CN109857146B - Layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution - Google Patents
Layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution Download PDFInfo
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Abstract
The invention discloses an unmanned aerial vehicle tracking control method, and belongs to the field of motion control. Comprises the following steps: acquiring self structural parameters of the unmanned aerial vehicle, a lift range provided by a propeller and real-time motion state information of the unmanned aerial vehicle and a tracked target; establishing a Newton Euler model, and adding a saturation characteristic into the model; according to the built model, a basic double closed-loop cascade PID deviation controller is built among four subsystems of pitch angle control, roll angle control, yaw angle control and height control; adding gravity feed-forward and attitude feed-forward according to the gravity parameters and the attitude information of the unmanned aerial vehicle; a saturation weight distributor is added in the pitch angle control subsystem and the roll angle control subsystem, and invalid increment generated due to the saturation characteristic of the propeller is eliminated; according to the attitude angle limit of the unmanned aerial vehicle and the motion information of the tracked target, a time optimal tracking controller is established and connected in series with the four subsystems for controlling the lower-layer attitude and height, and finally stable tracking is achieved.
Description
Technical Field
The invention relates to unmanned aerial vehicle control, in particular to a layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution.
Background
In recent years, with the development of unmanned aerial vehicle technology, the unmanned aerial vehicle gradually enters the visual field of people in various industries and merges the lives of people; the unmanned aerial vehicle is mainly used as a reconnaissance plane in the military field, and has the advantages of small volume, low manufacturing cost, convenience in use, low requirement on the operation environment, strong battlefield viability and the like; in the civil field, the method mainly comprises two aspects of aerial photography and carrying, and in the aerial photography field, the auxiliary shooting by using an unmanned aerial vehicle in the film and television industry has become a normal state; besides the film and television industry, the aerial photography unmanned aerial vehicle can be widely applied to the fields of national ecological environment protection, mineral resource exploration, marine environment monitoring, land utilization investigation, water resource development, crop growth monitoring and yield assessment, agricultural operation, natural disaster monitoring and evaluation, urban planning and municipal management, forest pest protection and monitoring, public safety, national defense industry and the like, and has wide market demand; in the field of carrying objects, agricultural irrigation unmanned aerial vehicles, fire-fighting unmanned aerial vehicles and express delivery unmanned aerial vehicles also enter practical stages;
although the application of the unmanned aerial vehicle is more and more extensive, the current unmanned aerial vehicle does not have the autonomous flight capability, and more depends on an operator to perform remote control operation, so that the unmanned aerial vehicle has many limitations; therefore, autonomous flight will be the main direction for future unmanned aerial vehicle research.
Disclosure of Invention
The invention aims to control the unmanned aerial vehicle to stably fly at the height set in the air, and stably track a ground moving target in an unbiased position and an unbiased speed; the method comprises the following specific steps:
a layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution comprises the following steps:
(1) acquiring structural parameters of the unmanned aerial vehicle, including the mass of the unmanned aerial vehicle, the gravity acceleration, the distance between the axis of the motor and the gravity center of the unmanned aerial vehicle, and the rotational inertia of the unmanned aerial vehicle in the xyz three directions; acquiring the range of the lift force provided by the propeller of the unmanned aerial vehicle; acquiring Euler angle attitude information and height information of the unmanned aerial vehicle and a velocity vector and a displacement vector of a tracked target in real time;
(2) establishing a Newton Euler model according to the parameter information of the unmanned aerial vehicle obtained in the step (1), and adding a saturation characteristic into the model according to the lift force range which can be provided by the propeller;
(3) according to the built model, a basic double-closed-loop cascade PID deviation controller is built among four subsystems of pitch angle control, roll angle control, yaw angle control and height control, and parameters are independently adjusted under the condition that coupling is temporarily not considered;
(4) adding gravity feed forward and attitude feed forward according to the gravity parameters of the unmanned aerial vehicle and the attitude information of the unmanned aerial vehicle, taking attitude and gravity coupling as disturbance of height control to offset, and estimating the attitude value of the unmanned aerial vehicle in the next discrete period by a Taylor expansion formula;
(5) adding a saturation weight distributor in the pitch angle control subsystem and the roll angle control subsystem to eliminate invalid increment generated due to the saturation characteristic of the propeller;
