A method, device and system for finite-time anti-disturbance control of a quadrotor aircraft

Abstract

The present invention discloses a finite-time self-disturbance rejection control method, device and system for a quadrotor aircraft, and relates to the field of aircraft control technology. First, an attitude dynamics model of a quadrotor aircraft with multi-source disturbances is established. Secondly, a reduced-order generalized parameter estimation observer with finite-time convergence characteristics is designed. Based on the parameter estimation scheme, the state observation problem is converted into a parameter estimation problem in combination with dynamic regression extension and hybrid technology. Then, a linear regression model is established, and a gradient descent observer is designed to estimate unmeasurable states and unknown disturbances online. Finally, the estimated quantity is introduced into a non-singular fast terminal sliding mode control law to obtain a finite-time controller without speed sensing. The present invention can still ensure that the output state accurately tracks a given value without the need for a speed sensor, and can suppress the influence of multi-source disturbances on the system, significantly reducing the hardware cost and failure rate of the quadrotor drone system, and improving the fault tolerance of the system.

Description

Technical Field

[0001] The present invention relates to a finite-time anti-disturbance control method, device and system for a quadrotor aircraft, belonging to the technical field of aircraft control. Background Art

[0002] A quadrotor is an aircraft that can take off and land vertically. It is widely used in military and civilian fields such as environmental detection, agricultural irrigation, and festival performances due to its advantages such as simple control and portability. A quadrotor is a rigid body system with six degrees of freedom and four control inputs, so it is a typical underactuated system, and there are some mutually coupled nonlinear terms in its various sub-channels. All these make the quadrotor extremely susceptible to various external environmental interferences during actual application. Therefore, achieving stable and accurate trajectory tracking control of quadrotors has become a research hotspot in recent years.

[0003] At present, there has been in-depth research on the trajectory tracking control of quadrotor aircraft. Some advanced control methods such as PID control, feedback linearization method, neural network control, etc. can overcome the instability problems caused by disturbances or unknown disturbances in the UAV system to a certain extent, but these methods require full state information, that is, when designing the controller, all state information must be known, which requires installing enough sensors in the system; but too many sensors not only increase the complexity and overall cost of the system, but also endanger the stability of the control system; for the current quadrotor aircraft system with multi-source disturbances, no relevant research results on speed sensorless control have been reported, especially the existing research results have failed to solve the problem of simultaneous online estimation of the linear velocity, angular velocity and unknown multi-source disturbances of this system. Summary of the invention

[0004] The purpose of the present invention is to provide a finite-time auto-disturbance rejection control method, device and system for a quadrotor aircraft. Under the framework of traditional auto-disturbance rejection, non-singular fast terminal sliding mode control and dynamic regression extension and hybrid technology are combined to realize the state observation of the quadrotor aircraft system speed and unknown disturbances.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions.

[0006] In a first aspect, the present invention provides a finite-time anti-disturbance control method for a quadrotor aircraft, comprising:

[0007] A quadrotor system model is established in the presence of multi-source disturbances; a corresponding tracking differentiator is designed based on the auto-disturbance rejection theory; according to the quadrotor system model, its state space model is obtained, so as to design a linear regression equation and obtain a gradient descent observer; the system speed and unknown disturbances are reconstructed by the gradient descent observer to obtain the reconstructed system speed and unknown disturbances; a non-singular fast terminal sliding mode controller is designed according to the quadrotor system model and the tracking differentiator; the reconstructed system speed and unknown disturbances are substituted into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and the finite-time auto-disturbance rejection control of the quadrotor system is realized according to the speed sensorless controller.

[0008] Furthermore, the quadrotor system model in the presence of multi-source disturbances includes:

[0009] ,

[0010] in, , , They are the three position sub-channels of the aircraft in the reference system; It is the rolling angle attitude sub-channel of the aircraft in the reference system; It is the pitch angle attitude sub-channel of the aircraft in the reference system; It is the yaw angle attitude sub-channel of the aircraft in the reference system; is the mass of the aircraft; is the acceleration due to gravity; They are , ,z, , , The first derivative of ; They are , ,z, , , The second-order derivative of The aircraft is in the reference frame , , Three-axis moment of inertia; , , is the translational resistance coefficient of the sub-channel at the corresponding position; , , is the air friction coefficient of the corresponding attitude sub-channel; , , , , , is the unknown disturbance of the corresponding subchannel; is the position system control rate of the quadrotor; yes The control rate of the attitude sub-channel, yes The control rate of the attitude sub-channel, yes Control rate of attitude subchannel; is the coupling term of the roll angle subchannel, is the coupling term of the pitch angle sub-channel, is the coupling term of the yaw angle sub-channel.

