CN109062042B - Limited time track tracking control method of rotor craft - Google Patents
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Abstract
The invention provides a finite-time track tracking control method of a rotor aircraft, which comprises the following steps: establishing a mathematical model of the rotor craft; the method comprises the following steps that a layered control scheme is adopted, a rotor craft is divided into an altitude channel, a translation system and an attitude system, and a controller is designed for each channel; aiming at a height channel, a finite time controller is designed to generate lift force required by flight, and an auxiliary system is introduced to compensate input saturation; aiming at a translational system, designing a finite time controller to generate an expected rolling angle and an expected pitching angle; aiming at an attitude system, a linear active disturbance rejection controller is designed to generate the moment required by flight. The control strategy provided by the invention can not only improve the convergence rate, tracking accuracy and disturbance resistance of the rotor craft, but also effectively compensate the influence of input saturation on the control performance; the control strategy provided by the invention has the advantages of simple design, less calculation amount, convenient realization and high practical application value.
Description
Technical Field
The invention relates to the technical field of automatic control of a rotor craft, in particular to a finite-time track tracking control method of the rotor craft.
Background
The natural vertical take-off and landing, autonomous hovering and high maneuvering flight capability of the rotor craft enable the rotor craft to be widely applied to various industries; meanwhile, due to the characteristics of underactuation, nonlinearity and strong coupling of the rotor craft and the variable external disturbance in the flight environment, great difficulty is brought to autonomous flight control of the rotor craft, and the rotor craft is highly concerned by experts and scholars in the control field.
The rotorcraft considered in the present invention is a coaxial twelve-rotor unmanned aircraft, the structure of which is shown in fig. 1. Twelve rotors are pairwise in one group and are arranged at the tail end of the connecting rod at an angle of gamma with the plane of the aircraft body to provide flying power, and the rotating directions of the two adjacent rotors are opposite. Various movements of the aircraft are achieved by varying the speed of rotation of the individual rotors:
height movement: while increasing or while decreasing the rotational speed of each rotor.
Rolling movement: omega1+Ω2+Ω11+Ω12≠Ω5+Ω6+Ω7+Ω8
Pitching motion: omega1+Ω2+Ω3+Ω4+Ω5+Ω6≠Ω7+Ω8+Ω9+Ω10+Ω11+Ω12
Yaw movement: omega1+Ω3+Ω5+Ω7+Ω9+Ω11≠Ω2+Ω4+Ω6+Ω8+Ω10+Ω12
Wherein omega1,Ω2,Ω3,Ω4,Ω5,Ω6,Ω7,Ω8,Ω9,Ω10,Ω11,Ω12The rotational speeds of the rotors 1,2,3,4,5,6,7,8,9,10,11,12, respectively.
The problems of attitude stabilization and track following control of rotorcraft have received much attention in recent years. The existing linear and nonlinear control methods such as PID control, LQR control, robust control, sliding mode control, model predictive control and the like can enable the rotorcraft to obtain a better control effect and inhibit disturbance action to a certain extent. However, most of the existing algorithms achieve only the asymptotic stability of the aircraft closed loop system and do not take into account the problem of input saturation. The rotorcraft has high real-time requirements during actual flight, needs to respond quickly to expected commands, and the limited time stability of the closed-loop system is very important for the aircraft. Meanwhile, due to the physical limitation of the aircraft, namely the limited rotating speed of the motor-driven rotor, the lift force provided by the aircraft is limited. Deviations of the actual control quantity from the ideal control quantity due to the problem of input saturation of the aircraft can reduce system control performance. It is a difficult point to ensure the finite time convergence characteristics of an aircraft while compensating for the negative effects of input saturation. The finite time control strategy can improve the convergence speed, the anti-interference capability and the tracking precision of the system, so that the finite time controller is designed for the displacement system of the rotor craft, the finite time track tracking performance of the craft is theoretically ensured, an auxiliary system for finite time convergence is introduced, the input saturation effect is compensated, and the finite time stability of the displacement system of the craft is not influenced.
