CN109839822B - Four-rotor unmanned aerial vehicle height control method for improving active disturbance rejection - Google Patents
Four-rotor unmanned aerial vehicle height control method for improving active disturbance rejection Download PDFInfo
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Abstract
The invention discloses a four-rotor unmanned aerial vehicle height control method for improving active disturbance rejection, which comprises the following steps: step one, establishing a nonlinear dynamic model of the quad-rotor unmanned aerial vehicle in the height direction based on a mechanism modeling method; decomposing the nonlinear dynamic model into a linear term and an uncertain term; thirdly, a tracking differentiator is utilized to obtain the expected position and speed values in the height direction; estimating a disturbance item in the system by using a first-order extended state observer; and fifthly, designing an error feedback control law based on a PD algorithm and feedforward control, and compensating the system uncertain item by using the value of the disturbance item estimated by the extended state observer. The invention constructs an acceleration-constant speed-deceleration flight mode by utilizing an improved tracking differentiator to plan an altitude flight strategy, so that the quad-rotor unmanned aerial vehicle can ascend (or descend) from one altitude to another altitude in the shortest time; and the maximum acceleration and the speed of the uniform speed section during flying can be set independently.
Description
Technical Field
The invention belongs to the field of automatic control of unmanned aerial vehicles, and particularly relates to a height control method of a quad-rotor unmanned aerial vehicle with improved active disturbance rejection.
Background
The stability control of the unmanned aerial vehicle is one of the core and the key points of the research of the unmanned aerial vehicle system, and the research of the unmanned aerial vehicle system not only has great practical significance, but also has profound theoretical significance.
Four rotor unmanned aerial vehicles have been fairly common in the market at present, but the flight control system that design interference killing feature is strong still problem than difficult. Especially when considering the condition that unmanned aerial vehicle carries the load, realize the stable control of direction of height and be a difficult problem of having the combatability.
Over the past decades, various control algorithms have been studied and implemented for stable control of drones. Common controllers include PID controllers, backstepping controllers, sliding mode controllers, and the like. The PID controller is widely applied to a modern unmanned aerial vehicle control system due to the advantages of simplicity and high efficiency. However, the control effect of the PID controller depends on the setting of three parameters, i.e., proportional, integral, and differential, too much, and is susceptible to a large influence when disturbed by an external force. It is therefore necessary to design a controller with good noise immunity.
The active disturbance rejection control technology is proposed by a Hanjing Qing researcher of the national academy of sciences system science institute, and the control method mainly comprises three parts: the tracking differentiator, the error feedback controller and the extended state observer still have good robust control effect under the condition of not depending on an accurate model of a system. In recent years, the control method is applied to the flight control of the unmanned aerial vehicle to a certain extent, but the existing parameter setting method of the active disturbance rejection controller is few, the nonlinear structure is still complex, and the actual application has certain difficulty; in addition, the current application cases are mostly seen in unmanned aerial vehicle attitude control, and there are still cases that the application is not successful in height control or horizontal direction. Therefore, the active disturbance rejection controller is simplified to a certain extent, and the high-altitude disturbance rejection controller has important engineering significance when being applied to the four-rotor unmanned aerial vehicle.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: how to improve the active disturbance rejection control algorithm to a certain extent is applied to the height control of the quad-rotor unmanned aerial vehicle, so that the quad-rotor unmanned aerial vehicle has better robust performance, and therefore, the method for controlling the height of the quad-rotor unmanned aerial vehicle with improved active disturbance rejection is provided.
The invention is realized by adopting the following technical scheme:
a method for controlling the height of a quad-rotor unmanned aerial vehicle with improved active disturbance rejection comprises the following steps:
step one, establishing a nonlinear dynamic model of the quad-rotor unmanned aerial vehicle in the height direction based on a mechanism modeling method;
decomposing the nonlinear dynamic model into a linear term and an uncertain term;
thirdly, on the basis of the second step, a tracking differentiator is utilized to obtain the expected position and speed value in the height direction;
step four, on the basis of the step three, estimating a disturbance term in the system by using a first-order extended state observer;
and step five, designing an error feedback control law based on a PD algorithm and feedforward control on the basis of the step four, and compensating the system uncertain item by using the value of the disturbance item estimated by the extended state observer.
