CN112965512A - Unmanned aerial vehicle wind-resistant control method based on propeller model - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle wind-resistant control method based on a propeller model, which is characterized in that wind disturbance is added into a dynamic model of a propeller as a variable, a power system of an unmanned aerial vehicle is analyzed, and further the influence of the wind disturbance is counteracted through a feedforward method; estimating the air density by a self-adaptive method to ensure that the air density approaches to a true value as much as possible; the inner ring adopts an active disturbance rejection controller, the outer ring adopts self-adaptive control, and wind disturbance is directly added into an unmanned aerial vehicle power system and added into a propeller model for calculating force and moment in the inner ring control; by adopting the active disturbance rejection control method, the problems of uncertainty of a dynamic model and inaccuracy of propeller model output can be solved, so that the attitude angle of the inner ring is stably tracked; in the outer loop control, the actual air density is estimated by adopting a self-adaptive control method, and a self-adaptive controller is designed to ensure that the whole unmanned aerial vehicle system can stably reach an expected target point.
Description
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle control, and particularly relates to a propeller model-based wind-resistant control method for an unmanned aerial vehicle.
Background
In recent years, unmanned aerial vehicles have been rapidly developed and have received much attention due to achievements in the fields of microelectronics, sensors, communications, and the like. Unmanned aerial vehicles have rapidly developed in the fields of detection, search and rescue, space imaging, transportation and the like. Along with the development of technology and the change of times demand, the accurate control to unmanned aerial vehicle in each item task is more and more strict, especially the stability of unmanned aerial vehicle flight, and only the stability of flight obtains guaranteeing can further use unmanned aerial vehicle to more aspects, is adapted to various different complicated occasions. Unmanned aerial vehicle can receive the interference of external factors such as gust at the actual flight in-process to can bring adverse effect to control effect, consequently, the study that has wind disturbance unmanned aerial vehicle control has become the characteristics of recent study.
Aiming at the problem of unmanned aerial vehicle control transformation control with wind disturbance, the following main solutions exist:
scheme 1: a suboptimal H-infinity controller is designed in the literature (Jasim W, Gu D, "Robust team formation Control for quadrotors," IEEE Transactions on Control Systems Technology, vol.26, No.4, pp.1516-1523, jul 2017.) for quadrotors to achieve formation with external interference. The literature (Escoreno J, Salazar S, Romero H, et al, "projector Control of a Quadrotor Subject to 2D Wind disorders," Journal of Intelligent & Robotic Systems, vol.70, pp.51-63, apr 2012.) adopts adaptive Control and counter-step Control techniques to solve the problem that a quad-rotor is subjected to two-dimensional unknown Wind interference. In the literature (objective a, Nabil a, "Quadrotor control for target tracking in presence of wind disturbance," Ukacc International reference on control. ieee, pp.25-30, jul 2014.), two nonlinear controllers are designed based on feedback linearization and a counter-step method, so that the robust trajectory stable tracking problem of the quadrotors under the condition of wind disturbance is realized. The literature (Bisheban M, Lee T, "geometrical Adaptive Control for a Quadrotor UAV with Wind interference Rejection," 2018IEEE Conference on Decision and Control, pp.2816-2821, mar 2018.) proposes a Geometric Adaptive Control scheme for a quad-rotor unmanned aerial vehicle, which successfully alleviates the influence of Wind Disturbance by using an online-regulated multi-layer neural network. A Reliable Control strategy for creep in Systems,49(10), 2059-.
Scheme 2: in documents (Qiu B, Xiong H, Fu J, "The position control of micro quad-rotor UAV based on ADRC," Chinese Automation convergence, ieee, pp.422-426, nov 2015.), a new method for controlling The position of a mini quad-rotor drone based on an active disturbance rejection controller is proposed. Transfer functions in all directions are solved in an inertial coordinate system, and a matching active-disturbance-rejection controller based on a complex algorithm is designed, so that good wind resistance is achieved. The literature (Wang Q, Xiong H, Qiu B, "The Attitution Control of Transmission Line Fault Inspection UAV Based on ADRC," 2017International reference on Industrial Information-Computing Technology, Intelligent Technology, Industrial Information integration IEEE Computer Society, pp.169-169, dec 2017.) studies The Attitude Control of a test drone, and The designed auto-disturbance rejection controller is verified by simulation experiments, which shows that The auto-disturbance rejection controller has a good Control effect on The flight Attitude of The drone.