Disclosure of Invention
The invention aims to solve the problem of finite time track tracking control of an aircraft under the condition of input saturation, provides a finite time control strategy based on a finite time auxiliary system, improves the convergence rate, tracking accuracy and anti-interference capability of an aircraft displacement system, and ensures the finite time stability of the displacement system.
In order to achieve the purpose, the invention provides the following technical scheme:
Fig. 1 depicts a block diagram of a coaxial twelve-rotor aircraft under consideration, and a chosen geographic coordinate system E ═ OgxgygzgAnd a body coordinate system B ═ Obxbybzb}。
The displacement system model of the aircraft is obtained according to the Newton Euler equation as follows:
where φ, θ, ψ represent the roll, pitch and yaw angles of the rotorcraft, respectively, x, y, z represent the position coordinates of the aircraft, u1Representing the control force of the aircraft, m representing the mass of the aircraft, dx,dy,dzRespectively representing the disturbance action acting on each channel of the aircraft displacement system, g representing the gravity acceleration and the control force u required by the flight1There are input saturation constraints as follows:
where u is the desired control force to be integrated, umaxIs the upper bound of the input saturation constraint, uminIs the lower bound of the input saturation constraint.
The attitude system model of the aircraft is obtained according to the Newton Euler equation as follows:
wherein p, q, r respectively represent the roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft, u2,u3,u4Indicating the control moment of the aircraft, Ix,Iy,IzRepresenting the moment of inertia of the aircraft about the aircraft body axes, dφ,dθ,dψRespectively representing the effects of the disturbances acting on the various channels of the aircraft attitude system.
The control relationship model of the rotorcraft is as follows:
wherein, M ═ u2,u3,u4]TThe total moment acting on the aircraft is represented,
Ω1,Ω2,Ω3,Ω4,Ω5,Ω6,Ω7,Ω8,Ω9,Ω10,Ω11,Ω12the rotational speeds of the rotors 1,2,3,4,5,6,7,8,9,10,11,12, respectively, l representing the distance between the centre of mass of the aircraft and the center of the rotor, k1Denotes the lift factor, k2Representing the reaction torque factor, IrThe rotary inertia of the rotor and the motor rotor is shown, and gamma represents the included angle between the rotating shaft of each rotor and the plane of the machine body.
And 2, designing a layered control scheme of the rotor craft. Fig. 2 shows a specific design process: the rotorcraft is divided into an altitude channel, a translation system and an attitude system, and a controller is designed separately for each channel. The control scheme decomposes the rotor craft into a plurality of second order subsystems, simplifies the design process.
Aiming at the altitude channel, the flight control force is designed by combining an auxiliary system and a limited time control strategy, so that the input saturation effect is compensated while the stability of the altitude channel in limited time is ensured. And designing a virtual control quantity based on a finite time control strategy for the translation channel, and calculating a desired rolling angle and a desired pitching angle based on the virtual control quantity. Aiming at the attitude channel, a linear active disturbance rejection controller is designed to generate a flight control moment. The hierarchical control scheme solves the control difficulty brought by the under-actuated characteristic of the rotor craft.
The state information η, ζ of the rotorcraft is obtained by onboard sensors (where η ═ Φ, θ, ψ)]T,ζ＝[x,y,z]T) Desired trajectory xd,yd,zdAnd desired yaw angle psidGenerated by the navigation system. Aiming at an altitude channel, a finite time controller is designed to generate an ideal flight control force u, and an auxiliary system xi is introduced1,ξ2Compensating for input saturation; aiming at a translation channel, a finite time controller is designed to generate a virtual control quantity
And calculating the expected roll angle phi through a nonlinear decoupling equationdAnd a pitch angle thetad(ii) a Aiming at the attitude channel, a linear active disturbance rejection controller is designed to generate a flight control moment M.