[0011] Furthermore, the discrete form of the tracking differentiator is:

[0012] ,

[0013] in: is the input reference signal of each sub-channel, Pick , , , , , One of the six subchannels of a quadrotor; for The tracking signal, for The first-order differential signal of for The tracking signal, for The second-order differential signal of They are The first derivative of is the speed factor of the first tracking differentiator, is the speed factor of the second tracking differentiator, is the filtering factor, is the fastest control comprehensive function;

[0014] in, The algorithm formula is as follows:

[0015] ,

[0016] in, represents the sampling step of the system, represents the speed factor of the system, , , , , , , All are intermediate variables in the design process of differential tracker.

[0017] Furthermore, the state space model of the quadrotor aircraft is obtained according to the system model of the quadrotor aircraft, so as to design a linear regression equation and obtain a gradient descent observer, which specifically includes:

[0018] Convert the quadrotor system model into a quadrotor system state space model:

[0019] ,

[0020] in, is the coordinate state variable of the quadrotor system, is the velocity state variable of the quadrotor system, They are , The first derivative of ; For The first constant of interest, For The relevant second constant, For Unrelated variables, is a constant, , is the second parameter to be estimated;

[0021] Dynamically expand the state space model of the above quadrotor system:

[0022] { g ˙ = A x x + b u X ˙ Axe = A x X Axe , X Axe ( 0 ) = 1 m ˙ x =− l m x + l [ X Axe A y A y or 2 ∫ 0 t X Axe dt ] , m x ( 0 ) = [ 0 0 ] T oh ˙ =− I + l ( l x 1 + A y x ) , oh ( 0 ) = l x 1 ( 0 ) ,

[0023] in, for The reconstruction state, is the state transfer matrix; is the first intermediate variable, is the second intermediate variable, is the original observer gain, , , , They are , , , The initial value of For time, They are , , , The first derivative of ;

[0024] The designed linear regression equation is:

[0025] ,

[0026] in, is a measurable variable, , is the unknown parameter vector, or = [ or 1 or 2 ] T ,in, is the first parameter to be estimated;

[0027] Then the gradient descent observer is:

[0028] { m e = [ α 1 s + β 1 or α 2 s + β 2 or ] q e = [ α 1 s + β 1 q α 2 s + β 2 q ] f ˙ =− l f + l m e T q e Oh ˙ =− l Oh + l m e T m e or ^ ˙ =− c det ( Oh ) ( det ( Oh ) or ^ − adj ( Oh ) g ) u ˙ =− c [ det ( Oh ) ] 2 u , u ( 0 ) = 1 ,

[0029] in, , , , are the dynamic expansion, , , , They are , , , The first derivative of , , , are the filter parameters, is the gradient descent observer gain, for The determinant of for The adjoint matrix of is the third intermediate variable, for The initial value of is the differential operator, is the output of the gradient descent observer, or ^ = [ or ^ 1 or ^ 2 ] T ,in, , for , The estimated value of .

[0030] Furthermore, the reconstructed expressions of the system speed and unknown disturbance are:

[0031] ,

[0032] in, is the unknown disturbance of the subchannel, i is 1, 2, 3, 4, 5, 6; , , , Respectively , , , The estimated value of , They are , The observed value of , They are , The initial value of .

[0033] Furthermore, when the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0034] When the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0035] When the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0036] in, ,

[0037] When the state space model of the quadrotor system is the roll angle observer of the attitude system, , , , , is the control input of the roll angle, ;

[0038] When the state space model of the quadrotor system is the pitch angle observer of the attitude system, , , , , is the control input of the roll angle, ;

[0039] When the state space model of the quadrotor system is the yaw angle observer of the attitude system, , , , , is the control input of the roll angle, .

[0040] Further, the non-singular fast terminal sliding mode controller is designed according to the quadrotor system model and the tracking differentiator; the reconstructed system speed and unknown disturbance are substituted into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and the finite-time auto-disturbance rejection control of the quadrotor system is realized according to the speed sensorless controller, specifically including:

[0041] Based on the quadrotor system model and tracking differentiator, the sliding mode function of the position system controller of the quadrotor system is constructed as:

[0042] ,

[0043] in, , , For three position sub-channels The corresponding sliding surface function is, , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , They are , , The expected value of , , Expected value , , The error from the actual value, , , for , , The first derivative of

[0044] but , , The first derivative of , , They are:

[0045] ,

[0046] in: ,

[0047] , , for , , The second derivative of

[0048] The selected index approach rate is as follows:

[0049] { s ˙ 1 = b x h x 2 | e ˙ x | h x 2 − 1 [ − k x 1 s 1 − k x 2 sign ( s 1 ) ] ， k x 1 > 0 , k x 2 > 0 s ˙ 2 = b y h y 2 | e ˙ y | h y 2 − 1 [ − k y 1 s 2 − k y 2 sign ( s 2 ) ] ， k y 1 > 0 , k y 2 > 0 s ˙ 3 = b z h z 2 | e ˙ z | h z 2 − 1 [ − k z 1 s 3 − k z 2 sign ( s 3 ) ] ， k z 1 > 0 , k z 2 > 0 ,

[0050] in: , , are the controller gains respectively, , , is the approach rate coefficient;