(6) according to the attitude angle limit of the unmanned aerial vehicle, the motion information of a tracked target is used as input, an upper time optimal tracking controller is established and is connected in series with four subsystems for controlling the lower attitude and the height, and stable tracking is finally realized;
in the step (2), on the basis of a basic Newton Euler mechanical model, the saturation characteristic of the lifting force is added: fmin＜F1、F2、F3、F4＜FmaxIn which F is1、F2、F3、F4Is the lift force generated by four propellers, FmaxIs provided by a single propellerMaximum lift provided, FminIs the minimum lift to keep the propeller from stalling;
in the step (4):
the gravity feed-forward added satisfies:
F′n＝Fn+Fbase，n＝1，2，3，4 (1)
wherein Fn' Propeller lift after gravity feed-forward is added to replace original FnM is the total mass of the unmanned aerial vehicle, g is the acceleration of gravity, FbaseIs gravity feed forward;
the added attitude feedforward satisfies the following conditions:
wherein FhIs the inner loop control increment of the altitude control subsystem, Fh' is the height controller increment after adding attitude feed forward, replacing the original Fh；
In the height subsystem, because the coupling of the attitude to the height is continuous, and the actual controller and the attitude feedback are discrete, the directly obtained attitude compensation has certain hysteresis, and the hysteresis degree is enhanced along with the increase of the discrete period; so the Taylor expansion is used in the control process to estimate the attitude disturbance in the next discrete period:
wherein theta ist、
A pitch angle and a roll angle with time t as a parameter; the discrete period is T, and the initial time in one period is T0The end of the cycle being at time t1，g(tε) Is the attitude compensation value after estimation;
in the step (5), a saturated weight distributor is added to an inner ring, namely an angular velocity ring, for cascade control of the pitch angle and the roll angle to distribute the control increments, the saturated weight distributor takes the pitch angle control increment, the roll angle control increment and the altitude increment as input, and takes the distributed pitch angle control increment and roll angle controllable increment as output; if the pitch angle increment and the roll angle increment do not enable the lift force of any propeller to be saturated, the original value output is kept, and if the pitch angle increment and the roll angle increment exceed the range, the pitch angle increment F is enabledθAnd roll angle increment
Keeping the original symbol, making:
wherein, FlimitIs the maximum incremental absolute value, F, for the propeller to reach saturationψlIs the adjustment margin left for keeping the yaw angle in balance; f'θAnd
then it is the output value after the saturation weight distributor;
in the step (6), the step of,
selecting a pitch angle theta and a roll angle in an attitude angle
As a control quantity of horizontal movement, the Euler angle posture description selects a ZYX cis-form;
and decomposing the relative position and the relative speed of the tracked target and the unmanned aerial vehicle into an x direction and a y direction by taking the relative position and the relative speed of the tracked target and the unmanned aerial vehicle as input quantities:
in the parameter equation, a is the relative speed in the x direction, b is the relative position in the x direction, c is the relative speed in the y direction, and d is the relative position in the y direction;
and thirdly, deducing, wherein the time optimal control of the system is bang-bang control, and the result is as follows:
max _ x is the mode of the maximum value input in the x direction of the tracking controller, max _ y is the mode of the maximum value input in the y direction of the tracking controller, and is the acceleration extreme value limited by the attitude angle in the unmanned aerial vehicle tracking system;
because the bang-bang control can vibrate when in a steady state value, the tracking controller is switched into a deviation control mode under the condition of approaching to the steady state, namely when the relative position and the relative speed of the unmanned aerial vehicle and the tracked target are small, so that the system is converged;
has the advantages that: the invention discloses a layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution, and particularly, the system is divided into an upper-layer tracking controller and a lower-layer attitude and height controller; the lower-layer attitude and height controller cancels the gravity disturbance and the attitude disturbance coupled on the height control subsystem by adding the gravity feedforward and the attitude feedforward, thereby improving the dynamic performance of the height control subsystem; the Taylor expansion is adopted to estimate the attitude disturbance, so that the hysteresis of the estimation of the attitude disturbance is reduced; meanwhile, aiming at the problem that invalid increment is generated due to the fact that the lifting force of the propeller has a saturation characteristic, a saturation weight distributor is designed, and disturbance of the invalid increment to the interior of the system is eliminated; the upper tracking controller takes position unbiased and speed unbiased as the final state constraint of the system, takes the system running time reaching the steady state as a performance index, designs a time optimal tracking controller, and switches to smoother deviation control when the system approaches the final state, so that the system can track the moving target; and finally, the upper and lower layer control systems are connected in series, so that the ground moving target is tracked by the quad-rotor unmanned aerial vehicle, and the system is converged.