Scheme 3: in the document (Khan W, Nahon M, "a propeller model for general flight conditions," International Journal of Intelligent Unmanned Systems, vol.3, pp.72-92, nov 2015.), a physically-based propeller model of the Unmanned aerial vehicle is proposed, which can predict all aerodynamic forces and moments under any general forward flight conditions, such as no flow, pure axial flow and pure lateral flow, by applying the theory of blade momentum.
Disclosure of Invention
In view of this, the invention aims to provide a propeller model-based wind-resistant control method for an unmanned aerial vehicle, which can quickly control wind disturbance, thereby achieving a good control effect.
An unmanned aerial vehicle wind-resistant control method based on a propeller model comprises the following steps:
aiming at the control of a four-rotor unmanned aerial vehicle, in the inner ring control, the pitch angle theta, the roll angle phi and the yaw angle psi of the unmanned aerial vehicle are acquired in real time and fed back to an attitude controller, and the moments U in three directions are output2,U3,U4Then, the data is input into the following control model:
calculating to obtain the lift force T generated by each propeller1,T2,T3,T4And corresponding moment M1,M2,M3,M4Substituting into the lifting force and the moment of each propeller represented by the following formula:
wherein N is the number of blades, C is the chord length, ρ is the air density under the real condition, and ClIs a coefficient of lift, CdIs the coefficient of resistance. RhIs the hub radius, RpIs the propeller radius; beta is the inflow angle of the plane of the propeller; Δ α is a differential amount of an azimuth angle, and Δ r is a differential amount of a radius;
wherein the axial induced velocity ViaOmega is the propeller speed, r is the radius, Vxy⊥Representing the in-plane velocity, V, of the wind speed along the plane of the propellerzThe axial speed of the wind speed along the rotating shaft of the propeller;
then, the relative velocity V is calculatedR；
Then according to the following formula:
and calculating the rotating speed omega of each propeller, and controlling the propellers.
Further, in the outer loop control of the unmanned aerial vehicle, the position controller is designed as:
wherein m represents the mass of the unmanned aerial vehicle, g represents the acceleration of gravity, e3＝(0 0 1)TIs a unit vector in the z direction;
and
errors in position and velocity, respectively, pdFor the desired drone position, P, K are positive fixed gain matrices and ε is an adaptive parameter, such that
Order to
Combining tracking errors
Obtaining:
wherein the content of the first and second substances,
is a constant number of times, and is,
the adaptive control rate is designed so that
Namely, it is
Selecting a Lyapunov function:
where γ is a positive number, assuming that P ═ PT,K＝KT,P>0,K>0，
The adaptive control rate is designed as follows:
preferably, the observer is designed as a linear state observer.
Preferably, the linear state observer is simplified to a unity gain double integrator.
Preferably, the closed-loop transfer function of the observer is
Wherein the gain is selected according to kd＝2ξωcAnd
ωcand ξ are the closed loop natural frequency and the damping ratio, respectively.
The invention has the following beneficial effects:
the invention provides a control method based on a propeller model, which takes wind disturbance as a variable to be added into a dynamic model of a propeller, analyzes a power system of an unmanned aerial vehicle and further counteracts the influence of the wind disturbance through a feedforward method. In the analysis of the power system, the air density is estimated by a self-adaptive method, so that the air density approaches to a true value as much as possible. The whole control system adopts a double-loop system, an inner loop adopts an active disturbance rejection controller, and an outer loop adopts a self-adaptive control method to realize that the unmanned aerial vehicle stably reaches a target point in a wind disturbance environment; in the inner ring control, wind disturbance is directly added into an unmanned aerial vehicle power system and added into a propeller model for calculating force and moment; by adopting the active disturbance rejection control method, the problems of uncertainty of a dynamic model and inaccuracy of propeller model output can be solved, so that the attitude angle of the inner ring is stably tracked; in the outer loop control, the actual air density is estimated by adopting a self-adaptive control method, and a self-adaptive controller is designed to ensure that the whole unmanned aerial vehicle system can stably reach an expected target point.
