CN115576341A - Unmanned aerial vehicle trajectory tracking control method based on function differentiation and adaptive variable gain - Google Patents
Unmanned aerial vehicle trajectory tracking control method based on function differentiation and adaptive variable gain Download PDFInfo
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Abstract
The unmanned aerial vehicle trajectory tracking control method based on function differentiation and adaptive variable gain comprises the following steps: 1. establishing a four-rotor unmanned aerial vehicle tracking control method model; 2. designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor; 3. designing a novel three-order self-adaptive variable gain finite time extended observer according to a control model; 4. designing an active disturbance rejection tracking controller, wherein one part of the active disturbance rejection tracking controller is compensated by an observer, and the other part of the active disturbance rejection tracking controller is designed as a fast sliding mode controller and is used for tracking the positions and postures of four rotors; 5. and (4) proving the closed loop stability of the whole track tracking control method according to the Lyapunov function. The method can compensate unknown interference and model uncertainty of the trajectory tracking control method of the quad-rotor unmanned aerial vehicle, accelerate the convergence speed of the system and improve the performance of the tracking control method.
Description
Technical Field
The invention belongs to the field of trajectory tracking control of quad-rotor unmanned aerial vehicles, and particularly relates to an unmanned aerial vehicle trajectory tracking control method based on functional differentiation and adaptive variable gain.
Background
Quad-rotor unmanned aerial vehicles are widely used in the fields of military reconnaissance, disaster search and rescue, mail delivery, terrain surveying, pesticide spraying and the like because of their lightness and flexibility. The four-rotor dynamical system has the characteristics of nonlinearity, strong coupling, modeling uncertainty, under-actuation and the like. Uncertain external interference exists in the actual flight process, such as conditions of turbulent wind field, self-positioning drift, variable load, motor fault and the like. These self characteristics and external disturbances present a significant challenge to trajectory tracking control of the quad rotors.
Aiming at the rapid and accurate track tracking control of the quad-rotor unmanned aerial vehicle under the condition of external interference, related scholars provide algorithms such as PID control, backstepping control and sliding mode variable structure control. The PID control is suitable for linear control, and parameter setting needs to be carried out again when the model parameters are changed under the condition that the model is known. The backstepping control ensures that each variable reaches a desired value to ensure the performance of the whole system by setting a plurality of intermediate variables and each-order derivative quantity of the system state, but the problem of dimension explosion exists along with the increase of the complexity of the system. The sliding mode variable structure control enables the system state to purposefully move according to the state track of a preset sliding mode, and the system has strong robustness on interference and unmodeled dynamics, but has the problem of buffeting. The active disturbance rejection control has a good inhibiting effect on an unknown part of a model and an unknown disturbance outside through the design of a tracking differentiator, an extended observer and a feedback controller, and is widely applied to the aspects of robot control, permanent magnet motor control and unmanned aerial vehicle control. The classical second-order slowest switch tracking differentiator has obvious buffeting phenomenon in the signal tracking process and is low in convergence speed far away from a balance point, and differential information is difficult to obtain accurately from a tracking signal containing interference noise. And the linear extended observer is easy to cause a spike effect, so that a larger initial value of the controller is caused. Meanwhile, the stability of the active disturbance rejection control is more important in the practical application of the certification and the parameter setting. The research of the active disturbance rejection controller has become a research hotspot in the field of tracking control.
The prior art is as follows:
the patent name: a sliding mode control-based adaptive trajectory tracking controller for parameter prediction and disturbance of a quad-rotor unmanned aerial vehicle and a design method thereof are disclosed, wherein the sliding mode control-based adaptive trajectory tracking controller comprises the following steps: CN202110841286.6, the invention provides a sliding mode control-based adaptive trajectory tracking controller for parameter prediction and disturbance of a quad-rotor unmanned aerial vehicle and a design method thereof, based on a nonlinear mechanical model of the quad-rotor unmanned aerial vehicle, according to an attitude angle target and a flight position target tracked by the quad-rotor unmanned aerial vehicle, an attitude control input function of a system is obtained by using a sliding mode variable structure control method, meanwhile, the system is predicted, and a predicted value is used for replacing an actual value to give adaptive control compensation in advance; obtaining a position control input function of the system by using a sliding mode variable structure control method, predicting the system, and replacing an actual value with a predicted value to give adaptive control compensation in advance; and reversely solving the expected values of the roll angle and the pitch angle of the quad-rotor unmanned aerial vehicle according to the expected yaw angle and the virtual control input, and using the expected values as reference inputs of the inner loop. The track tracking efficiency and the tracking precision of the unmanned aerial vehicle are effectively improved, and the stability of the self-adaptive track tracking controller is ensured.