Drawings
FIG. 1 is a block diagram of the overall control architecture of the system;
FIG. 2 is a graph of comparison results of height control simulations before and after gravity feed forward is added;
FIG. 3 is a graph of comparison results of height control simulations before and after adding attitude feedforward based on gravity feedforward;
FIG. 4 is a graph of a continuous signal, a zero-order keeper discrete signal, and a Taylor series estimated discrete signal for a height-controlled attitude product disturbance term;
FIG. 5 is a comparison of the rise time simulation results for a height control system with and without a weight assignor;
FIG. 6 is a response of the upper tracking controller in the case of an ideal attitude motion model, where the ideal attitude motion model refers to a response that the drone can respond without delay, oscillation, and overshoot given the drone attitude input, resulting in accelerations in the x and y directions;
fig. 7 shows the result of the tracking simulation of the control system as a whole, and the attitude motion model employs the attitude and height controller of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly understood, the control method is illustrated and explained in detail below with reference to the accompanying drawings and examples;
the invention provides a time optimal unmanned aerial vehicle tracking control method based on feedforward compensation and propeller saturation characteristic weight distribution, wherein a controller is mainly divided into two layers, as shown in figure 1; the upper layer is a tracking controller, and the lower layer is a posture and height controller;
the upper tracking controller uses a time optimal control method and is decomposed into an x direction and a y direction, the relative speeds and the relative positions of the unmanned aerial vehicle and the tracked target in the x direction and the y direction are respectively used as input, and the output is an expected pitch angle and a roll angle which are used as the input of a pitch angle control subsystem and a roll angle control subsystem;
the lower layer is divided into four subsystems of pitch angle control, roll angle control, yaw angle control and height control; the cascade PID deviation controller is used for correcting the input and the output of the system, and then corresponding feedforward compensation, saturation weight distribution and other improved methods are carried out, and the specific structure is shown in FIG. 1; wherein gravity feed forward is added to counteract gravity accumulated on the height control subsystem; the attitude feed-forward is used for counteracting an attitude trigonometric function product term coupled to the height control due to the attitude angle of the unmanned aerial vehicle, and since the coupling influence of the attitude on the height control is continuous, and the measurement value of the attitude is discrete and generates a certain hysteresis, the attitude value in the next discrete period is estimated by the Taylor expansion so as to reduce the hysteresis; the saturation weight value distributor is mainly used for solving the problem that invalid increment occurs due to superposition of three attitude angle increments and height increments because the lift force of the propeller has a saturation characteristic;
the invention provides a layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution, which is implemented according to the following steps:
acquiring structural parameters of the unmanned aerial vehicle, wherein the structural parameters comprise the mass of the unmanned aerial vehicle, the gravity acceleration, the length of a horn and the rotational inertia of the unmanned aerial vehicle in the xyz three directions; acquiring the range of the lift force provided by the propeller of the unmanned aerial vehicle; acquiring Euler angle attitude information and height information of the unmanned aerial vehicle and a velocity vector and a displacement vector of a tracked target in real time;
take the development platform of the DJI M100 unmanned aerial vehicle as an example, the total mass M is 3.2868kg, the arm length l is 0.325M, and the moment of inertia Jx＝0.05503kg*m2，Jy＝0.05503kg*m2，Jz＝0.097175kg*m2Maximum lift force F of propellermaxThe minimum lift that can be provided should be 0 at 21N, but to avoid stalling, F is setmin0.2N; attitude information of unmanned aerial vehicle is measured through inertiaThe height information can be measured by a barometer, ultrasonic waves, a visual sensor and the like; the speed vector and the displacement vector of the tracked target can be measured by the unmanned aerial vehicle through a visual sensor or the tracked target sends information to the unmanned aerial vehicle in a communication mode;