[0051] Substituting the exponential convergence rate expression selected above into , , Thus, the non-singular fast terminal sliding mode controller of the position system can be solved , , for:

[0052] ,

[0053] in: , , is the virtual control quantity of the position system, They are The first derivative of They are , , The second derivative of

[0054] Substitute the velocity and unknown disturbance of the reconstructed quadrotor system position system into the non-singular fast terminal sliding mode controller of the position system , , , the speed sensorless controller of the position system is obtained as:

[0055] ,

[0056] in: , , , , , , , , , , They are , , , , , , , , , , , An estimated value of

[0057] According to the speed sensorless controller of the position system, the virtual control input of the system is inversely solved to obtain the position system controller:

[0058] ,

[0059] in: , , They are , , Expected value;

[0060] The attitude system controller is designed as:

[0061] { u ^ 2 = I x [ 1 b ϕ h ϕ 2 sign ( e ˙ ^ ϕ ) | e ˙ ^ ϕ | 2 − h ϕ 2 ( 1 + a ϕ h ϕ 1 | e ϕ | h x 1 − 1 ) + ϕ ¨ d + K 4 I x ϕ ˙ ^ − f ^ ϕ − d ^ 4 + k ϕ 1 s ^ 4 + k ϕ 2 sign ( s ^ 4 ) ] u ^ 3 = I y [ 1 b i h i 2 sign ( e ˙ ^ i ) | e ˙ ^ i | 2 − h i 2 ( 1 + a i h i 1 | e i | h i 1 − 1 ) + i ¨ d + K 5 I y i ˙ ^ − f ^ i − d ^ 5 + k i 1 s ^ 5 + k i 2 sign ( s ^ 5 ) ] u ^ 4 = I z [ 1 b ψ h ψ 2 sign ( e ˙ ^ ψ ) | e ˙ ^ ψ | 2 − h ψ 2 ( 1 + a ψ h ψ 1 | e ψ | h ψ 1 − 1 ) + ψ ¨ d + K 6 I z ψ ˙ ^ − f ^ ψ − d ^ 6 + k ψ 1 s ^ 6 + k ψ 2 sign ( s ^ 6 ) ] ,

[0062] in, ,

[0063] in: , , is the intermediate variable, , , Expected value , , The error from the actual value, for The second-order derivative of , , is the sliding surface function corresponding to the three attitude sub-channels, , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , is the controller gain, , , is the approach rate coefficient, , , , , , , , , , , , , , , , , , for , , , , , , , , , , , , , , , , , The estimated value of .

[0064] In a second aspect, the present invention provides a finite-time anti-disturbance control device for a quadrotor aircraft, comprising:

[0065] Establish a module for modeling a quadrotor system in the presence of multiple sources of disturbance;

[0066] A design module is used to design the corresponding tracking differentiator based on the auto-disturbance rejection theory;

[0067] The reconstruction module is used to obtain the state space model of the quadrotor aircraft according to the system model, so as to design the linear regression equation and obtain the gradient descent observer; the system speed and unknown disturbance are reconstructed by the gradient descent observer to obtain the reconstructed system speed and unknown disturbance;

[0068] A control module is used to design a non-singular fast terminal sliding mode controller according to the quadrotor system model and the tracking differentiator; substitute the reconstructed system speed and unknown disturbance into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and implement finite-time anti-disturbance control of the quadrotor system according to the speed sensorless controller.

[0069] In a third aspect, the present invention provides a finite-time anti-disturbance control system for a quadrotor aircraft, comprising:

[0070] Memory, for storing computer programs / instructions;

[0071] A processor is used to execute the computer program / instructions to implement the steps of the above-mentioned four-rotor aircraft finite-time anti-disturbance control method.

[0072] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the above-mentioned finite-time anti-disturbance control method for a quadrotor aircraft.

[0073] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: 1. In view of the problem that the existing methods are limited in that all state quantity information is required to realize the control scheme, the present invention establishes a quadrotor system model of a quadrotor with multi-source disturbances, and proposes a construction method based on a generalized parameter observer. Based on the parameter estimation scheme, combined with dynamic regression expansion and hybrid technology, the state observation problem is converted into a parameter estimation problem, and then a linear regression model is established, and a gradient descent observer is designed to online estimate unmeasurable states and unknown disturbances; finally, the estimated quantity is introduced into a non-singular fast terminal sliding mode controller to obtain a speed-sensing finite-time controller without speed sensing, thereby avoiding the quadrotor system from using too many sensors, reducing the system failure rate, and improving the system fault tolerance, providing advanced technology for speed-sensing-free control of quadrotor systems, and having strong practical value.