The invention has the further improvement that in the step one, the nonlinear dynamic model of the quad-rotor unmanned aerial vehicle established based on the mechanism modeling method is as follows:
wherein z is the height of the drone in the geographic coordinate system,b is the lift coefficient of the rotor, omegaiThe rotation speeds of the four motors are 1,2,3 and 4, and theta and phi are a pitch angle and a roll angle of the unmanned aerial vehicle respectively; m is the mass of the unmanned aerial vehicle, g is the gravitational acceleration, DfzTo resolve the external force interference in the height direction, f in fz is the abbreviation of the word force, meaning force, and z represents the z-axis, i.e. the height direction;
in this model, u is the control input of unmanned aerial vehicle direction of height, also is the lift that four rotors of unmanned aerial vehicle can provide.
The invention further improves the method in that in the second step, the nonlinear dynamic model is decomposed into a linear term and an uncertain term, and the specific description is as follows:
in the formula uz=ucosφcosθ-mg,km=1/m,qz=kmDfzWherein k ismuzIs a linear term of the system model, qzIs an uncertainty term of the system model.
The invention is further improved in that in the third step, the expected height direction position and speed are obtained by using a tracking differentiator, as follows:
in the formula, x1(k) Denotes the desired height at time k, H denotes the final desired height, x2(k) Representing the desired altitude speed at time k; h denotes the step size, h0Representing a filter factor for preventing x1(k) Reach a final height H with oscillations, and H0Is greater than h; a iszmaxIs the maximum acceleration, V, allowed by the systemzmaxIs the maximum speed allowed by the system, and the Limit function represents the expected speed x2(k) Is limited to VzmaxInternal; fhan is also called the steepest control synthesis function, which is calculated as follows:
first step, intermediate quantity calculation:
secondly, solving a fhan function value:
in the formula, sign represents a sign function.
The invention is further improved in that in step four, the value of the uncertainty term is estimated using a first order extended state observer:
in the formula, evz(k) Representing the error of the velocity estimate at time k, z1(k) Representing estimated speed, vz(k) Representing the measured speed of the sensor, h representing the step size, z2Is an uncertainty term estimated by the observer, uzIs a control quantity, beta01And beta02Is an observer parameter; when beta is01And beta02When taken sufficiently large, z2The value will be close enough to the uncertainty term qz(ii) a Suppose the observer bandwidth is ωz0Then take β01=2ωz0,
The invention is further improved in that the actually measured speed of the sensor is obtained by fusion filtering algorithm of the height measured by ultrasonic waves or a barometer and the acceleration data measured by the accelerometer.
The further improvement of the invention is that in the fifth step, an error feedback control law based on a PD algorithm and feedforward control is designed, and the system uncertain item is compensated by using the value of the disturbance item estimated by the extended state observer, as follows:
in the formula, ez1(k +1) is the error between the desired altitude and the actual altitude at time k +1, z (k +1) is the altitude at time k +1, ez1(k +1) is the error between the desired speed and the actual speed at time k +1, uz0(k +1) is the PD algorithm chosen for the linear term, kzpAnd kzdIs the corresponding PD parameter, fh corresponds to the feed forward term; u. ofz(k +1) subtracting the estimate z of the uncertain term from this basis2(k +1), i.e. to compensate for the uncertainty term.