The limited time assistance system is first designed as follows:
wherein ξ1,ξ2Is a state variable of the auxiliary system, c1＞0,c2And the parameter more than 0, more than 0 and less than 1 is an auxiliary system parameter.
The compensation error is defined as:
wherein z isdIs the desired height and alpha is the virtual control quantity to be designed.
Design of virtual control amount α:
wherein k is1＞0,l1> 0,0 < sigma < 1 are the controller parameters to be designed.
Designing an ideal control quantity u:
wherein,
is the controller parameter to be designed.
The designed altitude controller can compensate input saturation effect and simultaneously ensure the limited time stability of an aircraft altitude channel.
The Lyapunov function was chosen as:
derivative V and bring the designed α and u into the result:
wherein,
γ1＝2k1,γ2＝2k2,
γ＝min{γ1,γ2},β＝min{β1,β2},ι＝(σ+1)/2，Dz＞|dzi is the perturbation dzThe upper bound of (c).
The designed height controller is able to compensate for input saturation effects and ensure limited time stability of the height channel.
And 4, designing a translation controller of the rotor craft, and designing the translation controller by adopting a finite time control strategy to generate an expected rolling angle and an expected pitching angle of the attitude system of the rotor craft, so that the convergence rate and the tracking precision of the translation system are improved, and the finite time stability of the translation system is ensured. According to the displacement information zeta ═ x, y, z]TDesired trajectory xd,yd,zdGiving a virtual control quantity
The tracking error is defined as:
[χ11,χ12,χ13]T＝[x-Υ1,y-Υ2,z-Υ3]T
wherein, [ x ]d,yd,zd]T＝[Υ1,Υ2,Υ3]TIndicates a desired trajectory, [ alpha ]1,α2,α3]TRepresenting the intermediate control quantity to be designed.
Design intermediate control quantity alphai：
Wherein, delta1i＞0,λ1i＞0,0＜μi< 1 is the controller parameter to be designed.
Designing virtual control quantities
Wherein, delta2i＞0,λ2i＞0,0＜μi< 1 is the controller parameter to be designed.
The Lyapunov function was chosen as:
to ViDerivative and convert the designed alphaiAnd
the carry-in yields:
wherein, deltai＝min{2δ1i,2δ2i},
[dx,dy,dz]T＝[d1,d2,d3]TRepresenting the effect of disturbances acting on the respective channels, Di＞|diI is the perturbation diThe upper bound of (c).
The designed virtual controller can ensure the limited time stability of the translational channel of the rotorcraft.
By means of a non-linear decoupling module according to the designed virtual control quantity
The desired roll angle and the desired pitch angle of the aircraft are calculated as:
and 5, designing an attitude controller of the rotor craft, introducing a linear active disturbance rejection algorithm to design the attitude controller so as to generate control moment required by flight, and improving the robustness of an attitude system. According to the attitude information eta ═ phi, theta, psi]TDesired attitude angle phid,θd,ψdThe flight control moment M is given.
Writing the attitude system of the rotorcraft as a unified second-order system form as follows:
wherein,
τi＝[u2,u3,u4]T,bi＝[1/Ix,1/Iy,1/Iz]T，[ΔIx,ΔIy,ΔIz]Tindicating uncertainty of the parameter, τidIs the total disturbance including coupling, parameter uncertainty and external disturbance, respectively
τ1d＝-((Iz+ΔIz)-(Iy+ΔIy))qr/(Ix+ΔIx)-ΔIxτφ/Ix(Ix+ΔIx)+dφ,
τ2d＝-((Ix+ΔIx)-(Iz+ΔIz))pr/(Iy+ΔIy)-ΔIyτθ/Iy(Iy+ΔIy)+dθ，
τ3d＝-((Iy+ΔIy)-(Ix+ΔIx))pq/(Iz+ΔIz)-ΔIzτψ/Iz(Iz+ΔIz)+dψ。
Will total disturbance tauidExpansion into a third state variable of the attitude system
And aiming at the extended system, an extended state observer is designed as follows:
wherein
Respectively represent
τidIs determined by the estimated value of (c),
denotes the estimation error, κi1＞0,κi2＞0,κi3> 0 is the observer gain.
