracking curve and a response control curve under conventional PID control, and it can be seen that, although the control strategy based on PID can better realize tracking a given trajectory, the tracking effect on an expected attitude command is not good. Further, fig. 8 shows a comparison curve of the two algorithms on the precision of the trajectory collaborative tracking control of the quad-rotor unmanned aerial vehicle, and it can be seen from the curve that the collaborative control strategy based on PID is applied to a given reference trajectory x in the x, y, z directionsref,yrefAnd zrefThe maximum steady-state tracking errors of the tracking error are respectively 0.02m,0.027m and 0.021 m; from the enlarged view of fig. 8, it can be seen that the cooperative control algorithm based on multivariate disturbance compensation proposed by the present subject has maximum steady-state tracking error of the order of 10 for a given reference trajectory in the x, y, z directions-5And m is about better than the tracking precision of a given reference track by a PID cooperative control algorithm. In addition, a comparison of the attitude tracking error curves of the two cooperative control algorithms is given in fig. 8, and a simulation result shows that the maximum attitude tracking errors of the PID in the three directions of the roll, the pitch and the yaw are respectively 1.7 × 10-3Radian 8 x 10-3 Radian sum 10-4Radian, and the maximum tracking error is about 10 when the algorithm proposed based on the invention tracks the expected attitude command-6Radian and tracking precision are obviously superior to those of a PID control algorithm.
Claims (3)
1. A multivariable interference compensation quadrotor unmanned aerial vehicle track and attitude cooperative control method is characterized by comprising the following specific steps:
first part, trajectory controller-disturbance compensator design: designing a multivariable track controller and an interference compensator with a finite time convergence characteristic aiming at an outer ring position subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the position subsystem and transmitting an interference estimation value to the track controller in real time, and the track controller ensures that high-precision rapid tracking of a reference track is realized within finite time and provides a feasible virtual control instruction for an attitude calculation module;
and in the second part, attitude calculation: based on the flight characteristics of the quad-rotor unmanned aerial vehicle, an analytic relation between a virtual control instruction and an expected attitude angle instruction is established, and the purpose of indirectly tracking a given reference trajectory is achieved while the follow-up inner-loop trajectory controller tracks the expected attitude;
third, attitude controller-disturbance compensator design: a multivariable attitude controller and an interference compensator with a finite time convergence characteristic are designed for an inner ring attitude subsystem based on a homogeneous theory, wherein the interference compensator is used for completing online observation of external interference of the attitude subsystem and transmitting an interference estimation value to the attitude controller in real time, and the attitude controller ensures that high-precision rapid tracking of an expected attitude is realized within finite time.
2. The multivariable interference compensation quadrotor unmanned aerial vehicle trajectory and attitude cooperative control method according to claim 1, which is implemented by the following steps:
the method comprises the following steps of firstly, analyzing a four-rotor unmanned aerial vehicle model based on multiple time scales: according to the multi-time scale characteristic of the unmanned aerial vehicle, dividing the unmanned aerial vehicle model with six degrees of freedom into a position subsystem and an attitude subsystem:
location subsystem
Attitude subsystem
Wherein xi is [ x, y, z ═ z]T∈R3Indicating the location of the drone; v ═ vx,vy,vz]TRepresenting the speed of the unmanned aerial vehicle in the directions of coordinate axes x, y and z; g represents the gravitational acceleration; e.g. of the typez＝[0，0，1]T；τfRepresenting the total lift of the unmanned aerial vehicle; m represents the mass of the drone; theta is phi, theta, psi]Representing an attitude angle vector of the unmanned aerial vehicle, wherein phi represents a pitch angle, theta represents a roll angle, and psi represents a yaw angle;
Ω＝[ωx,ωy,ωz]Trepresenting an attitude angular velocity vector; i ═ diag [ I ═ Ix,Iy,Iz]Representing an aircraft inertia matrix; τ ═ τ [ τ ]1,τ2，τ3]TRepresents a control torque; delta1And Δ2Respectively representing external interference suffered by the position subsystem and the attitude subsystem; the matrix W is defined as follows
