CN108121354A - Quadrotor unmanned plane tenacious tracking control method based on instruction filtering Backstepping - Google Patents
Quadrotor unmanned plane tenacious tracking control method based on instruction filtering Backstepping Download PDFInfo
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- 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
- G05D1/0816—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability
- G05D1/0825—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for aircraft to ensure stability using mathematical models
Abstract
The invention discloses a kind of quadrotor unmanned plane tenacious tracking control methods based on instruction filtering Backstepping, belong to unmanned vehicle automation field.The invention is directed to the dynamic mathematical models of rigid body quadrotor unmanned plane, it is characterised in that：Include the following steps：Step 101 establishes quadrotor unmanned plane mathematical model；Step 102, quadrotor pose control system for unmanned plane；By using above-mentioned technical proposal, the quadrotor unmanned plane tenacious tracking control method based on instruction filtering Backstepping proposes that a kind of new instruction filters Reverse Step Control, it solves the problems, such as traditional anti-" calculating expansion ", compared with traditional Backstepping, introduce the complicated parsing derivation process that wave filter avoids virtual controlling, the tracking control unit of structure is succinctly effective, effectively solves the problems, such as " calculating expansion ", the stability analysis of closed-loop system is finally completed using singular perturbation theorem.
Description
Technical Field
The invention belongs to the field of automatic control of unmanned aerial vehicles, and particularly relates to a four-rotor unmanned aerial vehicle stable tracking control method based on an instruction filtering backstepping method.
Background
Unmanned Aerial Vehicle (Unmanned Aerial Vehicle) refers to an Unmanned, autonomous or remotely operated Vehicle that utilizes aerodynamic force to carry the flight and can be recycled for reuse. It is capable of carrying either lethal or non-lethal loads, a hot spot when military weapons are being developed in the world today. Meanwhile, research, development, manufacture and application of the civil unmanned aerial vehicle industry are important marks for measuring the level of national technological innovation and high-end manufacturing industry. With the continuous reduction of the development and production cost of the unmanned aerial vehicle, the application range of the unmanned aerial vehicle is increasingly wide, the unmanned aerial vehicle has vigorous market demands and wide development prospects, and the unmanned aerial vehicle has increasingly prominent effect in national economic construction and can become an important industry for supporting the development of the national economy. Unmanned aerial vehicles can be divided into two types, fixed-wing unmanned aerial vehicles and rotor-wing unmanned aerial vehicles. Both types of drones rely on aerodynamic forces to provide the required forces and moments, but the mechanisms are completely different. The fixed wing drone relies on the high speed movement of the whole airframe relative to the air to obtain the required force and moment, so the obtained power is directly closely related to the movement speed of the airframe and the attitude of the airframe. Compare with it, the required power of rotor unmanned aerial vehicle and moment acquire through the rotation of the rotor of fixed mounting on the organism, and are irrelevant with organism current operating speed, state. The fixed wing unmanned aerial vehicle needs to have great speed, and is bulky when the during operation, and can not accomplish tasks such as hover, cruise, VTOL. Rotor unmanned aerial vehicle can solve above-mentioned problem effectively, at fields such as investigation, take photo by plane, and rotor unmanned aerial vehicle uses more and more extensively. Among the present rotor unmanned aerial vehicle most common, the deepest, the application range of research is four rotor unmanned aerial vehicle most extensively, and its advantage and characteristics include: the mechanical structure is simple, the control is convenient and flexible, the control performance is high, various actions can be realized in a small range, the cost is low, the flight performance is good, the reaction torque paddle does not need to be configured, the maneuvering capability is good, and the stable flight can be realized in a narrow space. Therefore, quad-rotor unmanned aerial vehicles are gaining more and more attention in mission execution in military or civilian fields such as search and rescue, aerial photography, exploration, remote monitoring, high-voltage line inspection and the like.
As is well known, the tracking control problem of the quad-rotor unmanned aerial vehicle directly determines the application effect in practice, so that the method has very important significance on the research of control.
The current situation of foreign research:
the research on the navigation and control of the quad-rotor unmanned aerial vehicle is earlier than the start of the research in China, and the well-known research teams comprise a quad-rotor unmanned aerial vehicle platform of Oakland university in New Zealand, a Kenzo laboratory of Chiba university in Japan, a STARMAC project of Stanford university in America, an ACL (Aerospace Controls Lab) laboratory of the national Ma-province institute of technology, an RRG (Robust Robotics Group) team and the like.
(1) Four-rotor unmanned aerial vehicle platform for Oakland university in New Zealand
A hardware platform of a four-rotor unmanned aerial vehicle at Oakland university is shown in the figure, and the size of the hardware platform is 40 centimeters X40 centimeters, and the mass of the hardware platform is 1.4 kilograms. The power device is composed of four outer rotor brushless motors, and the takeoff mass can reach 2.2 kilograms.