Based on the estimated value of the observer, the attitude controller is designed as follows:
wherein D isi1＞0,Di2> 0 is the gain of the controller,
is the desired attitude angle.
In general, the observer gain is taken as:
wherein,
is the observer bandwidth.
In general, the controller gain is taken to be:
the invention provides a finite-time track tracking control method of a rotor aircraft, aiming at ensuring the finite-time track tracking performance of the rotor aircraft when the input saturation effect exists. The advantages of the proposed method are:
(1) by introducing a finite time control strategy, the method improves the convergence rate, tracking accuracy and disturbance resistance of the displacement system of the rotorcraft, and ensures the finite time stability of the displacement system.
(2) The invention compensates the negative influence of the deviation of the ideal controlled variable and the actual controlled variable caused by the input saturation on the control performance of the rotor craft by introducing the auxiliary system with limited time convergence, and does not influence the limited time convergence characteristic of the displacement system.
(3) The algorithm provided by the invention still obtains stronger robustness even under the condition of not introducing any disturbance compensation mechanism, and simultaneously widens the selection range of the controller parameters.
Drawings
FIG. 1 is a block diagram of a rotary wing aircraft;
FIG. 2 is a control strategy diagram for a rotary wing aircraft;
FIG. 3 is a displacement x-tracking curve for a rotorcraft;
FIG. 4 is a displacement y-tracking curve for a rotorcraft;
FIG. 5 is a height z-tracking curve for a rotorcraft;
FIG. 6 is a 3-dimensional trajectory tracking curve for a rotorcraft;
FIG. 7 is a control force profile for a rotorcraft;
FIG. 8 is a state variable curve for a finite time assistance system;
detailed description of the preferred embodiments
The following describes the implementation process of the present invention in detail with reference to the attached drawings and simulation examples.
The invention provides a finite time track tracking control method of a rotor aircraft, wherein the related rotor aircraft is shown in figure 1, and the related control strategy schematic diagram is shown in figure 2, and the method mainly comprises the following steps: the system comprises a twelve-rotor aircraft module, a height controller module, a translation controller module, a nonlinear decoupling module and an attitude controller module. The function of each module is described below:
a twelve-rotor aircraft module: a mathematical model of the twelve-rotor aircraft is established through a Newton Euler equation, and the motion mechanism of the aircraft is described.
A height controller module: according to the acquired aircraft height information z and the expected track z generated by the navigation moduledDesigning an altitude controller to generate an ideal flight control force u and designing auxiliary system state information xi1,ξ2The compensation is given to the controller to counteract the ideal control force u and the saturation control force u generated by the input saturation1Deviation of flightThe controller controls the effect of performance.
A translation controller module: according to the collected aircraft displacement information zeta ═ x, y, z]TAnd a desired trajectory x generated by the navigation moduled,yd,zdDesigning a translation controller to generate a virtual control quantity
A nonlinear decoupling module: based on virtual control quantity generated by the flat controller module
Calculating the expected roll angle phi required by the attitude systemdAnd a desired pitch angle θd。
An attitude controller module: phi generated from a non-linear decoupling moduledAnd thetadPsi generated by navigation moduledAnd the collected attitude information eta of the aircraft is phi, theta, psi]TAnd designing an attitude controller to generate a flight control moment M.
The invention provides a finite time track tracking control method of a rotor aircraft, which well solves the problem of under-actuated characteristic of the aircraft, compensates the input saturation effect and ensures the finite time track tracking performance. The specific implementation steps are as follows:
1. and establishing a mathematical model of the rotor aircraft and describing the motion mechanism of the rotor aircraft.