The invention has the following beneficial technical effects:
1. the invention constructs an acceleration-constant speed-deceleration flight mode by utilizing an improved tracking differentiator to plan an altitude flight strategy, so that the quad-rotor unmanned aerial vehicle can ascend (or descend) from one altitude to another altitude in the shortest time; the maximum acceleration and the speed of the uniform speed section during flying can be set independently;
2. the invention estimates the interference quantity in the height direction by utilizing a first-order extended state observer and an observable speed quantity, and provides a method for selecting observer parameters;
3. according to the invention, the motion model in the height direction is divided into a linear part and an uncertain part, and corresponding control strategies are designed for the two parts in the final controller, so that the problem of insufficient anti-interference capability of the traditional PID controller is solved, and the anti-interference capability of the unmanned aerial vehicle carrying a load is especially improved. In a simulation experiment and an actual flight experiment, the unmanned aerial vehicle shows excellent robust stability performance.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a waveform diagram of a simulation experiment of the altitude active disturbance rejection control of the unmanned aerial vehicle, wherein U is shown in FIG. 2(a)zWithout subtracting the interference compensation z2The waveform of the simulation experiment of (1), and fig. 2(b) is uzBy subtracting the interference compensation z2The simulation experiment oscillogram of (1);
fig. 3 is a high immunity waveform diagram for a flight experiment of an unmanned aerial vehicle carrying a load.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described with reference to the accompanying drawings, simulation experiments and actual flight experiments.
As shown in fig. 1, the method for controlling the height of a quad-rotor drone with improved active-disturbance rejection provided by the invention comprises the following steps:
firstly, a nonlinear dynamic model of the quad-rotor unmanned aerial vehicle in the height direction is established based on a mechanism modeling method. The mathematical expression is as follows:
the model considers the nonlinear structure of the system and external interference, and accurately depicts the actual flight condition. In the model, the model is divided into a plurality of models,can be regarded as the control input of direction of height, also be the lift that four rotors of unmanned aerial vehicle can provide, b is the lift coefficient of rotor, omegai(i ═ 1,2,3,4) are the rotational speeds of the four motors. z is the height of the unmanned aerial vehicle in the geographic coordinate system, and theta and phi are the pitch angle and the roll angle of the unmanned aerial vehicle respectively. m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity, DfzTo resolve external force interference in the height direction. Can derive from the model, unmanned aerial vehicle receives rotor lift, unmanned aerial vehicle attitude angle, gravity and the common influence of disturbing external force in direction of height's motion.
In fact, most of the existing data simplify the model, interference items are not considered, and the invention fully considers the interference external force.
The nonlinear dynamical model is then decomposed into linear terms and uncertainty terms. The decomposed mathematical expression may be described as:in the formula uz=ucosφcosθ-mg,km=1/m,qz=kmDfz. Wherein k ismuzIs a linear term of the system model, qzIs an uncertainty term of the system model. After the model is decomposed, the design of the controller for the linear item and the uncertain item is facilitated.
And step two, decomposing the nonlinear dynamic model into a linear term and an uncertain term. The decomposed mathematical expression may be described as:in the formula uz=ucosφcosθ-mg,km=1/m,qz=kmDfz. Wherein the content of the first and second substances,kmuzis a linear term of the system model, qzIs an uncertainty term of the system model. After the model is decomposed, the design of the controller for the linear item and the uncertain item is facilitated.
Thirdly, a tracking differentiator is utilized to obtain the expected position and speed values in the height direction, and the recursion equation corresponding to the control period is as follows:
in the formula, x1(k) Denotes the desired height at time k, H denotes the final desired height, x2(k) Representing the desired altitude speed at time k; h denotes the step size, h0Represents a filter factor that prevents x1(k) The final height H is reached, and the vibration occurs, generally H is taken0Greater than h, e.g. take h0=10h;azmaxIs the maximum acceleration, V, allowed by the systemzmaxIs the maximum speed allowed by the system, and the Limit function represents the expected speed x2(k) Is limited to VzmaxAnd (4) the following steps. fhan is also called the steepest control synthesis function, which can be calculated according to the following formula:
in the formula, sign represents a sign function.