Drawings
FIG. 1 is a schematic diagram of the relative airflow experienced by a forward flying drone propeller;
FIG. 2 is a schematic view of the propeller frame aligned with in-plane velocity;
FIG. 3 is a schematic view of the converging flow, aerodynamic forces and moments experienced by a blade section in an oblique flow;
FIG. 4 is a graph of differential thrust produced by a propeller blade as a function of its azimuth angle;
FIG. 5 is (a) a propeller slipstream generally forward flight diagram; 5(b) differential part diagram of the ring; 5(c) mass flow chart through micro-segmentation;
FIG. 6 is a schematic diagram of the forces and moments experienced by a quad-rotor drone;
fig. 7 is a diagram of the overall control structure of a quad-rotor unmanned aerial vehicle;
FIG. 8 is a graph of inner ring attitude control for a quad-rotor drone;
FIG. 9 is a graph of an error in inner ring attitude for a quad-rotor drone;
FIG. 10 is a graph of the tracking in the x-direction for four cases;
FIG. 11 is a graph of the tracking in the y-direction for four cases;
FIG. 12 is a graph of the tracking in the z-direction for four cases;
FIG. 13 is a graph of the tracking error in the x-direction for four cases;
FIG. 14 is a graph of the tracking error in the y-direction for four cases;
fig. 15 is a graph of the tracking error in the z direction for four cases.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a control method based on a propeller model, which aims at the problem of unmanned aerial vehicle flight control in a wind disturbance environment in consideration of a three-dimensional space. According to the method, wind disturbance is added into a dynamic model of a propeller as a variable, a power system of the unmanned aerial vehicle is analyzed, and further the influence of the wind disturbance is eliminated through a feedforward method. In the analysis of the power system, the air density is estimated by a self-adaptive method, so that the air density approaches to a true value as much as possible. The whole control system adopts a double-loop system, an inner loop adopts an active disturbance rejection controller, and an outer loop adopts a self-adaptive control method to realize that the unmanned aerial vehicle stably reaches a target point in a wind disturbance environment.
The invention adopts a double-ring control frame, adds a propeller model in an inner ring and adopts an active disturbance rejection control method, and estimates the air density in an outer ring and adopts a self-adaptive control method. The technical scheme for realizing the invention is as follows:
step 1: in the inner ring control, wind disturbance is directly added into an unmanned aerial vehicle power system, the wind disturbance is expressed as wind speeds in three directions, and the wind disturbance is added into a propeller model to calculate force and moment. By adopting the active disturbance rejection control method, the problems of uncertainty of a dynamic model and inaccuracy of propeller model output can be solved, so that the attitude angle of the inner ring is stably tracked.
First, consider that a propeller, in its normal motion, experiences a wind velocity V at an angle to the propeller axis of rotation
Called the pitch angle (tilt angle), as shown in fig. 1, this velocity has two components, one being the axial velocity along the axis of rotation of the propeller
The other is the in-plane velocity along the plane of the propeller
At any given blade azimuth angle α, from the available in-plane velocities along the blade direction and perpendicular to the blade, as shown in fig. 2:
by using the theory of the blade element, the differential lift force, the resistance force and the moment acted on the blade element, namely dL, dD and dM and the resultant relative speed VRIn this regard, ω is the rotational speed of the propeller, and the induced rotational speed of the propeller is referred to as the induced speed, and is generally divided into axial, radial and tangential components. For the sake of simplicity, only the axial induced velocity V is considered in the present workiaSince it is the most important of the three, as can be represented in fig. 3:
as can be seen from fig. 3, the inflow angle β of the resultant velocity with respect to the plane of the propeller is:
using the Blade element theory (Blade-element theory), as shown in fig. 4, for N propeller blades, the differential thrust is:
where C is the chord length, ρ is the air density in the real case, ClIs a coefficient of lift, ClIs the coefficient of resistance.
Meanwhile, by using Momentum theory (Momentum theory), as shown in fig. 5, a differential thrust equation can be obtained:
equation (5) contains two unknowns, i.e., differential thrust dT and induced velocity ViaTherefore, the aerodynamic force (same as the aerodynamic moment analysis process) equation can be solved simultaneously with equation (4):
wherein R ishRadius of the hub, RpIs the propeller radius. In most of the calculation process, the air density ρ usually takes the nominal air density ρm，ρmIs a predefined constant mode air density (usually considering sea level standard atmosphere) and can yield:
the relationship between the force and moment at true air density and the force and moment at nominal air density can be obtained from equations (6) and (7):
and 2, in the outer loop control, estimating the actual air density by adopting a self-adaptive control method, so that the whole control effect is more accurate, and designing a self-adaptive controller to ensure that the whole unmanned aerial vehicle system can stably reach an expected target point.