Fig. 1 shows a block diagram of a coaxial twelve-rotor aircraft in question, the displacement system model of which is obtained according to the newton euler equation:
where phi, theta, psi denote the roll, pitch and yaw angles of the rotorcraft, respectively, x, y, z denote the position coordinates of the aircraft, which need to be measured by onboard sensors, m-2.5 kg denotes the mass of the aircraft, dx2sin (2 π t) is a perturbation on the x channel, which actsPerturbation d for the y-channelyIs a step signal of amplitude 2, d z1 is the perturbation acting on the z channel, and g 9.8ms-2Representing acceleration of gravity, u1Representing the control force of the aircraft, there are input saturation constraints as follows:
where u is the desired control force to be integrated, umax40N is the upper bound of the input saturation constraint, umin0N is the lower bound of the input saturation constraint.
The attitude system model of the rotor craft obtained according to the Newton Euler equation is as follows:
wherein p, q, r represent the roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft, u, respectively2,u3,u4Representing the aircraft control moment to be designed, Ix＝0.0081Nms-2,Iy＝0.0081Nms-2,Iz＝0.0142Nms-2Disturbance d representing the moment of inertia of the aircraft about each axis of the aircraft body and acting on the roll channelφIs a slope signal with the slope of 0.05, and acts on the disturbance d of the pitch channelθIs a square wave signal with the amplitude of 0.7, and acts on the disturbance d of the yaw channelψIs a step signal with an amplitude of 0.7.
The control relationship of the rotor craft is as follows:
wherein M is [ u ]2,u3,u4]TRepresenting the total moment, Ω, of the aircraft1,Ω2,Ω3,Ω4,Ω5,Ω6,Ω7,Ω8,Ω9,Ω10,Ω11,Ω12Representing the rotational speed of the rotor 1,2,3,4,5,6,7,8,9,10,11,12, respectively, l-0.5 m representing the distance between the centre of mass of the aircraft and the centre of the rotor, k1＝54.2×10-6Ns2Denotes the lift factor, k2＝1.1×10-6Nms-2Representing the reaction torque factor, IrThe rotary inertia of the rotor and the rotor of the motor is shown, and the included angle between the rotating shaft of each rotor and the plane of the machine body is shown as gamma 60 degrees.
2. A hierarchical control scheme for a rotorcraft is designed as shown in figure 2.
3. The height controller is designed to generate the ideal lift force u required by flight.
The design assistance system is as follows:
wherein ξ1,ξ2Is a state variable of the auxiliary system, c1＝0.5,c2＝0.78,υ＝0.8。
The compensation error is defined as:
design of virtual control amount α:
wherein k is1＝3,l1＝5,σ＝0.8。
Designing an ideal control quantity u:
wherein,
k2＝2,l2＝5。
4. designing a translation controller to generate virtual control quantities
The tracking error is defined as:
[χ11,χ12,χ13]T＝[x-Υ1,y-Υ2,z-Υ3]T
wherein, [ x ]d,yd,zd]T＝[Υ1,Υ2,Υ3]TRepresenting the desired trajectory.
Design intermediate control quantity alphaiComprises the following steps:
in the formula, delta1i＝[3,3,3]T,λ1i＝[2,2,2]T,μi＝[0.5,0.5,0.5]T。
Designing virtual control quantities
The following were used:
in the formula, delta2i＝[2,2,2]T,λ2i＝[1,1,1]T。
By non-linear solutionsA coupling module for controlling the amount of virtual control based on the design
Calculating a desired roll angle phidAnd a desired pitch angle θdComprises the following steps:
5. and designing an attitude controller to generate a flying moment M.