[0074] 2. Under the framework of traditional ADRC, the present invention designs a new non-singular fast terminal sliding mode control algorithm. Due to the introduction of the fast non-singular terminal sliding mode surface, the quadrotor trajectory tracking error is guaranteed to have a faster convergence speed than other traditional control algorithms. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 1 is a flow chart of a finite-time anti-disturbance control method for a quadrotor aircraft according to an embodiment of the present invention;

[0076] Figure 2 It is a control block diagram of the finite time active disturbance rejection control method designed in the example of the present invention;

[0077] Figure 3 In the embodiment of the present invention Schematic diagram of error simulation of the observer's observation state when there are multiple sources of disturbance in the channel;

[0078] Figure 4 In the embodiment of the present invention Schematic diagram of error simulation of the observer's observation state when there are multiple sources of disturbance in the channel;

[0079] Figure 5 is a schematic diagram of an output simulation of a quadrotor position system in an embodiment of the present invention;

[0080] Figure 6 Schematic diagram of output simulation of the attitude system of the quadrotor aircraft in an embodiment of the present invention. DETAILED DESCRIPTION

[0081] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0082] The term "and / or" is only a description of the association relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " generally indicates that the related objects are in an "or" relationship.

[0083] Example 1

[0084] like Figure 1 and Figure 2 As shown, this embodiment provides a finite-time anti-disturbance control method for a quadrotor aircraft, comprising:

[0085] Step 1: Establish a quadrotor system model with multi-source disturbances as follows:

[0086] ,

[0087] in, , , They are the three position sub-channels of the aircraft in the reference system; It is the rolling angle attitude sub-channel of the aircraft in the reference system; It is the pitch angle attitude sub-channel of the aircraft in the reference system; It is the yaw angle attitude sub-channel of the aircraft in the reference system; is the mass of the aircraft; is the acceleration due to gravity; They are , ,z, , , The first derivative of ; They are , ,z, , , The second-order derivative of The aircraft is in the reference frame , , Three-axis moment of inertia; , , is the translational resistance coefficient of the sub-channel at the corresponding position; , , is the air friction coefficient of the corresponding attitude sub-channel; , , , , , is the unknown disturbance of the corresponding subchannel; is the position system control rate of the quadrotor; yes The control rate of the attitude sub-channel, yes The control rate of the attitude sub-channel, yes Control rate of attitude subchannel; is the coupling term of the roll angle subchannel, is the coupling term of the pitch angle sub-channel, is the coupling term of the yaw angle sub-channel.

[0088] Step 2: Design a corresponding tracking differentiator based on the auto-disturbance rejection theory. The discrete form of the tracking differentiator is:

[0089] ,

[0090] in: is the input reference signal of each sub-channel, Pick , , , , , One of the six subchannels of a quadrotor; for The tracking signal, for The first-order differential signal of for The tracking signal, for The second-order differential signal of They are The first derivative of is the speed factor of the first tracking differentiator, is the speed factor of the second tracking differentiator, is the filtering factor, is the fastest control comprehensive function;

[0091] in, The algorithm formula is as follows:

[0092] ,

[0093] in, represents the sampling step of the system, represents the speed factor of the system, , , , , , , All are intermediate variables in the design process of differential tracker.

[0094] Step 3: According to the quadrotor system model, obtain its state space model, so as to design the linear regression equation and obtain the gradient descent observer; reconstruct the system speed and unknown disturbance through the gradient descent observer to obtain the reconstructed system speed and unknown disturbance. The specific process is as follows:

[0095] The method of obtaining the state space model of the quadrotor aircraft system based on the quadrotor aircraft system model, thereby designing a linear regression equation and obtaining a gradient descent observer specifically includes:

[0096] Convert the quadrotor system model into a quadrotor system state space model:

[0097] ,

[0098] in, is the coordinate state variable of the quadrotor system, is the velocity state variable of the quadrotor system, They are , The first derivative of ; For The first constant of interest, For The relevant second constant, For Unrelated variables, is a constant, , is the second parameter to be estimated;

[0099] Dynamically expand the state space model of the above quadrotor system:

[0100] { g ˙ = A x x + b u X ˙ Axe = A x X Axe , X Axe ( 0 ) = 1 m ˙ x =− l m x + l [ X Axe A y A y or 2 ∫ 0 t X Axe dt ] , m x ( 0 ) = [ 0 0 ] T oh ˙ =− I + l ( l x 1 + A y x ) , oh ( 0 ) = l x 1 ( 0 ) ,

[0101] in, for The reconstruction state, is the state transfer matrix; is the first intermediate variable, is the second intermediate variable, is the original observer gain, , , , They are , , , The initial value of For time, They are , , , The first derivative of ;

[0102] The designed linear regression equation is:

[0103] ,

[0104] in, is a measurable variable, , is the unknown parameter vector, or = [ or 1 or 2 ] T ,in, is the first parameter to be estimated;

[0105] Then the gradient descent observer is:

[0106] { m e = [ α 1 s + β 1 or α 2 s + β 2 or ] q e = [ α 1 s + β 1 q α 2 s + β 2 q ] f ˙ =− l f + l m e T q e Oh ˙ =− l Oh + l m e T m e or ^ ˙ =− c det ( Oh ) ( det ( Oh ) or ^ − adj ( Oh ) g ) u ˙ =− c [ det ( Oh ) ] 2 u , u ( 0 ) = 1 ,

[0107] in, , , , are the dynamic expansion, , , , They are , , , The first derivative of , , , are the filter parameters, is the gradient descent observer gain, for The determinant of for The adjoint matrix of is the third intermediate variable, for The initial value of is the differential operator, is the output of the gradient descent observer, or ^ = [ or ^ 1 or ^ 2 ] T ,in, , for , The estimated value of .