The method is characterized in that the input functions of a position subsystem and an attitude subsystem are respectively calculated by utilizing the control of a sliding mode variable structure, a prediction mechanism is designed, and unknown parameters of the unmanned aerial vehicle are adaptively compensated by utilizing a prediction value, so that the high-precision track tracking capability of the unmanned aerial vehicle in a disturbance environment is ensured. The method firstly designs a differential tracker combining a sigmoid function and a sliding mode terminal operator aiming at the problem of second derivative of an expected track required in a fast nonsingular controller, and obtains smooth track information. Meanwhile, for external interference, the three-order self-adaptive variable gain extended observer is designed, feedback compensation is carried out after an interference value is effectively estimated, and the performance of high-precision track tracking is achieved. Therefore, the two patents are completely different in the method of dealing with the external disturbance.
The patent name: four rotor unmanned aerial vehicle control method based on fuzzy extended state observer and self-adaptation slip mode, patent no: CN201610565104.6, the invention establishes a four-rotor unmanned aerial vehicle system model, initializes system state and controller parameters; designing a tracking differentiator; designing a nonlinear extended state observer; establishing a fuzzy rule; designing a parameter adaptive law; and designing an adaptive sliding mode controller. Designing an extended state observer, estimating uncertainty and external disturbance of a system model, determining an initial value of parameters of the extended state observer by a pole allocation method, introducing a fuzzy rule, and performing online setting on the parameters of the extended state observer; designing a parameter adaptive law to obtain an ideal controller gain; and a self-adaptive sliding mode controller is designed, so that the system tracking error is ensured to be fast and stable and converged to zero, and the fast and stable position tracking and attitude adjustment of the quad-rotor unmanned aerial vehicle are realized. The invention improves the system performance and realizes the rapid and stable position tracking and posture adjustment of the system.
The method comprises the steps of estimating uncertainty and external disturbance of a system model by designing an extended state observer, determining an initial value of parameters of the extended state observer by a pole allocation method, introducing a fuzzy rule, and performing online setting on the parameters of the extended state observer; designing a parameter adaptive law to obtain an ideal controller gain; and designing a self-adaptive sliding mode controller to ensure that the tracking error of the system is fast and stable and converges to a zero point.
The patent designs a third-order adaptive variable gain extended observer to estimate the external disturbance. Stability analysis is carried out on the designed extended observer to obtain stable necessary conditions, then a self-adaptive variable gain function which meets the conditions is designed, and the gain of the extended observer is adjusted on line without introducing a fuzzy rule. Secondly, the two patents are different in the design of sliding mode surfaces, and the control method of the four-rotor unmanned aerial vehicle based on the fuzzy extended state observer and the self-adaptive sliding mode adopts the simplest linear sliding mode surface, can only ensure that the error converges to the zero point, but cannot ensure the convergence time. The rapid nonsingular sliding mode surface adopted by the method can ensure rapid convergence in limited time, and is better in rapid high-precision track tracking performance. Thus, both patents differ in both the extended observer design and the sliding mode face design.
The research of the novel active disturbance rejection control quad-rotor unmanned aerial vehicle trajectory tracking control is developed, the estimation precision of external disturbance, the convergence rate and the control precision of tracking control can be improved, and a control algorithm with excellent performance is provided for the wide application of the quad-rotor unmanned aerial vehicle in complex environments such as military reconnaissance, disaster search and rescue, terrain survey and the like.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the unmanned aerial vehicle trajectory tracking control method based on function differentiation and adaptive variable gain, which can compensate unknown interference and model uncertainty of the four-rotor unmanned aerial vehicle trajectory tracking control method, accelerate the system convergence speed, enable the control error convergence to be zero in a limited time and improve the performance of the tracking control method.