the simulation result graphs of the invention are obtained by taking the parameters as examples for simulation;
secondly, establishing a Newton Euler model, and adding a saturation characteristic into the model according to the lift range provided by the propeller; the established newton euler model is as follows:
where m is the mass of the drone, θ,
Psi is F three Euler angles of unmanned aerial vehicle attitude description, namely a pitch angle, a roll angle and a yaw angle; sx、Sy、SzRespectively displacement in three coordinate axis directions of a geodetic coordinate system; f1、F2、F3、F4Lift force, M, generated by four propellers respectively1、M2、M3、M4Is the torque produced by four propellers, Jx、Jy、JzThe moment of inertia of the unmanned aerial vehicle around three coordinate axes, g is the gravity acceleration, and l is the length from the center of a propeller to the center of gravity of the unmanned aerial vehicle; it can be shown that: mn＝k·FnN is 1, 2, 3, 4, wherein k is related to the mechanical structure of the propeller and the length l of the horn, and does not need to obtain an accurate specific value, and can be adjusted by a PID parameter in a subsequent yaw angle control subsystem; the sixth equation of equation (8) may become:
then adding the saturation characteristic of the propeller into the model, wherein twelve cis-compasses exist when the Euler angle describes the posture, but no matter which cis-compasses are adopted, only the first two equations of the Newton Euler model are influenced, and the last four equations are not involved; therefore, the model of the present invention relating to the lower attitude and height controller is built as follows:
wherein FmaxIs the maximum lift that a single propeller can provide, FminIs the minimum lift to keep the propeller from stalling;
thirdly, establishing a basic double-closed-loop cascade PID deviation controller among four subsystems of pitch angle control, roll angle control, yaw angle control and height control according to the established model, and independently adjusting parameters under the condition of temporarily not considering coupling; the specific double closed-loop cascade PID deviation controller is built as shown in FIG. 1, and the problem of parameter adjustment of the PID controller is not described in detail herein;
adding gravity feed forward, attitude feed forward and estimating an attitude value of the unmanned aerial vehicle in the next discrete period by a Taylor expansion;
as can be seen from equation (11), in the altitude dynamics model, the second order differential amount of altitude
And a control quantity F1、F2、F3、F4The coupling is formed under the influence of a gravity accumulation term and an attitude trigonometric function product term in a nonlinear relation;
therefore, the invention adopts a gravity feedforward and attitude feedforward mode to compensate and offset two nonlinear disturbance terms so as to linearize the system, and then adopts a cascade PID mode to perform feedback control after linearization, as shown in FIG. 1, the specific mode is as follows:
firstly, for four subsystems for controlling the lower-layer attitude and height, a mechanical superposition model is as follows:
Fh，
Fθ，Fψrespectively the increment output by the height controller and the three attitude angle controllers;
adding a gravity feed-forward quantity F at the input endbaseWherein
Make Fn′＝Fn+Fbase，n＝1，2，3，4；Fn' Propeller lift after gravity feed-forward is added to replace original FnAnd because the control increment given by the three attitude angles is to increase two lift forces and reduce two lift forces simultaneously, F is not influenced1+F2+F3+F4Is calculated, then:
secondly, a feedforward product term is made on an incremental signal given by the height controller through a pitch angle and a roll angle fed back by the attitude controller system to counteract the product coupling of the attitude to the height control in the formula (13); to not change FbaseA value of FbaseRequired product compensation is added to FhAmong them, the following are obtained:
Fh' is the height controller increment after adding attitude feed forward, replacing the original FhAnd finally obtaining:
as can be seen from equation (15), the second order differential of the height after compensation
Controller increment F from original deviationhThe linear relation is formed;