The onboard control of the four-rotor unmanned aerial vehicle of Oakland university adopts a double-controller structure, one is a control processor, and the other is a telemetering processor (both controllers adopt Freescale HCS12 microprocessors). The sensors comprise height sensors (a pressure height measuring sensor SMD500, a sonar sensor MB 1040, a positioning sensor GPS < C04-4H) and a pose sensor IMU (3 DM-GX 1).
(2) Hardware platform of Japanese Qianye university four-rotor unmanned aerial vehicle
The four-rotor unmanned aerial vehicle platform of the university of thousand leaves is an indoor and outdoor universal hardware platform. The airframe itself employs an Ascending Technologies GmbH X-3D-BL quad-rotor aircraft, as shown. The fuselage mass is 400 grams and the payload 300 grams. The propulsion system comprises four brushless motors and four rotors, the full-load flight time is 12 minutes, and the no-load flight time can reach 20 minutes.
(3) Stanford University STARMAC series quad-rotor flying platform (framework of STARMAC Quadrotor UAV at Stanford University),
the STARMAC series of stanford university has undergone two generations of changes, and the STARMAC i aircraft body adopts the draganfly iii series in the united states, the effective load is about 113 g, and the aircraft can fly for ten minutes under the full-power condition. This flight platform utilizes two singlechip PIC 18g6520 to constitute dual controller structure, and the on-board sensor has Inertial Measurement Unit (IMU), difference global positioning system (difference GPS), SONAR ranging Sensor (SONAR) to and wireless transmission's bluetooth sensor etc.. The control algorithm and the control command of the aircraft are all completed by a ground station computer or a computer cluster.
After STARMAC i, STARMAC ii was further studied by stanford researchers to achieve good control. The STARMAC II aircraft body is self-made, the side length is 0.75 meters, the weight is 1.5 kilograms, and the effective load is 1 kilogram. The hardware platform of the four-rotor unmanned aerial vehicle is provided with three independent sensors for measuring and estimating the state of the aircraft.
The current situation of domestic research:
although research on quad-rotor unmanned aerial vehicles is later than international in China, the applications of quad-rotor unmanned aerial vehicles in various fields are gradually increased in recent years. The four-rotor unmanned Aerial vehicle is promoted by setting up International Airborne Robot Competition (IARC) asia-tai race area, and mainly focuses on control theory and application research.
Except for colleges and universities, the development of quad-rotor unmanned aerial vehicles is greatly promoted by domestic commercial companies. Among them, well known are Dajiang innovation (DJI) and Jifei (Xaircraft). Currently, quad-rotor unmanned aerial vehicles produced by these commercial companies are mainly used in civil fields such as aerial photography and entertainment.
(1) Tianjin university fresh bin teaching team unmanned aerial vehicle part work: in order to realize the autonomous flight system of the small quad-rotor unmanned aerial vehicle, a flight control method based on vision is designed, and an embedded control framework flight test platform is built. The unmanned take-off mass of the four rotor wings is 1.4kg, and the effective load is 5N. In the control process, the optical flow information and the attitude angle information are fused for estimating the horizontal position information of the unmanned aerial vehicle, and the acquired horizontal position information is used as the proportional-derivative-integral control outer loop feedback information of the inner and outer loop structures.
Different from the traditional control architecture test platform based on the ground station, the flight system adopts a test platform with an embedded control architecture. The platform relies on an airborne embedded computer to perform optical flow calculation and motion state estimation, and an airborne flight controller is adopted to execute a control algorithm. The embedded control architecture engineering is high in implementation difficulty, and is more beneficial to realizing full-autonomous flight control of the quad-rotor unmanned aerial vehicle. Test results show that the design method achieves a good full-autonomous flight control effect.
The method comprises the steps of firstly improving a traditional visual SLAM (singular localization and mapping) algorithm by increasing the number of extracted feature points and optimizing key frame storage, improving the safety of flight control of the unmanned aerial vehicle, successfully overcoming the problems of visual SLAM image loss and position drift of an optical flow method, then fusing the position and 3-dimensional acceleration information of the unmanned aerial vehicle by adopting an EKF (extended Kalman filter), obtaining more accurate position information, simultaneously improving signal output frequency, finally designing a PID (proportional integral derivative) and E (proportional integral derivative) by using the position information of the unmanned aerial vehicle obtained by the method, and increasing the effectiveness of the unmanned aerial vehicle, and further avoiding the influence of the flight control algorithm on the unmanned aerial vehicle on the time control of the unmanned aerial vehicle, thereby realizing the effect of flight control of the unmanned aerial vehicle, and improving the flight control system.