The orthogonal rotation matrix R is defined as follows
The second step, four rotor unmanned aerial vehicle trajectory control ware-interference compensator design: introducing virtual control variables for a position subsystem (1)
To ensure control signals taufContinuously, the location subsystem (1) is extended, defining the following augmentation variables:
defining quad-rotor unmanned aerial vehicle trajectory tracking error
Wherein x1ref＝[xref，yref，zref]A reference trajectory of the drone is represented,
denotes x1refThe i-th differential signal, the track tracking error-based augmentation dynamic system is expressed as:
aiming at a four-rotor unmanned aerial vehicle trajectory error augmentation system (6), the design control law is as shown in (7)
Wherein
In formula (7)
Equivalent to interference compensationMeans for achieving the synthetic interference in equation (6)
Is estimated in real time on-line, in equation (7), the parameter λ is selectediSo that the polynomial s4+λ4s3+λ3s2+λ2s+λ1Is a Hurwitz polynomial, the gain k of the interference compensator1And k2Satisfies the following conditions:
wherein L isoRepresenting location subsystem synthetic interference
Upper bound of (d), controller parameter ρiCalculated by equation (9):
thirdly, resolving the four-rotor unmanned aerial vehicle attitude: resolving through the attitude to obtain the analytic relation between the flight trajectory and the flight attitude of the quad-rotor unmanned aerial vehicle, and obtaining the total lift of the quad-rotor unmanned aerial vehicle at the same time, wherein the specific calculation process is as follows:
wherein τ'fiAnd i ═ 1,2, and 3 denote virtual control vectors τ'fThe ith element of (1), sφ＝sinφ，sθ＝sinθ，
cφ＝cosφ，cθ＝cosθ，
φrefAnd thetarefAn expected attitude angle command obtained through attitude calculation;
fourthly, designing a four-rotor unmanned aerial vehicle attitude controller-interference compensator: introducing intermediate variables for the attitude subsystem (2)
x5＝Θ，x6＝WΩ (13)
Defining attitude tracking errors
Wherein Θ isref＝[φref，θref，ψref]Representing the expected attitude of the unmanned aerial vehicle, the dynamic system based on the attitude tracking error is expressed as:
attitude error dynamic system (15) for quad-rotor unmanned aerial vehicle, control torque is designed as shown in (16)
Wherein
An interference compensator for the attitude subsystem for real-time on-line estimation of the complex interference to the attitude subsystem, in equation (16), λ5And λ6At an arbitrary normal value, the interference compensator gain k3And k4Satisfy the requirement of
k4>2LiWherein L isiRepresenting the upper bound of the attitude subsystem synthetic disturbance Δ', the controller parameter ρ5＝ρ/(2-ρ)，ρ6ρ, where ρ ∈ (0,1), the quad-rotor drone actual control torque may be calculated by (15) as: tau is IW-1τ'。
3. The method for cooperative control of trajectory and attitude of a multi-variable interference compensation quadrotor unmanned aerial vehicle according to claim 1, wherein the specific step of verifying validity comprises the steps of performing integrated design on the trajectory and attitude cooperative control system of the quadrotor unmanned aerial vehicle in Matlab/Simulink, and performing simulation experiments, wherein the simulation implementation process comprises the following steps:
1) reference trajectory of quad-rotor unmanned aerial vehicle: p is a radical ofref(t)＝pr0+a3pt3+a4pt4+a5pt5Wherein p isref(t) denotes a given reference trajectory in p ∈ { x, y, z } direction, pr0Representing the initial position, coefficient a3p，a4p，a5pBy the formula
Is calculated to obtain wherein
pfAnd tfRespectively representing the position of the terminal and the time of response, and taking t in simulationf20, x, y, z direction terminal position xf＝20,yf＝5,zf10, heading reference trajectory ψref＝0；
2) Physical parameters of the quad-rotor unmanned aerial vehicle: mass m of aircraft is 0.625kg, inertia parameter Ix＝2.3×10-3kgm2，Iy＝2.4×10-3kgm2，Iz＝2.6×10-3kgm2；
3) Setting parameters of the cooperative controller: trajectory controller-disturbance compensator parameter lambda1＝6，λ2＝15，λ3＝15，λ4＝6ρ＝0.75，Lo10; attitude controller-disturbance compensator parameter lambda5＝15，λ6＝20ρ＝0.7，Li＝10；
In the simulation test verification process, the sampling time is set to be a fixed step length of 1 millisecond, and the position ring external interference uses a time-varying function delta1＝50(1+cos(t)+sin(t))diag(Ix,Iy，Iz) Simulation is carried out, and the external interference delta of the attitude ring20.5(1+ cos (t) + sin (t)), and furthermore, the model was assumed in the simulation to have an inertial parameter uncertainty of 20%.
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