[0108] The reconstructed expressions of the system speed and unknown disturbance are:

[0109] ,

[0110] in, is the unknown disturbance of the subchannel, i is 1, 2, 3, 4, 5, 6; , , , Respectively , , , The estimated value of , They are , The observed value of , They are , The initial value of .

[0111] When the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0112] When the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0113] When the state space model of the quadrotor system is the position system When the subchannel observer is , , , , for The control input amount of the sub-channel, ;

[0114] in, ,

[0115] When the state space model of the quadrotor system is the roll angle observer of the attitude system, , , , , is the control input of the roll angle, ;

[0116] When the state space model of the quadrotor system is the pitch angle observer of the attitude system, , , , , is the control input of the roll angle, ;

[0117] When the state space model of the quadrotor system is the yaw angle observer of the attitude system, , , , , is the control input of the roll angle, .

[0118] Step 4: Design a non-singular fast terminal sliding mode controller according to the quadrotor system model and the tracking differentiator; substitute the reconstructed system speed and unknown disturbance into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; implement the finite-time active disturbance rejection control of the quadrotor system according to the speed sensorless controller, which specifically includes the following processes:

[0119] Based on the quadrotor system model and tracking differentiator, the sliding mode function of the position system controller of the quadrotor system is constructed as:

[0120] ,

[0121] in, , , For three position sub-channels The corresponding sliding surface function is, , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , They are , , The expected value of , , Expected value , , The error from the actual value, , , for , , The first derivative of

[0122] but , , The first derivative of , , They are:

[0123] ,

[0124] in: ,

[0125] , , for , , The second derivative of

[0126] The selected index approach rate is as follows:

[0127] { s ˙ 1 = b x h x 2 | e ˙ x | h x 2 − 1 [ − k x 1 s 1 − k x 2 sign ( s 1 ) ] ， k x 1 > 0 , k x 2 > 0 s ˙ 2 = b y h y 2 | e ˙ y | h y 2 − 1 [ − k y 1 s 2 − k y 2 sign ( s 2 ) ] ， k y 1 > 0 , k y 2 > 0 s ˙ 3 = b z h z 2 | e ˙ z | h z 2 − 1 [ − k z 1 s 3 − k z 2 sign ( s 3 ) ] ， k z 1 > 0 , k z 2 > 0 ,

[0128] in: , , are the controller gains respectively, , , is the approach rate coefficient;

[0129] Substituting the exponential convergence rate expression selected above into , , Thus, the non-singular fast terminal sliding mode controller of the position system can be solved , , for:

[0130] ,

[0131] in: , , is the virtual control quantity of the position system, They are The first derivative of They are , , The second derivative of

[0132] Substitute the velocity and unknown disturbance of the reconstructed quadrotor system position system into the non-singular fast terminal sliding mode controller of the position system , , , the speed sensorless controller of the position system is obtained as:

[0133] ,

[0134] in: , , , , , , , , , , They are , , , , , , , , , , , An estimated value of

[0135] According to the speed sensorless controller of the position system, the virtual control input of the system is inversely solved to obtain the position system controller:

[0136] ,

[0137] in: , , They are , , Expected value;

[0138] The attitude system controller is designed as:

[0139] { u ^ 2 = I x [ 1 b ϕ h ϕ 2 sign ( e ˙ ^ ϕ ) | e ˙ ^ ϕ | 2 − h ϕ 2 ( 1 + a ϕ h ϕ 1 | e ϕ | h x 1 − 1 ) + ϕ ¨ d + K 4 I x ϕ ˙ ^ − f ^ ϕ − d ^ 4 + k ϕ 1 s ^ 4 + k ϕ 2 sign ( s ^ 4 ) ] u ^ 3 = I y [ 1 b i h i 2 sign ( e ˙ ^ i ) | e ˙ ^ i | 2 − h i 2 ( 1 + a i h i 1 | e i | h i 1 − 1 ) + i ¨ d + K 5 I y i ˙ ^ − f ^ i − d ^ 5 + k i 1 s ^ 5 + k i 2 sign ( s ^ 5 ) ] u ^ 4 = I z [ 1 b ψ h ψ 2 sign ( e ˙ ^ ψ ) | e ˙ ^ ψ | 2 − h ψ 2 ( 1 + a ψ h ψ 1 | e ψ | h ψ 1 − 1 ) + ψ ¨ d + K 6 I z ψ ˙ ^ − f ^ ψ − d ^ 6 + k ψ 1 s ^ 6 + k ψ 2 sign ( s ^ 6 ) ] ,

[0140] in, ,

[0141] in: , , is the intermediate variable, , , Expected value , , The error from the actual value, for The second-order derivative of , , is the sliding surface function corresponding to the three attitude sub-channels, , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , , for The corresponding sliding surface parameters are: , , is the controller gain, , , is the approach rate coefficient, , , , , , , , , , , , , , , , , , for , , , , , , , , , , , , , , , , , The estimated value of .