In order to achieve the purpose, the invention adopts the technical scheme that:
the unmanned aerial vehicle trajectory tracking control method based on function differentiation and adaptive variable gain specifically comprises the following steps:
(1) Establishing a four-rotor unmanned aerial vehicle tracking control system model;
(2) Designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor;
in the step (2), designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor comprises the following steps:
(2.1) designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor, wherein the differential tracker comprises the following specific forms:
wherein σ = p/q, p < q, and p, q are odd numbers, α > 0, γ > 0, R > 0.V (t) is an input signal,
and
an original signal and a differential signal which are tracking signals v (t);
(3) Designing a novel three-order self-adaptive variable-gain finite time expansion observer according to a control model;
in the step (3), designing a novel three-order self-adaptive finite time expansion observer comprises the following steps:
(3.1) designing a novel three-order self-adaptive finite time expansion observer, wherein the specific form is as follows:
wherein, the variables defining the extended observer are respectively: controlSystem signal Z 1 First derivative Z of the control signal 2 And total interference observations Z 3 . Error variable of observer has e 1 ＝x 1 -Z 1 ，e 2 ＝x 2 -Z 2 ，e 3 ＝D-Z 3 The parameter satisfies 0.5 < lambda 1 ＜1，λ 2 ＝2λ 1 -1，l 1 (t)，l 2 (t)，l 3 (t) as a designed time-varying gain, by the law of adaptivity
Updating, on the premise of satisfying stability, designing L (t) as
(4) Designing an active disturbance rejection tracking controller, wherein one part of the active disturbance rejection tracking controller is compensated by an observer for total disturbance of the system, and the other part of the active disturbance rejection tracking controller is designed as a fast sliding mode controller for tracking the position and the posture of the four rotors;
(5) And (4) proving the closed loop stability of the whole track tracking control system according to the Lyapunov function.
As a further improvement of the invention, in the step (1), establishing a model of a tracking control system of a quad-rotor unmanned aerial vehicle comprises the following steps:
(1.1) establishing a kinematics model of the quad-rotor unmanned aerial vehicle:
rotation vector of four rotors under body coordinate system
Roll angle, pitch angle and yaw angle, respectively;
the angular velocity is under the coordinate system of the machine body; position vector of four rotors under body coordinate system
Linear velocities in three directions of
The kinematic model of a quad-rotor drone is represented as:
wherein R is ω Is a transformation matrix of the attitude change rate and the rotation angular velocity of the body, and is expressed as:
rotating matrix from body coordinate system to ground-fixed coordinate system
Expressed as:
(1.2) establishing a four-rotor unmanned aerial vehicle dynamic model:
the attitude dynamics model is established by the Euler equation as follows:
wherein,
a rotational inertia matrix of four rotors;
representing a gyro moment;
representing the moment generated by the propeller on the shaft of the body; x represents a vector cross product operation;
is a disturbance moment;
force analysis was performed on four rotors, as determined by newton's second law:
wherein, K f ＝diag(k x ，k y ，k z ) Is an air resistance coefficient matrix; g = [0, G)] T Is gravity; UT is the total pulling force acting on the four motors; d p (t)＝[d x ，d y ，d z ] T For the purpose of other disturbing resistances, it is,
is the tension of the ith motor, U r The tension of the four motors in the x, y and z axes is adopted;
(1.3) analyzing uncertainty of modeling of a control system and external interference:
defining a system state variable as X 1 ＝[x，y，z] T ，
X 3 ＝[φ，θ，ψ] T ，
Converting the dynamic model into a state space form with lumped disturbance due to external disturbance and model parameter identification errors;
wherein
Is the measured value of the system model parameter,. DELTA.. Cndot. -. Is the uncertain value of the model parameter, B 1 ＝[cosψsinθcosφ+sinψsinφ，sinψsinθsinφ-cosψsinφ，cosθcosφ] T ，Π 1 ＝diag(J y -J z ，J z -J x ，J x -J y )，∏ 2 ＝diag(-J r Ω r ，-J r Ω r ，0)，
Is a continuous smooth function, and the lumped disturbance is defined as