Estimating a disturbance item in the system by using the first-order extended state observer, wherein a recursion equation corresponding to the speed measurement period is as follows:
in the formula, evz(k) Representing the error of the velocity estimate at time k, z1(k) Representing estimated speed, vz(k) Indicating the speed of the actual measurement of the sensor, wherein the actual measurement speed can be measured by ultrasonic or barometerThe height of the quantity and the acceleration data measured by the accelerometer are obtained by a certain fusion filtering algorithm (such as Kalman filtering and complementary filtering). h denotes the step size, z2Is an indeterminate term estimated by the observer, uzIs a control quantity, beta01And beta02Is an observer parameter. When beta is01And beta02When taken sufficiently large, z2The value will be close enough to the undetermined term qz. Suppose the observer bandwidth is ωz0Then β may be taken01=2ωz0,
And fifthly, designing an error feedback control law based on a PD algorithm and feedforward control, and compensating the system uncertain item by using the value of the disturbance item estimated by the extended state observer. The recursion equation according to the control period is as follows:
in the formula, ez1(k +1) is the error between the desired altitude and the actual altitude at time k + 1, z (k +1) is the altitude at time k + 1, ez1(k +1) is the error between the desired speed and the actual speed at time k + 1, uz0(k +1) is the PD algorithm chosen for the linear term, kzpAnd kzdIs the corresponding PD parameter, fh corresponds to the feed forward term; u. ofz(k +1) subtracting the estimate z of the uncertainty term from this basis2(k +1), i.e. to compensate for the uncertainty term.
As an altitude flight planning strategy, in step three, the limit of the expected speed, namely x, is added on the basis of the classical tracking differentiator2(k+1)=Limit(x2(k+1),-Vzmax,Vzmax). In a general application scenario, the motion of the unmanned aerial vehicle in the height direction always wants to fly from a certain height hovering state to another height rapidly and then keep the hovering state, and the improved tracking differentiator enables the unmanned aerial vehicle to realize the motion from zero acceleration-constant speed-deceleration to zero-hovering stateThe speed of the state process and the uniform speed process is VzmaxAnd the absolute value of the acceleration during acceleration or deceleration is azmaxBy setting the two parameters, the unmanned aerial vehicle can fly according to the expected acceleration and speed, and the flying time is shortest.
And as an uncertainty estimation method, in the fourth step, a first-order extended state observer is selected to estimate the interference quantity. The observer requires that the speed of motion of the unmanned aerial vehicle in the direction of altitude be obtainable. In practical application, the velocity amount can be obtained by adopting height information measured by a barometer or ultrasonic waves and acceleration information measured by an accelerometer through a certain fusion filtering algorithm, and the commonly used filtering algorithm comprises Kalman filtering and complementary filtering. If the update frequency of the velocity data is ωz0Then the observer parameter may be taken as β01=2ωz0,
And as a control strategy, step five, designing corresponding controllers for linear terms and uncertain terms of the system model in step two respectively, and controlling. For control of the linear term, u is mainlyz0Completion, for uncertainty term, by uzBy subtracting an estimated quantity of uncertainty, i.e. by subtracting z2For uncertainty term qzCompensation is performed so as to realize the noise immunity in the height direction.
The following describes simulation experiments and flight experiments.
Suppose that in a certain application scene, the unmanned aerial vehicle takes off from the flat ground, needs to fly to the height of 100cm and then keeps hovering, and requires that the absolute value of the maximum acceleration of the unmanned aerial vehicle in the flying process is 30cm/s2Maximum speed is 30cm/s, simulation is carried out for 30s time and 8s<t<At 15s, an external force disturbance in the vertical direction of 2cos (2t) +3 (unit: N) is applied. The mass of the drone is 1.076kg and the maximum lift that the rotor can provide is 21N.