The software framework adopted by the experimental platform is composed of a vision SLAM module (oSLAM }, an optical flow sensor module (OFS }, an IMU Module (IMU), an EKF module (EKF) and a Control module (Control), wherein each module corresponds to one device or task and is completed in an independent sub-thread, time delay is avoided in the Control process, the creation and destruction of each sub-thread and the data exchange among the sub-threads are completed by a MAIN MAIN thread, and the vision SLAM module is mainly used for the operation of an algorithm of the vision SLAM, so that the 3-dimensional position information and attitude optical flow sensor module of the unmanned aerial vehicle in a vision coordinate system is mainly used for extracting the horizontal speed information of the unmanned aerial vehicle and calculating the horizontal position information of the IMU module and mainly used for extracting the triaxial acceleration and the triaxial angular speed information under a machine body coordinate system.
(2) Partial research results of Nanjing aerospace university, the quad-rotor unmanned aerial vehicle and the GCS carry out two-way communication through wireless data transmission, so that the unmanned aerial vehicle can be subjected to parameter setting through the GCS, and the real-time monitoring of the flight state can be realized. The remote controller has two main functions, namely, the remote controller is used for providing a command gesture and a heading in a gesture control experiment. And secondly, the device is used as a control backup in an autonomous flight experiment, and once a fault occurs, the device can be switched to an attitude stabilization mode or a manual mode in time to ensure flight safety.
At present, the research of the four-rotor unmanned aerial vehicle enters the hot tide, and the related technology and theory achieve substantial progress. However, there are a number of critical issues that need to be addressed.
In the field of quad-rotor unmanned aerial vehicles, research problems at home and abroad are roughly divided into two types. One type concerns the problems encountered when the quad-rotor unmanned aerial vehicle flies in various real environments, and analyzes and optimizes the structural parameters of the quad-rotor unmanned aerial vehicle, so that the quad-rotor unmanned aerial vehicle can be better applied to the field of actual engineering. Another type focuses on theoretical research, and comprises establishing an accurate mathematical model of the quad-rotor unmanned aerial vehicle on the premise of considering characteristics such as aerodynamic force, aerodynamic interference and the like. On the basis, various control algorithms are researched, and stable tracking flight of the quad-rotor unmanned aerial vehicle is guaranteed.
A quad-rotor drone is a typical under-actuated system with only 4 inputs but 6 outputs, and therefore, quad-rotor drone systems often exhibit non-linearity, strong coupling, and susceptibility to interference during flight, and thus the requirements on the controller are extremely strict. The control algorithm is mainly used for improving the control precision of the unmanned aerial vehicle and improving robustness and response speed, so that the research on the control method has great significance on the development prospect of the unmanned aerial vehicle.
The control method can be classified into a linear method and a nonlinear method. The linear control method comprises the following steps: PID control, LQR control, method, etc. In the non-linear field, commonly used control algorithms are feedback linearization, sliding mode method, back step method, and the like.
Feedback linear control methods mainly use output feedback or other methods to transform a nonlinear system into a closed-loop linear system. Thereby applying a controller design method of a linear system to design a control scheme. However, this method depends particularly on the accuracy and precision of the model parameters, and the effect is greatly reduced if some links are not considered.
The sliding mode control is different from other controls in that the 'structure' of the system is not fixed, but can be purposefully changed continuously according to the current state of the system (such as deviation and each order derivative thereof) in a dynamic process, so that the system is forced to move according to the state track of a preset 'sliding mode'. The sliding mode can be designed and is irrelevant to the parameters and disturbance of an object, so that the sliding mode control has the advantages of quick response, insensitive corresponding parameter change and disturbance, no need of system online identification, simple physical realization and the like. But has the disadvantage that in addition to the jitter in the output of the system controller, factors such as speed, inertia, acceleration, switching profile, etc. need to be addressed as they approach the sliding mode profile.
The backstepping method divides the system into a plurality of subsystems, selects a proper Lyapunov function for each subsystem, designs a corresponding virtual control law, and finally obtains the actual control input of the system through multi-step deduction. The backstepping method perfectly combines the control rate solving process with the selection of the Lyapunov function. However, the traditional backstepping method has a design defect: the "compute inflation" problem. During the design process of each subsystem, the derivative of the virtual control needs to be conducted for a plurality of times. In the control input of the nth step, the nth derivative is required for the virtual control. With the increase of the order of the system, the derivation of the analytical expression of the virtual control derivative is difficult, even cannot be realized, and the problem limits the application of the backstepping method in the actual engineering.
Aiming at the problem of 'calculation expansion', jay A.Farrell and the like propose a class of instruction filtering backstepping method control, a pseudo control signal is estimated through a first-order filter or a second-order filter, and a compensation tracking error signal is introduced on the basis of a state tracking error. Wherein the compensated tracking error signal has similar properties as the state tracking of the conventional back-stepping method.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: under the support of national science foundation project (approval number: 61603274), a method for stably tracking and controlling a quadrotor unmanned aerial vehicle based on an instruction filtering backstepping method is provided; this four rotor unmanned aerial vehicle stable tracking control method based on instruction filtering backstepping method provides a kind of neotype instruction filtering backstepping control, solves the traditional anti "calculation inflation" problem, compares with traditional backstepping method, introduces the complicated analytic derivation process that the wave filter avoided virtual control, and the tracking controller of structure is succinct effective, effectively solves "calculation inflation" problem, adopts singular disturbance theorem to accomplish closed-loop system's stability analysis at last.