(1.4) nonlinear decoupling:
to solve the coupling problem, a position virtual variable V = [ V ] is adopted x ，V y ，V z ] T As follows
The desired Euler angle (phi) can be obtained d ，θ d ) And total thrust u T As follows
As a further improvement of the present invention, in the step (4), designing a nonsingular fast sliding mode controller includes the following steps:
(4.1) defining a space state equation of the four-rotor tracking control system:
the system space state equation obtained by the two formulas in the step (1.3) is as follows:
for the design of sliding mode controller for position control subsystem, the position error and speed error are defined as follows
For the design of a sliding mode controller of an attitude control subsystem, the attitude error and the angular velocity error are defined as follows
(4.2) designing a fast nonsingular terminal sliding mode controller:
the fast nonsingular terminal sliding mode surface of the attitude subsystem is designed as
The fast nonsingular terminal sliding mode surface of the position subsystem is designed as
Where b is n Is a normal number, 1 < beta n ＜2，β n+1 ＜α n
Derived from sliding mode functions
Order to
Is obtained from the control law
As a further improvement of the present invention, in step (5), the closed-loop stability of the trajectory tracking control system is proved to include the following steps:
(5.1) taking the position subsystem X channel after decoupling as an example, the Lyapunov function is defined as follows:
carry into U X The derivative of equation (21) with respect to time is written as
The Lyapunov function of the location subsystem is selected as
Therefore, the stability of the position system is ensured, and the track tracking capability is ensured. The stability for the gesture subsystem proves similar and is not described in detail.
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the traditional method, the method can realize the high-precision tracking performance of the four-rotor aircraft with known or unknown disturbance and rapid convergence.
2. The method designs a tracking differentiator based on an improved Sigmoid function. In the structure of the tracking differentiator, a novel second-order differential tracker combining a sigmoid function and a sliding mode terminal attractor is designed, so that the global convergence rate of the tracking differentiator can be accelerated, and buffeting caused by high-frequency signals can be effectively reduced.
3. The method designs a limited time expansion observer of time-varying gain, can effectively solve the peaking effect brought by constant gain, and converges the observation error to zero in the effective time.
Drawings
Fig. 1 is a flowchart of a trajectory tracking control method for a quad-rotor unmanned aerial vehicle according to the present disclosure;
FIG. 2 is a graph comparing the effects of the method disclosed in the present invention and other conventional methods.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and detailed description, which will be understood as being illustrative only and not limiting in scope.
As shown in fig. 1, the invention discloses an unmanned aerial vehicle trajectory tracking control method based on functional differentiation and adaptive variable gain, comprising the following steps:
the method comprises the following steps: establishing a four-rotor unmanned aerial vehicle tracking control method model;
(1.1) establishing a four-rotor unmanned aerial vehicle kinematics model:
rotation vector of four rotors under body coordinate system
Roll angle, pitch angle and yaw angle, respectively;
the angular velocity is under the coordinate system of the machine body; position vector of four rotors under body coordinate system
Linear velocities in three directions of
The kinematic model of a quad-rotor drone is represented as:
wherein R is ω The transformation matrix of the attitude change rate and the body rotation angular velocity can be expressed as:
rotating matrix from body coordinate system to ground-fixed coordinate system
Can be expressed as:
(1.2) establishing a four-rotor unmanned aerial vehicle dynamics model:
the attitude dynamics model is established by the Euler equation as follows:
wherein,
a rotational inertia matrix of four rotors;
representing a gyro moment;
representing the moment generated by the propeller on the body axis; x represents a vector cross product operation;
is a disturbing moment.