thirdly, because the attitude-to-height coupling in the formula (13) is continuous, and the actual controller and attitude feedback are discrete, the directly obtained attitude compensation has certain hysteresis, and the hysteresis degree is enhanced along with the increase of the discrete period; is provided with
θt、
A pitch angle and a roll angle with time t as a parameter; the discrete period is T, and the initial time in one period is T0The end of the cycle being at time t1From the Lagrange's median theorem, it can be known that there must be a t0To t1At a certain time t in betweenεAnd (2) making:
therefore, if g (t) can be obtainedε) I.e. the discrete value g (t) of the zero-order keeper can be replaced0) Since it is calculated as t0At time, only g (t)0) And the period T is a known quantity that is currently determined, so the pair g (T) is required1) And g (t) a function;
since the first order differential of the attitude angle can be measured, the angular velocity can be measured, and the second order differential can be calculated by equation (11), the taylor series can be applied to g (t)1) Carrying out estimation;
approximating g (t) as a linear function, we obtain from equation (16):
from equation (17) and equation (18), we can obtain:
thus, the attitude compensation value g (t) is obtainedε)；
Adding a saturation weight distributor in the pitch angle control subsystem and the roll angle control subsystem to eliminate invalid increment generated due to the saturation characteristic of the propeller;
as can be seen from the formula (11), for three Euler angle motion models, we can construct a controller by controlling the lift difference of the four propellers in pairs, so that the system becomes a linear second-order system, but the incremental signals of the three attitude angle controllers and the height controller are superposed on the force F1、F2、F3、F4In view of the fact that the propellers are capable of providing lift with a saturation characteristic, the following can occur, if not by way of limiting superposition:
incremental signals for single attitude angle control, should be such that F1、F2、F3、F4The two forces in the middle increase and the two decrease, but due to the effect of the other signals and the saturated nature of the forces themselves, so that:
increasing the lift force of the propeller to FmaxThe lift force of the propeller can be effectively reduced by the reduction amount;
② the reduced amount leads the lifting force of the propeller to reach FminThe lift force of the propeller can be effectively increased by the increased amount;
this results in: half or less than half of the attitude increment signals are invalid, thereby reducing the attitude adjustment effect; at the same time, lead to a postureIncremental signal pair F1+F2+F3+F4The value of (a) has an effect, which is equivalent to adding a disturbance signal in the height control; therefore, the invention adds a saturation weight distributor to the inner ring of the attitude controller, namely the angular velocity ring, to perform weighted distribution on the increment for leading the lifting force of the propeller to reach saturation, thereby inhibiting the generation of invalid increment;
the method specifically comprises the following steps: inputting angular velocity increment signals of a pitch angle and a roll angle into a saturation weight distributor, simultaneously inputting increment signals of height control into the saturation weight distributor, and outputting the distributed pitch angle increment signals and roll angle increment signals by the saturation weight distributor; the distribution mode is as follows: preferably, the increment of the height controller is not limited, but a certain attitude angle adjustment allowance is reserved. Then, within the remaining incremental range, the pitch angle increment and the roll angle increment do not cause the force of any propeller to reach F under the condition of keeping a certain yaw angle adjusting allowancemaxOr FminIf the pitch angle exceeds the range, the original value is kept to be output, and if the pitch angle exceeds the range, the pitch angle is increased by FθAnd roll angle increment
Keeping the original symbol, making:
wherein, FlimitIs the maximum incremental absolute value, F, for the propeller to reach saturationψlIs the adjustment margin left for keeping the yaw angle in balance; f'θAnd
then it is the output value after the saturation weight distributor;