The technical scheme adopted by the invention for solving the technical problems in the prior art is as follows:
a four-rotor unmanned aerial vehicle stable tracking control method based on a command filtering backstepping method comprises the following steps:
101, establishing a mathematical model of a quad-rotor unmanned aerial vehicle; the method specifically comprises the following steps:
according to a Newton-Euler formula, a dynamic equation set of the quad-rotor unmanned aerial vehicle is established:
wherein x, y, z are the position coordinates of the drone, k x ,k y ,k z Is a constant coefficient, and m is the mass of the unmanned aerial vehicle; and isThe attitude of the quad-rotor unmanned aerial vehicle is shown, phi (t) is a rolling angle, theta (t) is a pitching angle, and psi (t) is a yaw angle; u shape 1 Is the total lift of the unmanned aerial vehicle, U = [ U = [ U ] 2 ,U 3 ,U 4 ] T Is a control input to the attitude controller; g is the acceleration of gravity and the acceleration of gravity,is the rotational inertia of the unmanned aerial vehicle;
the attitude kinematics equation set of the quad-rotor unmanned aerial vehicle is as follows:
expressing the attitude dynamics equation of the quad-rotor unmanned aerial vehicle in a vector form:
wherein, the first and the second end of the pipe are connected with each other,
the kinetic equation of the attitude of the quad-rotor unmanned aerial vehicle is expressed in a strict feedback form:
wherein, the first and the second end of the pipe are connected with each other,
step 102, a four-rotor unmanned aerial vehicle attitude control system:
to four rotor unmanned aerial vehicle's attitude dynamics equation (4), based on singular disturbance analysis design instruction filtering backstepping control U, consider coordinate transformation:
wherein z is 2 Is the error in the tracking of the track,respectively representing a virtual feedback control law and a filtered virtual control law, s 2 Is the filtering error;
in the design process of each step, the virtual feedback control alpha is designed firstly i+1 (i =1,2,3.. N), and then approximating the virtual control function using a non-linear inverse-cut filterUntil the final step designs a real control law U = alpha n+1 ；
The first step is as follows:
according to the formula (5), the attitude tracking error dynamically satisfies:
building a smooth feedback control input alpha 2 As follows, to stabilize equation (6):
where ρ is 1 Is a positive gain matrix of appropriate dimensions;
approximating the filter control vector by an arctangent filter
Wherein tau is η Is the filter gain;
the second step is that:
tracking error z 2 The derivative along the trajectory (4) satisfies:
the control inputs U are designed as follows:
where ρ is 2 Is the positive gain matrix to be designed;
state error subsystemExpressed as:
an attitude closed loop system is formed by a state error subsystem (13) and a filter subsystem (9), and the dynamic equation is as follows:
wherein, defineAndis a vector field function, the expression is:
the stability analysis of the closed loop system (14) is a standard singular disturbance problem; taking into account the expression, equation, of G (-)With a single stand-aloneAnd H (z) = α; will be provided withSubstituting into F (-) one can derive the dynamics of the reduced order system as:
to facilitate stability analysis, a new state variable is definedThus, the dynamic equation for the boundary layer system is expressed as:
wherein epsilon η :＝t η /τ η A time variable representing "stretch";
andthe solutions of equations (16) and (17), respectively.
Further: also comprises the following steps:
step 103, analyzing stability; the method comprises the following specific steps:
the following definitions 1 and 2 are introduced;
definition 1: the notation e (t, epsilon) is defined as e (t, epsilon) = o (epsilon), i.e. there is a constantSo that
Definition 2: when given for any given constantExist ofSo that the following holds:time, systemExponential stability is satisfied at equilibrium point ε → 0;
the Extended Tikhonov's Theorem is introduced to prove the stability of the attitude closed-loop system (14);
considering an attitude dynamics model (4), an attitude instruction filtering backstepping controller (11) and an attitude filter (9) of the unmanned aerial vehicle; for all control gain matrices, there is a suitably small constant τ ** Is epsilon (0, 1), when tau is epsilon (0, tau) ** ) In the process, the state tracking error of the whole closed-loop system meets the semi-global exponential stability; in other words, with the decrease of tau, the command filtering backstepping attitude control (11) can realize the control performance of the traditional backstepping;
and (3) proving that: definition ofAndare an immediate set containing the origin about z and xi, respectively; for the attitude singular disturbance system (16), if the following conditions are all satisfied:
(R1) pairFunctions F (-), G (-), and their relationIs continuously bounded, the functions H (z) andhas a bound to the first partial derivative of its argument, anLipschitz for z, consistent for t;
(R2) the origin of the attitude reduction system (16) is globally exponentially stable, i.e. there is a Lyapunov function V (z) satisfying W 1 (z)≤V(z)≤W 2 (z) andwherein W 1 (z),W 2 (z) and W 3 (z) is inInternally is a continuous positive definite function;
(R3) the origin of the boundary layer system (17) is exponentially stable, consistent for (t, z);
the attitude closed loop system (14) satisfies Extended Tikhonov's Theorem;
defining constantsSatisfy the requirement ofAndis the attraction zone for the z-axis,is the attraction zone of xi;
obviously, the attitude closed-loop system (14) satisfies the conditions (R1) - (R3) of the singular disturbance theorem; thus, for each tight subsetHas a constant τ * E (0, 1) such that for allAnd τ ∈ (0, τ) * ) The unique solution of the odd-even perturbation problem exists in [0, ∞ ]
And is
Is consistent for t ∈ [0, ∞);
wherein z is * (t),Ξ * (t/τ) is the global exponential stability solution of system attitude loop equations (16) and (17), respectively;
in addition, for any t a >, 0, presence of tau ** <τ * So that t e [ t ∈ ] a Infinity), then there are:
namely:
thus, there are
Obviously, the attitude closed loop system (14) is exponentially stable when τ → 0;
the attitude ring systems (16) and (17) are globally exponentially stable, and the attraction zone of the origin can be arbitrarily enlarged by reducing tauThe pose ring systems (16) and (17) are thus semi-globally stable.