Step one, a tracking differentiator is utilized to obtain the expected position and speed values in the height direction, and a recursion equation corresponding to a control period is as follows:
if the control period in the height direction is 0.01s, h is 0.01, h0=0.1。
Estimating a disturbance item in the system by using the first-order extended state observer, wherein a recursion equation corresponding to a speed measurement period is as follows:
if the speed measurement period is 0.01s, then h is 0.01, β01=2ωz0=2/h=200,β02=ωz0 210000. Since m is 1.076, k is preferablem=1/1.076≈1。
Estimating a disturbance item in the system by using the first-order extended state observer, wherein a recursion equation corresponding to a speed measurement period is as follows:
if the speed measurement period is 0.01s, then h is 0.01, β01=2ωz0=2/h=200,β02=ωz0 210000. Since m is 1.076, k is preferablem=1/1.076≈1。
And step three, designing an error feedback control law based on a PD algorithm and feedforward control, and compensating the system uncertain item by using the value of the disturbance item estimated by the extended state observer. The recursion equation according to the control period is as follows:
for PD parameters, only take kzpAnd kzdThe stability requirement can be met when the values are all larger than zero, and k can be taken according to the characteristics of the unmanned parameters taken in the simulation experimentzp=kzd=4。
Figure 2 shows the results of two sets of comparative simulation experiments. (a) In the figure, a PD control algorithm after the PD parameters are adjusted is used, and the interference compensation quantity z is not subtracted2(ii) a (b) In the figure, the high active disturbance rejection control algorithm proposed by the present invention is used, and the disturbance compensation quantity z is subtracted2. It can be seen that when there is no interference in the first 8s, there is an interference-free compensation amount z2The height control effect is not influenced, and the unmanned aerial vehicle can reach the designated height quickly without overshoot; at 8s<t<After 15s interference addition, the compensation quantity z without interference2In time, namely under a general PID algorithm, an actual height curve (a green curve in a graph) deviates from an expected height, interference is cancelled after 15s, the actual height cannot be recovered to the expected height, and finally, the overshoot reaches 33%; while there is an interference compensation quantity z2Time, i.e. under the active disturbance rejection control algorithm, albeit at 8s<t<The height curve within 15s has a little fluctuation, but the fluctuation is very small, the maximum overshoot in the whole flight process is about 0.022%, and the anti-interference effect is obvious.
For an actual flight experiment, a common F450 frame on the market is selected as an experimental object, and after the experimental object is assembled, the specific parameters of the machine body are as follows:
table 1 quad-rotor unmanned aerial vehicle airframe parameters
In table 1, m is the mass of the unmanned aerial vehicle, b is the lift coefficient of the rotor, l is the arm length of the unmanned aerial vehicle, and Ix、Iy、IzThe moment of inertia around the x axis, the y axis and the z axis respectively, and g is the gravity acceleration.
During the experiment, before taking off, hang a 325g Li-Po battery under four rotor unmanned aerial vehicle, the length of suspension rope is 0.1m, and unmanned aerial vehicle flight target height is 1.1m, begins to receive the weight interference of battery when flight height reaches 0.1m, and after the battery liftoff, unmanned aerial vehicle still received the battery and rocked the interference that brings. The flight experiment is shown in fig. 3.
The experimental data were imported into MATLAB and compared with those without interference (with battery, take-off at constant height), and the results are shown in fig. 3.
As can be seen from fig. 3, when no disturbance is applied (no battery is suspended), the actual flight curve of the position and the speed can well track the expected position-speed curve, three processes of acceleration, uniform speed and deceleration are well realized, overshoot hardly occurs, and the position steady-state error is less than 1 cm; after the suspension battery is subjected to increased disturbance, although the position and speed curve has certain fluctuation, the actual fluctuation range is smaller, and finally the fluctuation range can still approach to stability, the position error is gradually reduced, and the anti-disturbance effect is good.
According to simulation experiments and actual flight experiments, the high active disturbance rejection method provided by the invention can achieve the expected disturbance rejection effect.