[0142] See also Figure 3 to Figure 6 In the MATLAB2022 environment, a simulation verification test is carried out on a finite time anti-disturbance control method designed by the present invention for a quadrotor aircraft:

[0143] First, build a simulation module in MATLAB to conduct the entire quadrotor simulation experiment. The relevant model parameters used by the quadrotor are: , , , , , , ; Set the initial position state of the system to: , the initial state of the posture is set to: ; The system disturbance is set to: , The desired trajectory of the aircraft is set to: , , , .

[0144] In the present invention, the parameters of the non-singular fast terminal sliding mode controller designed based on the observer have a direct impact on the performance of the flight control system; the larger the parameter value, the stronger the control ability, but it will also cause a larger control error. If the parameter is too small, the system is prone to oscillation; combined with the control ability and control performance requirements of the quadrotor actuator, plus the results of the previous theoretical derivation, the reasonable design of the observer parameters is: , , , ; The controller parameters are: , , , , , , , , , , ; The tracking differentiators of the six subsystems have the same parameters: , , .

[0145] Combination Figure 3 and Figure 4 , it can be seen that the observer can observe the speed and unknown disturbance of the quadrotor system in a very short time, which can reflect that the observer designed by the present invention has good performance;

[0146] Combination Figure 5 and Figure 6 , it can be seen that in the presence of disturbances, the actual trajectory can still quickly track the expected trajectory, and the tracking effect is good. This shows that the controller designed by the present invention has a good control effect.

[0147] This implementation process applies the reduced-order generalized parameter estimation observer and non-singular fast speed sliding mode control technology to the control of the quadrotor system. The verification results show that this method has excellent control performance. When the system speed and disturbance cannot be measured, it can not only make the output trajectory quickly track the desired trajectory, but also well suppress the influence of external interference on the system, which significantly improves the stability and reliability of the quadrotor system. It should be pointed out that since no speed sensor is required, the system's fault tolerance is improved and the failure rate is reduced.

[0148] Example 2

[0149] Based on the same inventive concept as that of Example 1, this embodiment provides a finite-time anti-disturbance control device for a quadrotor aircraft, comprising:

[0150] Establish a module for modeling a quadrotor system in the presence of multiple sources of disturbance;

[0151] A design module is used to design the corresponding tracking differentiator based on the auto-disturbance rejection theory;

[0152] The reconstruction module is used to obtain the state space model of the quadrotor aircraft according to the system model, so as to design the linear regression equation and obtain the gradient descent observer; the system speed and unknown disturbance are reconstructed by the gradient descent observer to obtain the reconstructed system speed and unknown disturbance;

[0153] A control module is used to design a non-singular fast terminal sliding mode controller according to the quadrotor system model and the tracking differentiator; substitute the reconstructed system speed and unknown disturbance into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and implement finite-time anti-disturbance control of the quadrotor system according to the speed sensorless controller.

[0154] Example 3

[0155] This embodiment provides a finite-time anti-disturbance control system for a quadrotor aircraft, comprising:

[0156] Memory, for storing computer programs / instructions;

[0157] A processor is used to execute the above-mentioned computer program / instructions to implement the steps of the above-mentioned four-rotor aircraft finite-time anti-disturbance control method.

[0158] Example 4

[0159] This embodiment provides a computer-readable storage medium having a computer program / instruction stored thereon. When the computer program / instruction is executed by a processor, the steps of the above-mentioned finite-time anti-disturbance control method for a quadrotor aircraft are implemented.

[0160] In view of the problem that existing methods are limited in that all state quantity information is required to implement the control scheme, the present invention proposes a construction method based on a generalized parameter observer, thereby avoiding the use of too many sensors in the quadrotor system, reducing the system failure rate, and improving the system fault tolerance. It provides advanced technology for speed sensorless control of quadrotor systems and has strong practical value.

[0161] In the framework of traditional ADRC, this paper designs a new non-singular fast terminal sliding mode control algorithm. Due to the introduction of the fast non-singular terminal sliding mode surface, the quadrotor trajectory tracking error is guaranteed to have a faster convergence speed than other traditional control algorithms.

[0162] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0163] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure one A process or multiple processes and / or boxes Figure one A device that provides the functions specified in a block or multiple blocks.

[0164] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure one A process or multiple processes and / or boxes Figure one A function specified in one or more boxes.

[0165] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure one A process or multiple processes and / or boxes Figure one The steps for the functions specified in one or more boxes.