Further: and step 104, simulation and experiment.
The invention has the advantages and positive effects that:
by adopting the technical scheme, the traditional backstepping design has the problem of 'calculation expansion' due to the increase of the complexity of system dynamics and the system sequence. The Command Filter Backstepping Control (CFBC) method utilizes an arctangent filter in the control law design, avoids repeated partitioning of virtual control, and forms a relatively simple controller compared to the traditional backstepping design. The problem that an object mathematical model is not differentiable in a backstepping method is solved, and therefore the generation of 'calculation expansion' is avoided. The proposed instruction filtering backstepping control also has the following advantages:
(1) Closed loop stability can only be ensured by appropriate adjustment of the filter parameter τ, rather than turning τ down and turning p up the control gain ρ i
(2) Steady-state tracking accuracy independent of high control gain ρ i Thus increasing ρ i There is no need to reduce the steady state tracking error.
(3) Thus, a simple but effective strategy for gain selection and system commissioning is: the control gain ρ can be appropriately selected i (ii) a That considerationBy the time of sampling, the noise level and the initial conditions, the filter parameter τ can be reduced.
(4) Tracking performance recovery can be controlled by reducing τ.
Drawings
FIG. 1 is a schematic structural view of a four-rotor of the prior art;
FIG. 2 is a schematic diagram of a semi-physical experiment of the system of the present invention;
FIG. 3 is a schematic diagram of a simulation using a Quanser system as a platform according to the present invention;
FIG. 4 is a graph comparing the tracking effect of roll angle of example 1;
FIG. 5 is a comparison of the pitch tracking effect of example 1;
FIG. 6 is a comparison of the effect of tracking yaw angle of example 1;
FIG. 7 is a graph comparing the response of roll angle output of example 2;
FIG. 8 is a comparison of the pitch output response of example 2;
FIG. 9 is a graph comparing the effects of yaw angle output responses of example 2.
Detailed Description
For a further understanding of the invention, its nature and utility, reference should be made to the following examples, taken in conjunction with the accompanying drawings, in which:
referring to fig. 1 to 9, a method for controlling stable tracking of a quad-rotor drone based on a command filtering backstepping method includes:
step 1, four rotor unmanned aerial vehicle mathematical model
According to a Newton-Euler formula, a dynamic equation of the quad-rotor unmanned aerial vehicle is established as follows:
wherein the x is a linear or branched chain alkyl group,y, z are the position coordinates of the drone, k x ,k y ,k z Is a constant coefficient, and m is the mass of the unmanned aerial vehicle. And is provided withThe attitude of the quad-rotor unmanned aerial vehicle is shown, phi (t) is a rolling angle, theta (t) is a pitching angle, and psi (t) is a yaw angle. U shape 1 For total lift of unmanned aerial vehicle, U = [ U = 2 ,U 3 ,U 4 ] T Is the control input of the attitude controller. g is the degree of acceleration by gravity,is the rotational inertia of the unmanned aerial vehicle.