And transforming the attitude system model into a uniform second-order system form as follows:
wherein,
τi＝[u2,u3,u4]T,bi＝[1/Ix,1/Iy,1/Iz]T，[ΔIx,ΔIy,ΔIz]Tthe expression parameter is uncertain and satisfies Δ Ix＝0.1Ix,ΔIy＝-0.1Iy,ΔIz＝0.1Iz，τidIs the total perturbation effect containing coupling, parameter uncertainty and external perturbation, respectively expressed as
τ1d＝-((Iz+ΔIz)-(Iy+ΔIy))qr/(Ix+ΔIx)-ΔIxτφ/Ix(Ix+ΔIx)+dφ,
τ2d＝-((Ix+ΔIx)-(Iz+ΔIz))pr/(Iy+ΔIy)-ΔIyτθ/Iy(Iy+ΔIy)+dθ，
τ3d＝-((Iy+ΔIy)-(Ix+ΔIx))pq/(Iz+ΔIz)-ΔIzτψ/Iz(Iz+ΔIz)+dψ。
Will total disturbance tauidExpansion to a third state variable
And designing an extended state observer as follows:
in the formula
Respectively represent
τidIs determined by the estimated value of (c),
denotes the estimation error, κi1＞0,κi2＞0,κi3> 0 represents the observer gain. In general, the observer gain is taken as:
wherein, ω is1＝75,ω2＝75,ω 320 is the bandwidth of the observer.
Based on the estimated value of the observer, the attitude controller is designed as follows:
in the formula,
representing desired attitude angle, Di1＞0,Di2> 0 represents the controller gain. In general, the controller gain is taken to be:
wherein, ω is1c＝25,ω2c＝25,ω3cAnd 7 is the controller bandwidth.
In order to verify the feasibility and the effectiveness of the algorithm provided by the invention, a track tracking simulation experiment of a coaxial twelve-rotor aircraft is carried out on a Matlab/Simulink platform.
The desired trajectory for a rotorcraft is a planar horizontal rectangular trajectory as follows:
in the formula,
the initial conditions of the rotorcraft were chosen as: zeta0＝[x0,y0,z0]T＝[0.5,-0.5,0]Tm，
η0＝[φ0,θ0,ψ0]T＝[0,0,0.2]Trad
Fig. 3-5 are results of trajectory tracking for a rotorcraft. As can be seen from the figure, the displacement channels x, y and z of the rotorcraft have the advantages of high response speed, good dynamic performance, small overshoot, capability of tracking an expected track in a short time, no influence of external disturbance action and high tracking precision. At the same time, the selection of the initial position does not affect the control effect of the aircraft.
Figure 6 is the result of 3-dimensional trajectory tracking for a rotorcraft. The results in fig. 6 further illustrate the effectiveness of the proposed algorithm of the present invention to achieve high accuracy tracking performance and robustness of the rotorcraft.
Fig. 7 is a control force curve for a rotorcraft, and fig. 8 is a state variable curve for a finite time auxiliary system. Fig. 7 illustrates that input saturation occurs during the experiment, and fig. 8 illustrates that the negative effects of input saturation are effectively compensated by the auxiliary system.
In conclusion, the control method provided by the invention improves the convergence rate, tracking accuracy and disturbance resistance of the rotor craft, enables the rotor craft to track the expected track within a limited time, effectively compensates the negative effect of the input saturation effect, and improves the safety of the aircraft.
The above detailed description describes the method for finite-time track following control of a rotorcraft according to the present invention, but the present invention is not limited to the above embodiments. Other embodiments, which can be devised by those skilled in the art without any creative work and under the same principle and essence of the present invention, such as color enhancement, modification and alteration, shall fall within the protection scope of the present invention.