Force analysis was performed on four rotors as follows from newton's second law:
wherein, K f ＝diag(k x ，k y ，k z ) Is an air resistance coefficient matrix; g = [0,0,g)] T Is gravity; u shape T Is the total pulling force acting on the four motors; d p (t)＝[d x ，d y ，d z ] T As other interference resistance.
Is the tension of the ith motor, U T The tensile force of the four motors in the three axes of x, y and z is shown.
(1.3) modeling uncertainty and external interference by an analysis control method:
defining a system state variable as X 1 ＝[x，y，z] T ，
X 3 ＝[φ，θ，ψ] T ，
Due to external disturbance and model parameter identification errors, the kinetic model is converted into a state space form with lumped disturbance.
Wherein
Is the measured value of the system model parameter,. DELTA.. Cndot. -. Is the uncertain value of the model parameter, B 1 ＝[cosψsinθcosφ+sinψsinφ，sinψsinθsinφ-cosψsinφ，cosθcosφ] T ，∏ 1 ＝diag(J y -J z ，J z -J x ，J x -J y )，∏ 2 ＝diag(-J r Ω r ，-J r Ω r ，0)，
Is a continuous smoothing function. The definition of the lumped perturbation is
(1.4) nonlinear decoupling:
to solve the coupling problem, a position virtual variable V = [ V ] is adopted x ，V y ，V z ] T As follows
A desired euler angle (phi) can be obtained d ，θ d ) And total thrust u T As follows
Step two: designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor;
(2.1) designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor, wherein the differential tracker has the specific form:
wherein σ = p/q, p < q, and p, q are odd numbers, α > 0, γ > 0, R > 0.V (t) is an input signal,
and
which are the original signal and the differential signal of the tracking signal v (t).
(3.1) designing a novel three-order self-adaptive finite time expansion observer, wherein the specific form is as follows:
wherein, the variables defining the extended observer are respectively: control signal Z 1 First derivative Z of the control signal 2 And total interference observation Z 3 . Error variable of observer has e 1 ＝x 1 -Z 1 ，e 2 ＝x 2 -Z 2 ，e 3 ＝D-Z 3 The parameter satisfies 0.5 < lambda 1 ＜1，λ 2 ＝2λ 1 -1，l 1 (t)，l 2 (t)，l 3 (t) as a designed time-varying gain, by the law of adaptivity
Updating, on the premise of satisfying stability, designing L (t) as
Step four: designing nonsingular fast sliding mode controller
(4.1) defining a space state equation of a four-rotor tracking control method:
the system space state equation obtained from equation (6) and equation 7 is:
for the sliding mode controller designed for the position control subsystem, the position error and the speed error are defined as follows
For the design of a sliding mode controller of an attitude control subsystem, the attitude error and the angular velocity error are defined as follows
(4.2) designing a fast nonsingular terminal sliding mode controller:
the fast nonsingular terminal sliding mode surface of the attitude subsystem is designed as
The fast nonsingular terminal sliding mode surface of the position subsystem is designed as
Where b is n Is a normal number, 1 < beta n ＜2，β n+1 ＜α n
Derived from sliding mode functions
Order to
Is obtained from the control law
Step five: the closed loop stability of the trajectory tracking control method proves that the position subsystem X channel after decoupling is taken as an example, and the Lyapunov function is defined as follows:
carry into U X The derivative of equation (21) with respect to time can be written as
The Lyapunov function of the position subsystem can be selected as
Therefore, the stability of the position system is ensured, and the track tracking capability is ensured. The stability for the gesture subsystem proves similar and is not described in detail.