Claims (4)
1. A method for controlling the height of a quad-rotor unmanned aerial vehicle with improved active disturbance rejection is characterized by comprising the following steps:
step one, establishing a nonlinear dynamic model of the quad-rotor unmanned aerial vehicle in the height direction based on a mechanism modeling method, specifically:
wherein z is the height of the drone in the geographic coordinate system,b is the lift coefficient of the rotor, omegaiThe rotation speeds of four motors are 1,2,3 and 4, and theta and phi are a pitch angle and a roll angle of the unmanned aerial vehicle respectively; m is the mass of the unmanned aerial vehicle, g is the acceleration of gravity, DfzTo resolve the external force interference in the height direction, f in fz is the abbreviation of the word force, meaning force, and z represents the z-axis, i.e. the height direction;
in the model, u is the control input of the unmanned aerial vehicle in the height direction and is the lift force provided by four rotor wings of the unmanned aerial vehicle;
step two, decomposing the nonlinear dynamic model into a linear term and an uncertain term, wherein the specific description is as follows:
in the formula uz=u cosφcosθ-mg,km=1/m,qz=kmDfzWherein k ismuzIs a linear term of the system model, qzIs an uncertainty of the system model;
and step three, on the basis of the step two, utilizing a tracking differentiator to obtain the expected position and speed values in the height direction as follows:
in the formula, x1(k) Denotes the desired height at time k, H denotes the final desired height, x2(k) Representing the desired altitude speed at time k; h denotes the step size, h0Representing a filter factor for preventing x1(k) Reach a final height H with oscillations, and H0Is greater than h; a iszmaxIs the maximum acceleration, V, allowed by the systemzmaxIs the maximum speed allowed by the system, and the Limit function represents the expected speed x2(k) Is limited to VzmaxInternal; fhan is also called the steepest control synthesis function, which is calculated as follows:
first step, intermediate quantity calculation:
secondly, solving a fhan function value:
in the formula, sign represents a sign function;
step four, on the basis of the step three, estimating a disturbance term in the system by using a first-order extended state observer;
and step five, designing an error feedback control law based on a PD algorithm and feedforward control on the basis of the step four, and compensating the system uncertain item by using the value of the disturbance item estimated by the extended state observer.
2. A method for improved active disturbance rejection quad-rotor drone altitude control according to claim 1, wherein in step four, the value of the uncertainty term is estimated using a first order extended state observer:
in the formula, evz(k) Representing the error of the velocity estimate at time k, z1(k) Representing estimated speed, vz(k) Representing the measured speed of the sensor, h representing the step size, z2Is an uncertainty term estimated by the observer, uzIs a control quantity, beta01And beta02Is an observer parameter; when beta is01And beta02When taken sufficiently large, z2The value will be close enough to the uncertainty term qz(ii) a Suppose the observer bandwidth is ωz0Then take β01=2ωz0,
3. The method for controlling the altitude of a quad-rotor drone with improved active disturbance rejection according to claim 2, wherein the measured speed of the sensors is obtained by fusion filtering of the measured altitude of the ultrasonic or barometer and the measured acceleration data of the accelerometer.
4. The method for controlling the height of a quad-rotor unmanned aerial vehicle with improved active disturbance rejection according to claim 2, wherein in step five, an error feedback control law based on a PD algorithm and a feedforward control is designed, and a system uncertainty term is compensated by using a value of a disturbance term estimated by an extended state observer, as follows:
in the formula, ez1(k +1) is the error between the desired altitude and the actual altitude at time k +1, z (k +1) is the altitude at time k +1, ez1(k +1) is the error between the desired speed and the actual speed at time k +1, uz0(k +1) is the PD algorithm chosen for the linear term, kzpAnd kzdIs the corresponding PD parameter, fh corresponds to the feed forward term; u. ofz(k +1) subtracting the estimate z of the uncertainty term from this basis2(k +1), i.e. to compensate for the uncertainty term.
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