[0166] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. A finite-time anti-disturbance control method for a quadrotor aircraft, characterized in that: include: Establish a quadrotor system model in the presence of multiple sources of disturbance; Design the corresponding tracking differentiator based on the auto-disturbance rejection theory; According to the quadrotor system model, its state space model is obtained, so as to design a linear regression equation and obtain a gradient descent observer; the system speed and unknown disturbance are reconstructed by the gradient descent observer to obtain the reconstructed system speed and unknown disturbance; A non-singular fast terminal sliding mode controller is designed according to the quadrotor system model and the tracking differentiator; the reconstructed system speed and unknown disturbance are substituted into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and a finite-time auto-disturbance rejection control of the quadrotor system is realized according to the speed sensorless controller; The discrete form of the tracking differentiator is: Among them: A d is the input reference signal of each sub-channel, A d Take one of the six sub-channels of the quadrotor aircraft: x, y, z, φ, θ, ψ; v A1 A d The tracking signal, v A2 v A1 The first-order differential signal, v A3 v A2 The tracking signal, v A4 v A1 The second-order differential signal of They are v A1 、v A2 、v A3 、v A4 The first derivative of A1 is the speed factor of the first tracking differentiator, r A2 is the speed factor of the second tracking differentiator, h0 is the filter factor, and fhan(·) is the fastest control synthesis function; Among them, the fhan(·) algorithm formula is as follows: Among them, h represents the sampling step of the system, r represents the speed factor of the system, d, d0, y1, f1, f2, a0, a are all intermediate variables in the design process of the differential tracker; The method of obtaining the state space model of the quadrotor aircraft system based on the quadrotor aircraft system model, thereby designing a linear regression equation and obtaining a gradient descent observer specifically includes: Convert the quadrotor system model into a quadrotor system state space model: Among them, x1 is the coordinate state variable of the quadrotor system, x2 is the speed state variable of the quadrotor system, are the first-order derivatives of x1 and x2 respectively; A x is the first constant related to x2, A y is the second constant related to x2, b u is a variable unrelated to x2, f x is a constant, f x =1, η2 is the second parameter to be estimated; Dynamically expand the state space model of the above quadrotor system: Among them, ξ is the reconstructed state of x2, X Ax is the state transfer matrix; m x is the first intermediate variable, ω is the second intermediate variable, λ is the original observer gain, X AX (0), m x (0), ω(0), and x1(0) are respectively Ax 、m x , ω, the initial value of x1, t is the time, are ξ, X Ax 、m x , the first derivative of ω; The designed linear regression equation is: q=m x T or, Among them, q is the measurable variable, q=λx1-ω, η is the unknown parameter vector, η=[η1η2] T , where η1 is the first parameter to be estimated; Then the gradient descent observer is: Among them, m e ,q e , f, Ω are the dynamic expansion amounts, They are f, Ω, The first-order derivative of υ, α1, β1, α2, β2 are filter parameters, γ is the gradient descent observer gain, det(Ω) is the determinant of Ω, adj(Ω) is the adjoint matrix of Ω, υ is the third intermediate variable, υ(0) is the initial value of υ, s is the differential operator, is the output of the gradient descent observer, in, are the estimated values ​​of η1 and η2; The reconstructed expressions of the system speed and unknown disturbance are: Among them, d i is the unknown disturbance of the subchannel, i is 1, 2, 3, 4, 5, 6; Respectively represent x2, d i , η2, η1, are the observed values ​​of η1 and η2 respectively, are the initial values ​​of η1 and η2 respectively; The method of designing a non-singular fast terminal sliding mode controller according to the quadrotor system model and the tracking differentiator; substituting the reconstructed system speed and the unknown disturbance into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and implementing the finite-time anti-disturbance control of the quadrotor system according to the speed sensorless controller specifically includes: Based on the quadrotor system model and tracking differentiator, the sliding mode function of the position system controller of the quadrotor system is constructed as: Among them, s1, s2, and s3 are the sliding surface functions corresponding to the three position sub-channels x, y, and z, and a x 、b x 、h x1 、h x2 is the sliding surface parameter corresponding to x, a y 、b y 、h y1 、h y2 is the sliding surface parameter corresponding to y, a z 、b z 、h z1 、h z2 is the sliding surface parameter corresponding to z, x d ,y d 、z d are the expected values ​​of x, y, and z respectively, and e x 、e y 、e z The expected values ​​x d ,y d 、z d The error from the actual value, for e x 、e y 、e z The first derivative of Then the first-order derivatives of s1, s2, and s3 are They are: in: for e x 、e y 、e z The second derivative of The selected index approach rate is as follows: Where: k x1 , k y1 , k z1 are the controller gains, k x2 , k y2 , k z2 is the approach rate coefficient; Substituting the exponential convergence rate expression selected above into Thus, the non-singular fast terminal sliding mode controller u of the position system can be solved x 、u y 、u z for: Where: u x 、u y 、u z is the virtual control quantity of the position system, are the first-order derivatives of x, y, and z, respectively, x d ,y d 、z d The second derivative of Substitute the velocity and unknown disturbance of the reconstructed quadrotor system position system into the non-singular fast terminal sliding mode controller u of the position system x 、u y 、u z , the speed sensorless controller of the position system is obtained as: in: u x 、u y 、u z , Estimated values ​​of d1, d2, and d3; According to the speed sensorless controller of the position system, the virtual control input of the system is inversely solved to obtain the position system controller: Where: φ d ,θ d , d are the expected values ​​of φ, θ, and ψ respectively; The attitude system controller is designed as: in, Where: f φ 、f θ 、f ψ is the intermediate variable, e φ 、e θ 、e ψ is the expected value φ d ,θ d , d The error from the actual value, is φ d ,θ d , d The second-order derivative of , s4, s5, s6 are the sliding surface functions corresponding to the three attitude sub-channels, a φ 、b φ 、h φ1 、h φ2 is the sliding surface parameter corresponding to φ, a θ 、b θ 、h θ1 、h θ2 is the sliding surface parameter corresponding to θ, a ψ 、b ψ 、h ψ1 、h ψ2 is the sliding surface parameter corresponding to ψ, k φ1 , k θ1 , k ψ1 is the controller gain, k φ2 , k θ2 , k ψ2 is the approach rate coefficient, for u2, u3, u4, d4, d5, d6, s1, s2, s3, f φ 、f θ 、f ψ The estimated value of .