Claims (9)
1. A method of limited-time track following control of a rotary-wing aircraft, the method comprising the steps of:
step 1, establishing a mathematical model of a rotor craft, wherein the model comprises a displacement system model, an attitude system model and a control relation model of the craft;
step 2, designing a layered control scheme of the rotor craft, dividing the craft into an altitude channel, a translation system and an attitude system, and designing a controller for each channel independently, wherein the control scheme decomposes the rotor craft into a plurality of second-order subsystems, thereby simplifying the design process;
step 3, designing a height controller of the rotor craft, designing the height controller based on a finite time control strategy to generate control force required by flight, introducing an auxiliary system to compensate input saturation, and ensuring the finite time convergence characteristic and the anti-interference capability of a height channel;
step 4, designing a translation controller of the rotor craft, and designing the translation controller by adopting a finite time control strategy to generate an expected rolling angle and an expected pitching angle of the attitude system of the rotor craft, so that the convergence rate and the tracking accuracy of a translation system are improved, and the finite time stability of the translation system is ensured;
step 5, designing an attitude controller of the rotor craft, and introducing a linear active disturbance rejection algorithm to design the attitude controller so as to generate control moment required by flight, so that the robustness of an attitude system is improved;
the inputs of the altitude controller module of the rotorcraft in step 3 are the altitude channel state quantity z and the expected trajectory zdAnd auxiliary system state quantity xi1,ξ2The output is the ideal control force u, and the design process of the height controller is as follows:
firstly, designing an auxiliary system with limited time convergence as follows:
wherein ξ1,ξ2Is a state variable of the auxiliary system, c1＞0,c2More than 0, and more than 0 and less than 1 are auxiliary system parameters;
the compensation error is defined as:
e1＝z-zd-ξ1,
wherein z isdIs the desired height, α is the virtual control quantity to be designed;
the design virtual control quantity is as follows:
wherein k is1＞0,l1The parameters of the controller to be designed are more than 0, and more than 0 and less than 1;
the ideal control force is designed as follows:
wherein,
k2＞0,l2> 0,0 < sigma < 1 are the controller parameters to be designed.
2. A method for finite time track following control of a rotary-wing aircraft according to claim 1, wherein in step 1 the rotary-wing aircraft is a coaxial twelve-rotor aircraft, and the displacement system model of the aircraft is:
where φ, θ, ψ represent the roll, pitch and yaw angles of the rotorcraft, respectively, x, y, z represent the position coordinates of the aircraft, u1Representing the control force of the aircraft, m representing the mass of the aircraft, dx,dy,dzRespectively representing the disturbance action acting on each channel of the aircraft displacement system, g representing the gravity acceleration and the control force u required by the flight1There are input saturation constraints as follows:
where u is the desired control force to be integrated, umaxIs the upper bound of the input saturation constraint, uminIs the lower bound of the input saturation constraint.
3. A method for finite time track following control of a rotary-wing aircraft according to claim 1, wherein the attitude system model of the aircraft in step 1 is:
wherein p, q, r respectively represent the roll angular velocity, pitch angular velocity and yaw angular velocity of the aircraft, u2,u3,u4Indicating the control moment of the aircraft, Ix,Iy,IzRepresenting the moment of inertia of the aircraft about the aircraft body axes, dφ,dθ,dψRespectively representing the effects of the disturbances acting on the various channels of the aircraft attitude system.
4. A method for finite time track following control of a rotary-wing aircraft according to claim 1, wherein the model of the control relationship of the aircraft in step 1 is as follows:
wherein M ═ u2,u3,u4]TThe total moment acting on the aircraft is represented,
Ω1,Ω2,Ω3,Ω4,Ω5,Ω6,Ω7,Ω8,Ω9,Ω10,Ω11,Ω12representing the rotational speed of the rotor 1,2,3,4,5,6,7,8,9,10,11,12, l representing the distance between the centre of mass of the aircraft and the centre of the rotor, k1Denotes the lift factor, k2Representing the reaction torque factor, IrThe rotary inertia of the rotor and the motor rotor is shown, and gamma represents the included angle between the rotating shaft of each rotor and the plane of the machine body.