In order to verify the track tracking control performance of the quad-rotor unmanned aerial vehicle disclosed by the invention, the mass of the unmanned aerial vehicle is m =1.65kg, the distance from a rotor to the center of the unmanned aerial vehicle is l =0.225m, and the moment of inertia is [ J ] x J y J z ]＝[0.01782 0.01782 0.03191]kg m 2 The moment of inertia of the motor is J r ＝0.00099kg m 2 The air damping coefficient matrix is [ k ] x k y k z ]＝[0.005567 0.0005567 0.005567]N(m/s) 2 The moment damping coefficient matrix is [ k ] φ k θ k ψ ]＝[0.06579 0.06579 0.06579]Nm (rad/s) 2, external interference d x ＝0.2sin(0.2t)+0.1cos(0.3t)，d y ＝0.4cos(0.5t)+0.2，d z =0.2cos (0.1 t + pi/4) +0.1, compared with a traditional sliding mode steering control assistant steering system, the error is shown in fig. 2, wherein, in the graph, "-. Tangle-solidup" is a tracking curve of traditional active disturbance rejection control, and "-" is a four-rotor tracking curve based on a sigmoid differential tracker and a variable gain observer disclosed by the invention, the specific comparison effect is as follows:
in the traditional method, the root-mean-square errors of tracking control in the x direction, the y direction and the z direction are respectively 0.5441m,0.3506m and 0.9744m; the tracking control root mean square errors in the x, y and z directions of the method provided by the invention are respectively 0.1002m,0.3909m and 0.343434m.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any modifications or equivalent variations made in accordance with the technical spirit of the present invention may fall within the scope of the present invention as claimed.
Claims (4)
1. The unmanned aerial vehicle trajectory tracking control method based on the function differentiation and the adaptive variable gain comprises the following specific steps, and is characterized in that: the method comprises the following steps:
(1) Establishing a four-rotor unmanned aerial vehicle tracking control system model;
(2) Designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor;
in the step (2), designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor comprises the following steps:
(2.1) designing a differential tracker combining an improved Sigmoid function and a sliding mode terminal attractor, wherein the differential tracker comprises the following specific forms:
wherein σ = p/q, p < q, and p, q are odd numbers, α > 0, γ > 0, R > 0, v (t) is an input signal,
and
an original signal and a differential signal which are tracking signals v (t);
(3) Designing a novel three-order self-adaptive variable-gain finite time expansion observer according to a control model;
in the step (3), designing a novel three-order self-adaptive finite time extended observer comprises the following steps:
(3.1) designing a novel three-order self-adaptive finite time expansion observer, wherein the specific form is as follows:
wherein, the variables defining the extended observer are respectively: control signal Z 1 First derivative Z of the control signal 2 And total interference observation Z 3 . Error variable of observer has e 1 ＝x 1 -Z 1 ，e 2 ＝x 2 -Z 2 ，e 3 ＝D-Z 2 The parameter satisfies 0.5 < lambda 1 ＜1，λ 2 ＝2λ 1 -1，l 1 (t)，l 2 (t)，l 3 (t) adaptive law for designed time-varying gain
Updating, on the premise of satisfying stability, designing L (t) as
(4) Designing an active disturbance rejection tracking controller, wherein one part of the active disturbance rejection tracking controller is compensated by an observer, and the other part of the active disturbance rejection tracking controller is designed as a fast sliding mode controller and is used for tracking the positions and postures of four rotors;
(5) And (4) proving the closed loop stability of the whole track tracking control system according to the Lyapunov function.