at this point, the design of the lower-layer attitude and height controller is finished; FIG. 2 is a comparison result graph of the height control simulation before and after adding the gravity feedforward under the condition that the attitude disturbance is zero, and it can be seen that the control effect is obviously improved after adding the gravity feedforward in (2-b); FIG. 3 is a graph showing comparison results of height control simulation before and after attitude feed forward is added based on gravity feed forward, and it can be seen that in (3-b) after attitude feed forward is added, the output reduction due to attitude-to-height coupling is significantly offset and improved; FIG. 4 is a diagram of a continuous signal of a height-controlled attitude product disturbance term, a discrete signal of a zero-order keeper and a discrete signal obtained by Taylor expansion estimation, wherein (4-a) is the continuous signal of attitude disturbance and the discrete signal of the zero-order keeper, and (4-b) is the continuous signal of attitude disturbance and the discrete signal of Taylor series estimation, so that it can be obviously seen that an estimated value can represent an original continuous signal in a period, and the hysteresis influence of the signal dispersion on a system is reduced; FIG. 5 is a comparison of the rise time simulation results for a height control system with and without a weight assignor; obviously, after the weight distributor is added, the height control can reach a steady state more quickly due to lack of disturbance of invalid increment of the posture, and the rising time is selected as an index because the overshoot is small, the oscillation is small and the rising time can represent the dynamic performance of the height control system more according to an output characteristic curve;
and (VI) according to the attitude angle limit of the unmanned aerial vehicle, establishing an upper-layer time optimal tracking controller by taking the motion information of the tracked target as input, and connecting the upper-layer time optimal tracking controller in series with the four subsystems for controlling the lower-layer attitude and height to finally realize stable tracking.
Firstly, the control quantity is selected, the unmanned plane flies by means of the horizontal acceleration provided by the inclination of three Euler angles, so that four control modes can be selected: firstly, controlling a pitch angle, a roll angle and a yaw angle; controlling a pitch angle and a roll angle; controlling a pitch angle and a yaw angle; controlling the roll angle and the yaw angle; the Euler angle attitude description has twelve compliance rules, and each compliance rule can cause the formula of the unmanned aerial vehicle displacement to change, so that the horizontal displacement model of the unmanned aerial vehicle can be simplified by selecting a proper control quantity and a proper Euler angle compliance rule; the first two equations in the formula (9) are unmanned plane horizontal displacement models of an XYZ (Z-Z) cis-compass;
the invention selects the control mode II and ZYX compliance rules, and the following are provided:
therefore, the horizontal displacement model of the unmanned aerial vehicle is simplified, and the control quantity is to select the pitch angle theta and the roll angle according to the formula (21)
The trigonometric function product term cannot be counteracted like the height control; because the control target is used for tracking the ground moving target at a fixed set height, the method comprises the following steps
Namely:
equation (21) becomes:
the design purpose of the tracking controller is to enable the unmanned aerial vehicle to move the target on the air finally tracking without position deviation and speed deviation, namely, the control end state is required to meet the following requirements:
because no requirements for energy consumption and the like exist, the control index is the system regulation time, and an optimal controller is designed according to the system regulation time to obtain the optimal control index
And
then byThe optimal attitude value is calculated by a formula (23) and is connected to the lower-layer tracking and attitude controller in series; the advantage of doing so is to carry on the trigonometric function calculation between the upper and lower layer controllers through layering to the nonlinear trigonometric function term that is difficult to deal with in the control system, thus make the upper and lower layer controller do not contain the trigonometric function term per se, become the linear system;
firstly, establishing a state equation:
wherein u is1Is an acceleration in the x direction, i.e.
u2Is an acceleration in the y direction, i.e.