Because attitude control is the key and the basis of the whole flight control, the following contents only study the attitude part, and the attitude kinematics equation of the four-rotor unmanned plane is as follows:
expressing the attitude dynamics equation of the quad-rotor unmanned aerial vehicle in a vector form:
wherein, the first and the second end of the pipe are connected with each other,
the invention aims to effectively solve the problems of complex design and poor effect of the existing four-rotor flight attitude controller, and provides a method for command filtering backstepping stable tracking control of a four-rotor unmanned aerial vehicle. Designing the control input U = [ U ] of the controller by using a relatively simple algorithm 2 ,U 3 ,U 4 ] T The attitude control of the quad-rotor unmanned aerial vehicle is completed, and the kinetic equation of the attitude of the quad-rotor unmanned aerial vehicle can be expressed asThe strict feedback form is as follows:
wherein, the first and the second end of the pipe are connected with each other,
step 2, four-rotor unmanned aerial vehicle attitude control system
And aiming at an attitude dynamics equation (4) of the quad-rotor unmanned aerial vehicle, designing a command filtering backstepping control U based on singular disturbance analysis. Similar to the conventional backstepping method, consider the coordinate transformation:
wherein z is 2 Is the error of the tracking of the object,respectively representing the virtual feedback control law and the filtering virtual control law, s 2 Is the filtering error. In the design process of each step, the virtual feedback control alpha is designed firstly i+1 (i =1,2,3.. N), and then approximating the virtual control function using a non-linear inverse cut filterUntil the final step designs a real control law U = alpha n+1 。
The first step is as follows:
according to formula (5), the attitude tracking error dynamically satisfies:
building a smooth feedback control input alpha 2 As follows, to stabilize equation (6):
where ρ is 1 Is a dimensionally appropriate positive gain matrix.
Thus, there are:
approximating the filter control vector by an arctangent filter
Wherein τ is η Is the filter gain.
The second step:
tracking error z 2 The derivative along the trajectory (4) satisfies:
the control inputs U are designed as follows:
where ρ is 2 Is the positive gain matrix to be designed.
Thus, there are
To sum up, the state error subsystemCan be expressed as:
an attitude closed loop system is formed by a state error subsystem (13) and a filter subsystem (9), and the dynamic equation is as follows:
wherein, defineAndis a vector field function, the expression is:
the stability analysis of the closed loop system (14) is a standard singular disturbance problem. Taking into account the expression, equation, of G (-)With a single stand-aloneAnd H (z) = α. Will be provided withSubstituting into F (-) one can deduce the dynamics of the reduced order system as:
to facilitate stability analysis, a new state variable is definedThus, the dynamic equation for the boundary layer system can be expressed as:
wherein epsilon η :＝t η /τ η Time variable representing "stretch".
Definition ofAndthe solutions of equations (16) and (17), respectively.
Step 3. Stability analysis
The following definitions 1 and 2 were introduced to facilitate the stability analysis of the system.
Definition 1: the symbol e (t, epsilon) is defined as e (t, epsilon) = omicron (epsilon), i.e. there is a constantSo that
Definition 2: when given for any given constantExist ofSo that the following holds:time, systemExponential stability is satisfied at the equilibrium point ε → 0.
The stability of the attitude closed loop system (14) is proved by introducing Extended Tikhonov's Theorem.
And considering an attitude dynamics model (4), an attitude instruction filtering backstepping controller (11) and an attitude filter (9) of the unmanned aerial vehicle. For all control gain matrices, there is a suitably small constant τ ** Is epsilon (0, 1), when tau is epsilon (0, tau) ** ) And in time, the state tracking error of the whole closed-loop system meets the semi-global exponential stability. In other words, as τ decreases, the command filter backstepping attitude control (11) can achieve the control performance of conventional backstepping.
And (3) proving that: definition ofAndare the tight sets containing the origin about z and xi, respectively. For the attitude singular disturbance system (16), if the following conditions are all satisfied:
(R1) pairFunctions F (-), G (-), and their relationIs continuously bounded, the functions H (z) andhas a bound to the first partial derivative of its argument, andlipschitz for z, consistent for t;
(R2) the origin of the attitude reduction system (16) is globally exponentially stable, i.e. there is a Lyapunov function V (z) satisfying W 1 (z)≤V(z)≤W 2 (z) andwherein W 1 (z),W 2 (z) and W 3 (z) is inInternally is a continuous positive definite function;
(R3) the origin of the boundary layer system (17) is exponentially stable and consistent for (t, z).
The pose closed loop system (14) satisfies Extended Tikhonov's Theorem.
Defining constantsSatisfy the requirement ofAndis the attraction zone for the z-axis,is an attraction zone of xi.
Obviously, the attitude closed-loop system (14) satisfies the conditions (R1) - (R3) of the singular disturbance theorem. Thus, for each tight subsetPresence constant τ * E (0, 1) such that for allAnd τ ∈ (0, τ) * ) The unique solution of the odd-even perturbation problem exists in [0, ∞ ]
And is
Is consistent for t ∈ [0, ∞).
Wherein z is * (t),Ξ * (t/τ) is the global exponential stability solution of system attitude loop equations (16) and (17), respectively.
In addition, for any t a >, 0, presence of tau ** <τ * So that t e [ t ∈ ] a And infinity), then there are:
namely:
thus, there are
It is clear that the attitude closed loop system (14) is exponentially stable when τ → 0.