2. The method of claim 1, wherein the method comprises: in the step (1), the establishment of the quad-rotor unmanned aerial vehicle tracking control system model comprises the following steps:
(1.1) establishing a four-rotor unmanned aerial vehicle kinematics model:
rotation vector of four rotors under body coordinate system
Roll angle, pitch angle and yaw angle, respectively;
the angular velocity is the angular velocity under the body coordinate system; position vector of four rotors under body coordinate system
Linear velocities in three directions of
The kinematic model of a quad-rotor drone is represented as:
wherein R is ω Is a transformation matrix of the attitude change rate and the rotation angular velocity of the body, and is expressed as:
rotation matrix from body coordinate system to earth-fixed coordinate system
Expressed as:
(1.2) establishing a four-rotor unmanned aerial vehicle dynamic model:
the attitude dynamics model is established by the Euler equation as follows:
wherein,
a rotational inertia matrix of four rotors;
representing a gyro moment;
representing the moment generated by the propeller on the body axis; x represents a vector cross product operation;
is a disturbance moment;
force analysis was performed on four rotors as follows from newton's second law:
wherein, K f ＝diag(k x ，k y ，k z ) Is an air resistance coefficient matrix; g = [0, G)] T Is gravity; u shape T Is the total pulling force acting on the four motors; d p (t)＝[d x ，d y ，d z ] T For the purpose of other disturbing resistances, it is,
is the tension of the ith motor, U T The tension of the four motors in the x, y and z axes is adopted;
(1.3) analyzing uncertainty of modeling of a control system and external interference:
defining a system state variable as X 1 ＝[x，y，z] T ，
X 3 ＝[φ，θ，ψ] T ，
Converting the dynamic model into a state space form with lumped disturbance due to external disturbance and model parameter identification errors;
wherein
Is the measured value of the system model parameter, Δ (-) is the uncertain value of the model parameter, B 1 ＝[cosψsinθcosφ+sinψsinφ，sinψsinθsinφ-cosψsinφ，cosθcosφ] T ,Π 1 ＝diag(J y -J z ，J z -J x ，J x -J y ),Π 2 ＝diag(-J r Ω r ，-J r Ω r ，0),
Is a continuous smooth function, and the lumped disturbance is defined as
(1.4) nonlinear decoupling:
to solve the coupling problem, a position virtual variable V = [ V ] is adopted x ，V y ，V z ] T As follows
The desired Euler angle (phi) can be obtained d ，θ d ) And total thrust u T As follows
3. The unmanned aerial vehicle trajectory tracking control method based on functional differentiation and adaptive variable gain according to claim 2, wherein in the step (4), designing a nonsingular fast sliding mode controller comprises the following steps:
(4.1) defining a space state equation of the four-rotor tracking control system:
the system space state equation obtained by the two formulas in the step (1.3) is as follows:
for the design of sliding mode controller for position control subsystem, the position error and speed error are defined as follows
For the design of a sliding mode controller of an attitude control subsystem, the attitude error and the angular velocity error are defined as follows
(4.2) designing a fast nonsingular terminal sliding mode controller:
the fast nonsingular terminal sliding mode surface of the attitude subsystem is designed as
The rapid nonsingular terminal sliding mode surface of the position subsystem is designed as
Where b is n Is a normal number, 1 < beta n ＜2，β n+1 ＜α n
Derived from sliding mode functions
Order to
Is obtained from the control law
4. The method for trajectory tracking control of unmanned aerial vehicle based on functional differentiation and adaptive variable gain according to claim 1, wherein in step (5), the closed-loop stability certification of the trajectory tracking control system comprises the following steps:
(5.1) taking the position subsystem X channel after decoupling as an example, the Lyapunov function is defined as follows:
carry into U X The derivative of equation (21) with respect to time is written as
The Lyapunov function of the location subsystem is selected as
Therefore, the stability of the position system is ensured, and the track tracking capability is ensured. The stability for the gesture subsystem proves similar and is not described in detail.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116300668A (en) * | 2023-05-26 | 2023-06-23 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
| CN116880165A (en) * | 2023-05-30 | 2023-10-13 | 济宁医学院 | Model reference self-adaptive finite time control method of non-contact suspension grabbing system |
| CN116909314A (en) * | 2023-08-14 | 2023-10-20 | 南通大学 | Track tracking control method of fixed-wing unmanned aerial vehicle under wind disturbance |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN116300668A (en) * | 2023-05-26 | 2023-06-23 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
| CN116300668B (en) * | 2023-05-26 | 2023-08-08 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
| CN116880165A (en) * | 2023-05-30 | 2023-10-13 | 济宁医学院 | Model reference self-adaptive finite time control method of non-contact suspension grabbing system |
| CN116880165B (en) * | 2023-05-30 | 2024-01-30 | 济宁医学院 | Model reference self-adaptive finite time control method of non-contact suspension grabbing system |
| CN116909314A (en) * | 2023-08-14 | 2023-10-20 | 南通大学 | Track tracking control method of fixed-wing unmanned aerial vehicle under wind disturbance |
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