Then establishing a time optimal performance index functional J:
tfobtaining a parameter equation in the x direction and the y direction according to a plane motion function of a tracking target when the system is in the last state:
wherein a is the relative velocity difference in the x-direction and b is the relative displacement difference in the x-direction; c is the relative velocity difference in the y-direction, d is the relative displacement difference in the y-direction; the x direction and the y direction are the same, so that only the x direction is proved, and the y direction is proved to be the same; constructing a Hamiltonian equation in the x direction:
H＝1+λ1x2+λ2u1 (28)
λ1and λ2Is a Lagrange multiplier, according to a regular equationObtaining by solution:
c1、c2all are undetermined constant values, and then the cross section condition is solved to obtain:
c1＝-c1*t+c2 (30)
then, according to the principle of minima, one can obtain:
max _ x is the mode of the maximum value input in the x direction of the tracking controller, max _ y is the mode of the maximum value input in the y direction of the tracking controller, and is the acceleration extreme value limited by the attitude angle in the unmanned aerial vehicle tracking system; the optimal control accords with the bang-bang control law, and the problem becomes a dynamic planning problem because the input which can be acquired when the unmanned aerial vehicle flies is the relative speed and the relative position between the unmanned aerial vehicle and the tracking target at every moment; the core of the problem becomes the understanding of the system of equations:
obtaining by solution:
similarly, there is also solution in y direction:
max _ y is the mode of the maximum value input by the tracking controller in the y direction, and is the acceleration extreme value limited by the attitude angle in the unmanned aerial vehicle tracking system; the time optimal controller is constructed through a formula (33) and a formula (34), the attitude response of an ideal state is realized, no delay and no oscillation are realized, and the control method is freely controllable; the simulation results of the ideal state attitude response are shown in fig. 6, which are respectively a tracking characteristic curve of x, a tracking characteristic curve of y, and a comprehensive tracking characteristic curve; because the coordinate axes all contain the time axis t, the system can be converged, namely the tracking position and the tracking speed are unbiased;
in an actual system, an ideal attitude characteristic does not exist, the actual attitude characteristic is delayed and overshoots, and bang-bang control cannot stabilize the system, so that when the end state is approached, a deviation controller is used for replacing the bang-bang control to enable the system to be converged; the upper-layer tracking controller and the lower-layer attitude and height controller are connected in series, so that all controller designs of the invention are completed, the final simulation effect is shown in fig. 7, and it can be seen that when the unmanned aerial vehicle tracks a ground moving target, the system can be converged after several oscillations, and the tracking position and speed are unbiased.
Claims (3)
1. A layered unmanned aerial vehicle tracking control method based on feedforward and weight distribution is characterized by comprising the following steps:
(1) acquiring structural parameters of the unmanned aerial vehicle, including the mass of the unmanned aerial vehicle, the gravity acceleration, the distance between the axis of the motor and the gravity center of the unmanned aerial vehicle, and the rotational inertia of the unmanned aerial vehicle in the xyz three directions; acquiring the range of the lift force provided by the propeller of the unmanned aerial vehicle; acquiring Euler angle attitude information and height information of the unmanned aerial vehicle and a velocity vector and a displacement vector of a tracked target in real time;
(2) establishing a Newton Euler model according to the parameter information of the unmanned aerial vehicle obtained in the step (1), and adding a saturation characteristic into the model according to the lift force range which can be provided by the propeller; fmin＜F1、F2、F3、F4＜FmaxIn which F is1、F2、F3、F4Is the lift force generated by four propellers, FmaxIs the maximum lift that a single propeller can provide, FminIs the minimum lift to keep the propeller from stalling;
(3) according to the built model, a basic double-closed-loop cascade PID deviation controller is built among four subsystems of pitch angle control, roll angle control, yaw angle control and height control, and parameters are independently adjusted under the condition that coupling is temporarily not considered;
(4) adding gravity feed-forward and attitude feed-forward according to the gravity parameters of the unmanned aerial vehicle and the attitude information of the unmanned aerial vehicle, taking attitude and gravity coupling as disturbance of height control to offset, and estimating the attitude value of the unmanned aerial vehicle in the next discrete period by a Taylor expansion formula;