The attitude ring systems (16) and (17) are globally exponentially stable, and the attraction zone of the origin can be arbitrarily enlarged by reducing tauThe attitude ring systems (16) and (17) are thus semi-globally stable.
And 4, simulating and testing.
The specific operation process of the preferred embodiment is as follows: the application of the command-filtering backstepping control technique to quad-rotor flight control first considers the basic structural and dynamic characteristics of a quad-rotor system. As shown in fig. 1, the body of the quad-rotor aircraft is fixedly connected to a rigid crisscross structure, four independent motors drive the rotors to rotate to provide flight power, and the rotation speed of the rotors can be controlled by changing the rotation speed of the motors, so as to finally realize the control of the flight attitude and position of the aircraft. The four-rotor aircraft is a typical underactuated strong coupling system because the four-rotor aircraft has four drives, i.e. four input quantities, but has six degrees of freedom output quantities. Rotors on the same diagonal rotate in the same direction, while adjacent rotors rotate in opposite directions. The front rotor serves as the nose of the body, and the rear rotor serves as the tail of the body. The front rotor and the rear rotor rotate anticlockwise as a group of positive propellers, and the left rotor and the right rotor rotate clockwise as a group of negative propellers, so that the design can eliminate the self-reactive torque of the body. In this rotation mode, the main motion states that can be achieved by a quad-rotor aircraft are: vertical motion, pitch motion, roll motion, yaw motion, and the like.
The schematic diagram of the system control structure of the present invention is shown in fig. 2, and the attitude control is performed on the system, so that the flight quality is improved, and the specific steps are as follows.
Example 1:
performing stable tracking control on the system, and selecting the initial attitude angle of the four-rotor aircraft asThe ideal values of the attitude angles were all set to be sinusoidal signals with amplitude of 1, frequency of 0.05Hz, and experimental time of 25s.
The final pose tracking results of the system are shown in fig. 4 to 6. The attitude tracking method has the advantages that pitching, rolling and yawing can quickly and accurately track given attitude signals, and the system can simultaneously give consideration to steady-state performance and dynamic performance in the attitude tracking process.
Example 2:
and (5) carrying out disturbance test on the system. When the system is operated to 12s, external disturbance torque is added to the stable pitch channel, and the output response of the system is shown in fig. 7 to 9. Fig. 7 to 9 show that the attitude channel has a large overshoot during the disturbance, but can still track the ideal signal quickly and stably after the disturbance disappears.
The invention researches the attitude control problem of the four-rotor aircraft, designs the instruction filtering backstepping controller by utilizing the dynamic model information of the attitude system of the four-rotor aircraft and considering factors such as the internal uncertainty and the external disturbance of the model, and analyzes the stability of a closed-loop system. The embodiment result shows that the command filtering backstepping controller designed by the invention can effectively realize the attitude control of the four-rotor aircraft.
The embodiments of the present invention have been described in detail, but the description is only for the preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. All equivalent changes and modifications made within the scope of the present invention shall fall within the scope of the present invention.
Claims (3)
1. The utility model provides a four rotor unmanned aerial vehicle stable tracking control method based on instruction filtering backstepping method which characterized in that: the method comprises the following steps:
101, establishing a mathematical model of a quad-rotor unmanned aerial vehicle; the method specifically comprises the following steps:
according to a Newton-Euler formula, a dynamic equation set of the quad-rotor unmanned aerial vehicle is established:
wherein x, y, z are the position coordinates of the unmanned aerial vehicle, k x ,k y ,k z Is a constant coefficient, and m is the mass of the unmanned aerial vehicle; and isThe attitude of the quad-rotor unmanned aerial vehicle is shown, phi (t) is a rolling angle, theta (t) is a pitch angle, and psi (t) is a yaw angle; u shape 1 Is the total lift of the unmanned aerial vehicle, U = [ U = [ U ] 2 ,U 3 ,U 4 ] T Is a control input for the attitude controller; g is the acceleration of gravity, and g is the acceleration of gravity,is the rotational inertia of the unmanned aerial vehicle;
the attitude kinematics equation set of the quad-rotor unmanned aerial vehicle is as follows:
expressing the attitude dynamics equation of the quad-rotor unmanned aerial vehicle in a vector form:
wherein the content of the first and second substances,
the kinetic equation of the attitude of the quad-rotor unmanned aerial vehicle is expressed in a strict feedback form:
wherein the content of the first and second substances,
step 102, a four-rotor unmanned aerial vehicle attitude control system:
to four rotor unmanned aerial vehicle's attitude dynamics equation (4), based on singular disturbance analysis design instruction filtering backstepping control U, consider coordinate transformation:
wherein z is 2 Is the tracking error, α 2 ,Respectively representing a virtual feedback control law and a filtered virtual control law, s 2 Is the filtering error;
in the design process of each step, the virtual feedback control alpha is designed firstly i+1 (i =1,2,3.. N), and then approximating the virtual control function using a non-linear inverse-cut filterUntil a real control law U = alpha is designed in the last step n+1 ；
The first step is as follows:
according to formula (5), the attitude tracking error dynamically satisfies:
building a smooth feedback control input alpha 2 As follows, to stabilize equation (6):
where ρ is 1 Is a positive gain matrix of appropriate dimensions;
approximating the filter control vector by an arctangent filter
Wherein τ is η Is the filter gain;
the second step is that:
tracking error z 2 The derivative along the trajectory (4) satisfies:
the design control input U is as follows:
where ρ is 2 Is the positive gain matrix to be designed;
state error subsystemExpressed as:
an attitude closed loop system is formed by a state error subsystem (13) and a filter subsystem (9), and the dynamic equation is as follows:
wherein, define Andis a vector field function, the expression is:
the stability analysis of the closed loop system (14) is a standard singular disturbance problem; taking into account the expression, equation, of G (-)Has a single rootAnd H (z) = α; will be provided withSubstituting into F (-) one can derive the dynamics of the reduced order system as:
to facilitate stability analysis, a new state variable is definedThus, the dynamic equation for the boundary layer system is expressed as:
wherein epsilon η :＝t η /τ η A time variable representing "stretch";
andthe solutions of equations (16) and (17), respectively.