Four rotor unmanned aerial vehicle atress schematic diagrams as in fig. 6, unmanned aerial vehicle's translation dynamics model can be expressed as:
wherein x, y and z represent the position of the unmanned aerial vehicle, theta is a pitch angle, phi is a roll angle, psi is a yaw angle, m is mass and g is a gravity constant.
The rotokinematic model of a quad-rotor drone may be represented as
Wherein, Ix,Iy,IzThe inertia moment is corresponding to the coordinate axes of x, y and z. U shape1For the total lift that four rotor unmanned aerial vehicle receive, U2,U3,U4For the moments in three directions, the calculation formula is:
wherein, T1,T2,T3,T4Lift, M, generated for each propeller of four rotors, respectively1,M2,M3,M4The moments generated for each propeller of the quadrotors, respectively, are calculated by equation (6) analyzed above.
First, a virtual controller is designed
Namely, it is
Substituting the virtual controller (12) into the four-rotor dynamic model (9) can obtain
From the above equation, it can be obtained that ρ is taken as ρ when calculatingmTime, actual control input ux,uy,uzAnd a desired control input ux,d,uy,d,uz,dThe relationship between
Designing an inner ring active disturbance rejection controller:
roll angle sub-equation kinetic equation
Wherein
Let z be1＝φ
The roll angle equation is written in the form of an equation of state:
wherein z is3＝d0As a state of augmentation of the addition,
the control input U is U2。
The linear state observer (LESO) is designed as
Wherein the content of the first and second substances,
is in a pair state z1,z2,z3Observed value of l1,l2,l3To observe the gain factors, the gain factors are chosen such that the following E matrix is Hurwitz:
through the reasonable design of the state observer, the controller is provided:
ignoring estimation errors
Substituting the controller (20) into equation (16) reduces to a unity gain double integrator
Wherein the output y is the roll angle phi, u0Selective PD control
u0＝kp(r-z1)-kdz2 (22)
The closed loop transfer function can be obtained by equation (21) and equation (22)
Wherein the gain is selected according to kd＝2ξωcAnd
ωcand ξ are the closed loop natural frequency and the damping ratio, respectively.
The pitch angle theta and yaw angle psi subsystems are designed as above, i.e. equation (16) is changed to
Wherein the content of the first and second substances,
the other design process is the same as the roll angle phi design process.
Designing an outer ring self-adaptive controller:
translational kinetic equation of quad-rotor drone:
wherein, p ═ x y z)TFor unmanned plane position, up＝(ux uy uz)TControl input for three directions, e3＝(0 0 1)TThe unit vector in the z direction can be obtained according to equation (15)
We mean that the control input is u-up,dSubstituting these relationships into equation (26) yields:
the position controller is designed as follows:
wherein the content of the first and second substances,
and
errors in position and velocity, respectively, pdFor the desired drone position, P, K are positive fixed gain matrices and ε is an adaptive parameter, such that
Order to
Equation (27) can be derived for both the left and right sides-mv:
wherein the content of the first and second substances,
substituting equation (28) into equation (29) in combination with the tracking error
It is possible to obtain:
wherein the content of the first and second substances,
because of the fact that
Is constant, therefore
The adaptive control rate is designed so that
Namely, it is
Selecting a Lyapunov function:
where γ is a positive number, assuming that P ═ PT,K＝KT,P>0,K>0，
Design the adaptive control rate as
The derivative equation for the lyapunov function (31) can be found as:
the stability of the system can be seen, with a final tracking error of 0.
Next, we performed simulation experiments on the proposed control method. The simulation under four conditions is carried out, wherein the four conditions respectively comprise original double-loop pid control, disturbance solving by adding a wind model on the original basis, air density estimation by adding an air density estimation model on the original basis, and air density estimation by adding the wind model on the original basis. The desired position of the quad-rotor unmanned aerial vehicle is given for the four conditions respectively, and the actual unmanned aerial vehicle position output is tracked. Fig. 7 shows a structural block diagram of the whole unmanned aerial vehicle control system.
Fig. 8 shows the case of angle tracking for four-rotor drone with three expected attitude angles of 15 °, 20 °, and 0 ° respectively in the inner loop test, and fig. 9 shows that the angle tracking error is finally stabilized at 0.