5. The method for the finite-time track following control of the rotorcraft according to claim 1, wherein flight control force is designed for the altitude channel in step 2 by combining an auxiliary system and a finite-time control strategy, the input saturation effect is compensated while the finite time stability of the altitude channel is ensured, virtual control quantity is designed for the translational channel based on the finite-time control strategy, a desired roll angle and a desired pitch angle are calculated based on the virtual control quantity, a linear active disturbance rejection controller is designed for the attitude channel to generate flight control torque, and the control difficulty caused by the under-actuated characteristic of the rotorcraft is solved by the layered control scheme.
6. A method for finite time track following control of a rotary wing aircraft according to claim 1, wherein the altitude controller is configured to compensate for input saturation while ensuring finite time stability of the altitude path of the aircraft:
choosing a Lyapunov function as:
derivative V and bring the designed alpha and u into
To obtain:
wherein,
γ1＝2k1,γ2＝2k2,
γ＝min{γ1,γ2},β＝min{β1,β2},ι＝(σ+1)/2，Dz＞|dz| represents the perturbation dzThe upper bound of (c).
7. A method according to claim 1, wherein the input to the translational controller module of the rotorcraft in step 4 is displacement information ζ ═ x, y, z]TDesired trajectory xd,yd,zdThe output being a virtual control quantity
The design process of the translation controller is as follows:
the tracking error is defined as:
[χ11,χ12,χ13]T＝[x-Υ1,y-Υ2,z-Υ3]T,
wherein, [ x ]d,yd,zd]T＝[Υ1,Υ2,Υ3]TIndicates a desired trajectory, [ alpha ]1,α2,α3]TRepresenting an intermediate control quantity to be designed;
the design intermediate control quantity is as follows:
wherein, delta1i＞0,λ1i＞0,0＜μi< 1 is the controller parameter to be designed;
the design virtual control quantity is as follows:
wherein, delta2i＞0,λ2i＞0,0＜μi< 1 is the controller parameter to be designed;
the desired roll and pitch angles of the aircraft may then be controlled by the designed virtual control quantities
Expressed as:
8. a method for finite time track following control of a rotary-wing aircraft according to claim 7, wherein the translational controller is designed to ensure the finite time stability of the aircraft translational path:
choosing Lyapunov function as
To ViDerivative and convert the designed alphaiAnd
bringing in
To obtain:
wherein, deltai＝min{2δ1i,2δ2i},
[dx,dy,dz]T＝[d1,d2,d3]TRepresenting the effect of disturbances acting on the respective channels, Di＞|diI is the perturbation diThe upper bound of (c).
9. A method according to claim 1, wherein the input to the attitude controller module of the rotorcraft in step 5 is attitude information η ═ phi, theta, psi]TDesired attitude angle phid,θd,ψdThe attitude controller is designed as follows:
the rotorcraft attitude system module is written in a unified second-order system form as follows:
wherein,
τi＝[u2，u3，u4]T，bi＝[1/Ix，1/Iy，1/Iz]T，[ΔIx，ΔIy，ΔIz]Tindicating uncertainty of the parameter, τidIs the total disturbance including coupling, parameter uncertainty and external disturbance, respectively
τ1d＝-((Iz+ΔIz)-(Iy+ΔIy))qr/(Ix+ΔIx)-ΔIxτφ/Ix(Ix+ΔIx)+dφ，
τ2d＝-((Ix+ΔIx)-(Iz+ΔIz))pr/(Iy+ΔIy)-ΔIyτθ/Iy(Iy+ΔIy)+dθ，
τ3d＝-((Iy+ΔIy)-(Ix+ΔIx))pq/(Iz+ΔIz)-ΔIzτψ/Iz(Iz+ΔIz)+dψ；
Will total disturbance tauidExpansion to a third state variable
And aiming at the extended system, an extended state observer is designed as follows:
wherein,
respectively represent
τidIs determined by the estimated value of (c),
denotes the estimation error, κi1＞0,κi2＞0,κi3Observer gain is > 0;
based on the estimated value of the observer, the attitude controller is designed as follows:
wherein,
is the gain of the controller and is,
is the desired attitude angle.
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