2. The finite-time anti-disturbance control method for a quadrotor aircraft according to claim 1, characterized in that: The quadrotor system model in the presence of multi-source disturbances includes: Among them, x, y, and z are the three position sub-channels of the aircraft in the reference system; φ is the roll angle attitude sub-channel of the aircraft in the reference system; θ is the pitch angle attitude sub-channel of the aircraft in the reference system; ψ is the yaw angle attitude sub-channel of the aircraft in the reference system; m is the mass of the aircraft; g is the gravitational acceleration; are the first-order derivatives of x, y, z, φ, θ, and ψ respectively; are the second-order derivatives of x, y, z, φ, θ, and ψ, respectively, x ,I y ,I z are the x, y, and z axis moments of inertia of the aircraft in the reference system; K1, K2, and K3 are the translational drag coefficients of the corresponding position subchannels; K4, K5, and K6 are the air friction drag coefficients of the corresponding attitude subchannels; d1, d2, d3, d4, d5, and d6 are the unknown disturbances of the corresponding subchannels; u1 is the position system control rate of the quadrotor aircraft; u2 is the control rate of the φ attitude subchannel, u3 is the control rate of the θ attitude subchannel, and u4 is the control rate of the ψ attitude subchannel; is the coupling term of the roll angle subchannel, is the coupling term of the pitch angle sub-channel, is the coupling term of the yaw angle sub-channel.

3. The finite-time anti-disturbance control method for a quadrotor aircraft according to claim 2, characterized in that: When the state space model of the quadrotor system is the position system x When the subchannel observer is used, x1 = x, b u =u x ,u x for x The control input of the subchannel, η2 = d1; When the state space model of the quadrotor system is the y subchannel observer of the position system, x1 = y, b u =u y ,u y is the control input of the y subchannel, η2=d2; When the state space model of the quadrotor system is the z-subchannel observer of the position system, x1 = z, b u =u z ,u z is the control input of the z subchannel, η2=d3; in, When the state space model of the quadrotor system is the roll angle observer of the attitude system, x1 = φ, u2 is the control input of the roll angle, When the state space model of the quadrotor system is the pitch angle observer of the attitude system, x1 = θ, u3 is the control input of the pitch angle, When the state space model of the quadrotor system is the yaw angle observer of the attitude system, x1 = ψ, u4 is the control input of the yaw angle, 4. The finite-time anti-disturbance control device for a quadrotor aircraft according to the finite-time anti-disturbance control method for a quadrotor aircraft according to claim 1, characterized in that: include: Establish a module for modeling a quadrotor system in the presence of multiple sources of disturbance; A design module is used to design the corresponding tracking differentiator based on the auto-disturbance rejection theory; The reconstruction module is used to obtain the state space model of the quadrotor aircraft according to the system model, so as to design the linear regression equation and obtain the gradient descent observer; the system speed and unknown disturbance are reconstructed by the gradient descent observer to obtain the reconstructed system speed and unknown disturbance; A control module is used to design a non-singular fast terminal sliding mode controller according to the quadrotor system model and the tracking differentiator; substitute the reconstructed system speed and unknown disturbance into the non-singular fast terminal sliding mode controller to obtain a speed sensorless controller; and implement finite-time anti-disturbance control of the quadrotor system according to the speed sensorless controller.

5. A finite-time anti-disturbance control system for a quadrotor aircraft, characterized in that: include: Memory, for storing computer programs / instructions; A processor is used to execute the computer program / instructions to implement the steps of the finite-time anti-disturbance control method for a quadrotor aircraft according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the finite-time anti-disturbance control method for a quadrotor aircraft described in any one of claims 1 to 3 are implemented.

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