In the simulation, the wind disturbance is assumed to be vx＝0m/s,vy＝2m/s,
Given the expected position x of the drone is 1, y is 2, and z is 3, fig. 10 to 12 show the result graphs of the drone reaching the expected position in the three directions x, y, and z in the four cases, and fig. 13 to 15 show the position tracking error curves in the four cases in the three directions x, y, and z, from which we can clearly see that in the x and y directions, the tracking error difference is not large in the four cases, and finally stabilizes at 0, and the drone can reach the expected position well. However, a relatively obvious difference exists in the z direction, the inner ring and the outer ring cannot well reach the expected positions by adopting a PID controller, wind is not added into a propeller model, disturbance cannot be controlled in time, a large steady-state error exists, and an unstable phenomenon occurs if the wind speed is larger; density compensation is added on the basis of the original double-ring PID, an error exists in the initial control stage, and the error finally tends to 0 along with the increase of time; in situA propeller model with wind speed is added on the basis of the initial double-ring PID, so that the wind resistance effect can be well achieved; a propeller model with wind speed and density compensation are added on the basis of the original double-ring PID, so that the wind disturbance resisting effect can be well achieved, and the adjusting time can be greatly shortened.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The unmanned aerial vehicle wind-resistant control method based on the propeller model is characterized by comprising the following steps:
aiming at the control of a four-rotor unmanned aerial vehicle, in the inner ring control, the pitch angle theta, the roll angle phi and the yaw angle psi of the unmanned aerial vehicle are acquired in real time and fed back to an attitude controller, and the moments U in three directions are output2,U3,U4Then, the data is input into the following control model:
calculating to obtain the lift force T generated by each propeller1,T2,T3,T4And corresponding moment M1,M2,M3,M4Substituting into the lifting force and the moment of each propeller represented by the following formula:
wherein N is the number of blades, C is the chord length, ρ is the air density under the real condition, and ClAs a lifting systemNumber, CdIs the coefficient of resistance. RhIs the hub radius, RpIs the propeller radius; beta is the inflow angle of the plane of the propeller; Δ α is a differential amount of an azimuth angle, and Δ r is a differential amount of a radius;
wherein the axial induced velocity ViaOmega is the propeller speed, r is the radius, Vxy⊥Representing the in-plane velocity, V, of the wind speed along the plane of the propellerzThe axial speed of the wind speed along the rotating shaft of the propeller;
then, the relative velocity V is calculatedR；
Then according to the following formula:
and calculating the rotating speed omega of each propeller, and controlling the propellers.
2. A propeller model-based unmanned aerial vehicle wind-resistant control method according to claim 1, wherein in the outer loop control of the unmanned aerial vehicle, the position controller is designed to:
wherein m represents the mass of the unmanned aerial vehicle, g represents the acceleration of gravity, e3＝(0 0 1)TIs a unit vector in the z direction;
and
errors in position and velocity, respectively, pdFor desired unmanned planeLet P, K be a positive fixed gain matrix and ε be an adaptive parameter, such that
Order to
Combining tracking errors
Obtaining:
wherein the content of the first and second substances,
is a constant number of times, and is,
the adaptive control rate is designed so that
Namely, it is
Selecting a Lyapunov function:
where γ is a positive number, assuming that P ═ PT,K＝KT,P>0,K>0，
The adaptive control rate is designed as follows:
3. the propeller model-based unmanned aerial vehicle wind-resistant control method according to claim 1, wherein the observer is designed as a linear state observer.
4. The propeller model-based unmanned aerial vehicle wind-resistant control method of claim 3, wherein the linear state observer is simplified into a unity gain double integrator.
5. The propeller model-based unmanned aerial vehicle wind-resistant control method according to claim 4, wherein the closed-loop transfer function of the observer is
Wherein the gain is selected according to kd＝2ξωcAnd
ωcand ξ are the closed loop natural frequency and the damping ratio, respectively.
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| CN113408646A (en) * | 2021-07-05 | 2021-09-17 | 上海交通大学 | External disturbance classification method and system for unmanned aerial vehicle |
| CN114527776A (en) * | 2022-01-07 | 2022-05-24 | 鹏城实验室 | Unmanned aerial vehicle wind disturbance resisting control method and device, terminal and storage medium |
| CN115016291A (en) * | 2022-07-13 | 2022-09-06 | 西北工业大学 | Aircraft anti-interference attitude control system and method based on wind field information |
| CN115576242A (en) * | 2022-10-09 | 2023-01-06 | 南方科技大学 | High wind resistance control system and method based on vector control |
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