the gravity feed-forward added satisfies:
F′n＝Fn+Fbase，n＝1，2，3，4 (1)
wherein, Fn(n ═ 1, 2, 3, 4) represents the lift of the four propellers of the original quad-rotor drone, Fn' Propeller lift after gravity feed-forward is added to replace original FnM is the total mass of the unmanned aerial vehicle, g is the acceleration of gravity, FbaseIs gravity feed forward;
the added attitude feedforward satisfies the following conditions:
wherein FhIs the inner loop control increment of the altitude control subsystem, Fh' is the height controller increment after adding attitude feed forward, replacing the original Fh；θ、
The pitch angle and the roll angle of the unmanned aerial vehicle are respectively;
in the height subsystem, because the coupling of the attitude to the height is continuous, and the actual controller and the attitude feedback are discrete, the directly obtained attitude compensation has certain hysteresis, and the hysteresis degree is enhanced along with the increase of the discrete period; so the Taylor expansion is used in the control process to estimate the attitude disturbance in the next discrete period:
wherein theta ist、
A pitch angle and a roll angle with time t as a parameter; the discrete period is T, and the initial time in one period is T0The end of the cycle being at time t1，g(tε) Is the attitude compensation value after the estimation,
is an attitude disturbance term in the height control system; g (t)0) I.e. is to0The time of day is brought into the value of the formula because
Is the Taylor expansion, so g' (t)0)、g″(t0) Is then g (t)0) First order differential and second order differential.
(5) Adding a saturation weight distributor in the pitch angle control subsystem and the roll angle control subsystem to eliminate invalid increment generated due to the saturation characteristic of the propeller;
(6) according to the attitude angle limit of the unmanned aerial vehicle, the motion information of the tracked target is used as input, an upper time optimal tracking controller is established and is connected in series with the four subsystems for controlling the lower attitude and the height, and stable tracking is finally realized.
2. The feed-forward and weight assignment based hierarchical unmanned aerial vehicle tracking control method according to claim 1, characterized in that: in the step (5), a saturated weight distributor is added to an inner ring, namely an angular velocity ring, for cascade control of the pitch angle and the roll angle to distribute the control increments, the saturated weight distributor takes the pitch angle control increment, the roll angle control increment and the altitude increment as input, and takes the distributed pitch angle control increment and roll angle controllable increment as output; if the pitch angle increment and the roll angle increment do not enable the lift force of any propeller to be saturated, the original value output is kept, and if the pitch angle increment and the roll angle increment exceed the range, the pitch angle increment F is enabledθAnd roll angle increment
Keeping the original symbol, making:
wherein, FlimitIs the maximum incremental absolute value, F, for the propeller to reach saturationψlIs the adjustment margin left for keeping the yaw angle in balance; f'θAnd
then it is the output value after the saturation weight distributor;
3. the feed-forward and weight assignment based hierarchical unmanned aerial vehicle tracking control method according to claim 1, characterized in that: in the step (6), the step of,
selecting a pitch angle theta and a roll angle in an attitude angle
As a control quantity of horizontal movement, the Euler angle posture description selects a ZYX cis-form;
and decomposing the relative position and the relative speed of the tracked target and the unmanned aerial vehicle into an x direction and a y direction by taking the relative position and the relative speed of the tracked target and the unmanned aerial vehicle as input quantities:
in the parameter equation, a is the relative speed in the x direction, b is the relative position in the x direction, c is the relative speed in the y direction, and d is the relative position in the y direction;
and thirdly, deducing, wherein the time optimal control of the system is bang-bang control, and the result is as follows:
max _ x is the mode of the maximum value input in the x direction of the tracking controller, max _ y is the mode of the maximum value input in the y direction of the tracking controller, and is the acceleration extreme value limited by the attitude angle in the unmanned aerial vehicle tracking system; u. of1(t)、u2(t) acceleration of the upper tracking controller in x and y directions, respectively;
and fourthly, because the bang-bang control can vibrate when in a steady state value, the tracking controller is switched into a deviation control mode under the condition of approaching to the steady state, namely when the relative position and the relative speed of the unmanned aerial vehicle and the tracked target are small, so that the system is converged, and the tracking position and the tracking speed are unbiased.
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