2. The command filter backstepping based quad-rotor unmanned aerial vehicle stable tracking control method according to claim 1, wherein: also comprises the following steps:
step 103, analyzing stability; the method comprises the following specific steps:
the following definitions 1 and 2 are introduced;
definition 1: the notation e (t, epsilon) is defined as e (t, epsilon) = o (epsilon), i.e. there is a constantSo that < e (t, epsilon) < k epsilon,
definition 2: when given for any given constantExist ofSo that the following holds: | e (t) | | is less than or equal to | e (0) | | exp (-lambadat) + epsilon,time, systemThe exponential stability is satisfied at the equilibrium point ε → 0;
the Extended Tikhonov's Theorem is introduced to prove the stability of the attitude closed-loop system (14);
considering an attitude dynamics model (4), an attitude instruction filtering backstepping controller (11) and an attitude filter (9) of the unmanned aerial vehicle; for all control gain matrixes, a proper small constant tau x e (0, 1) exists, and when tau e (0, tau x), the state tracking error of the whole closed-loop system meets the semi-global index stability; in other words, with the decrease of tau, the command filtering backstepping attitude control (11) can realize the control performance of the traditional backstepping;
and (3) proving that: definition ofAndare an immediate set containing the origin about z and xi, respectively; for the attitude singular disturbance system (16), if the following conditions are all satisfied:
(R1) pairFunctions F (-), G (-), and their relationIs continuously bounded, the functions H (z) andhas a bound to the first partial derivative of its argument, andlipschitz for z, consistent for t;
(R2) the origin of the attitude reduction system (16) is globally exponentially stable, i.e. there is a Lyapunov function V (z) satisfying W 1 (z)≤V(z)≤W 2 (z) andwherein W 1 (z),W 2 (z) and W 3 (z) is inInternally is a continuous positive definite function;
(R3) the origin of the boundary layer system (17) is exponentially stable, consistent for (t, z);
the attitude closed loop system (14) satisfies the Extended Tikhonov's Theorem;
defining constantsSatisfy the requirement ofAnd c<min ||z||＝r W 1 (z),Is the attraction zone for the z-axis,is an attraction zone of xi;
obviously, the attitude closed-loop system (14) satisfies the conditions (R1) - (R3) of the singular disturbance theorem; thus, for each tight subsetHas a constant τ * E (0, 1) such that for allAnd τ ∈ (0, τ) * ) The singular disturbance problem is that there is a unique solution z (t, τ) within [0, ∞ ],
and is
Is consistent for t ∈ [0, ∞);
wherein z is * (t),Ξ * (t/τ) is the global exponential stability solution of system attitude loop equations (16) and (17), respectively;
in addition, for any t a >, 0, presence of tau ** <τ * So that t e [ t ∈ ] a Infinity), then there are:
namely:
thus, there are
Obviously, the attitude closed loop system (14) is exponentially stable when τ → 0;
the attitude ring systems (16) and (17) are globally exponentially stable, and the attraction zone of the origin can be arbitrarily enlarged by reducing tauThe attitude ring systems (16) and (17) are thus semi-globally stable.
3. The method for stably tracking and controlling the quad-rotor unmanned aerial vehicle based on the instruction filtering backstepping method according to claim 2, wherein the method comprises the following steps: also comprises the following steps:
and 104, simulating and testing.
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| CN112130584B (en) * | 2020-09-22 | 2022-04-29 | 苏州科技大学 | Finite time self-adaptive control method of four-rotor aircraft based on command filtering |
| CN113504785A (en) * | 2021-07-04 | 2021-10-15 | 哈尔滨理工大学 | Autonomous adjustment method for flight attitude of unmanned aerial vehicle |
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