An improved second-order active disturbance rejection control method for attitude control of quadrotor UAV

Abstract

An improved second-order self-disturbance rejection control method for attitude control of a quad-rotor drone. Compared with the prior art, the beneficial effects of the present invention are: faster response speed, the optimized linear extended state observer transfer function algorithm greatly improves the response speed of the control system; the control system is more stable, and in the control system response process, the amplitude change of the optimized linear extended state observer transfer function algorithm is smoother; high control accuracy, by optimizing the control algorithm, the phase lag is significantly reduced, and the accuracy and stability of the control are improved; parameters are easy to set, and the present invention introduces an adaptive control method for real-time adjustment of the PD link control parameters of the PD controller, which can compensate for the tracking error caused by the controller parameter deviation and disturbance, which not only simplifies the parameter setting process, but also improves the control accuracy of the control system and enhances the anti-disturbance performance of the controller.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicles, and in particular to an attitude control method for a quad-rotor unmanned aerial vehicle with improved second-order anti-disturbance control. Background Art

[0002] A quadrotor drone is a multi-rotor helicopter that can take off and land vertically and hover freely. It has the advantages of small size, simple structure, easy maintenance and good maneuverability. It has broad application prospects in military, civil and scientific research fields, and has become one of the research hotspots at home and abroad in recent years.

[0003] Compared with fixed-wing aircraft, quadcopters are cheaper, have simpler frame structures, and better flight stability. However, quadcopters are under-driven, strongly coupled, nonlinear systems with four inputs and six outputs. Due to the complexity of its dynamic model, the uncertainty of model parameters, and modeling inaccuracy, as well as the complexity of the actual flight environment of quadcopters, higher requirements are placed on the design of controllers with strong robustness and interference resistance.

[0004] The main disadvantages of the existing technology are: the PID attitude control method cannot achieve progressive adjustment when there is model uncertainty and non-constant external interference in the system, and there will be residual errors. The application of fuzzy adaptive cascade PID attitude control method requires accurate modeling of the dynamics of the UAV, including the inertial characteristics, torque coupling and nonlinear effects of the aircraft. Secondly, the fuzzy adaptive cascade PID controller needs to adjust too many parameters, including cascade PID parameters, fuzzy rule weights and adaptive algorithm parameters. In addition, the attitude control of the quadcopter UAV requires real-time response and high-frequency control instructions; the fuzzy adaptive cascade PID control method involves complex calculations and parameter adjustment processes, which will lead to high computational complexity and delay. The neural network attitude control method has the ability of self-organization and self-learning, strong fault tolerance and file nature, but its stability is poor, the learning speed is slow, and it is difficult to meet the requirements of the quadcopter UAV to maintain attitude stability in real time. The traditional self-disturbance rejection attitude control has the problems of difficulty in obtaining the value of proportional differential gain, failure to provide sufficient disturbance compensation when the disturbance frequency increases, etc., and the traditional self-disturbance rejection control algorithm is mainly based on linear control theory and technology, and there may be certain limitations for the disturbance rejection control of nonlinear systems.

[0005] The stability of the attitude of a quadrotor UAV largely determines the quality of the UAV's mission completion. Therefore, the improved second-order active disturbance rejection attitude control method for quadrotors has important engineering significance and application value in practical applications. Summary of the invention

[0006] The present invention provides an improved second-order anti-disturbance control method for the attitude control of a quad-rotor UAV, aiming to solve the problems of slow control speed, weak stability, low control accuracy and difficult parameter setting in the prior art control system.

[0007] The present invention provides an improved second-order anti-disturbance control method for attitude control of a quad-rotor unmanned aerial vehicle, the attitude control method comprising the following steps:

[0008] Establishing an attitude dynamics model of the quadrotor drone;

[0009] Establishing the motion equation and state equation of the second-order control system of the quadrotor drone to obtain multiple state variables of the quadrotor drone; estimating the multiple state variables of the quadrotor drone in real time by using a linear extended state observer to obtain estimated values ​​of the state variables; and compensating the total disturbance of the quadrotor drone by using the linear extended state observer;

[0010] Defining the control quantity of the second-order control system of the quadrotor drone;

[0011] A second-order active disturbance rejection controller is established through a PD controller and the linear extended state observer to optimize the control amount of the quadrotor drone;

[0012] An adaptive control method is established by defining an algorithm of a tracking differentiator, defining a filter tracking error, and defining an adaptive law, wherein the adaptive control method is used to adjust a PD link control parameter in the PD controller in real time;

[0013] A transfer function is obtained according to the estimated value of the linear extended state observer, an active disturbance rejection control law of a proportional derivative term is established to optimize the transfer function, and the transfer function is output as a control signal.

[0014] Preferably, the posture dynamics model is expressed as the following relationship:

[0015]

[0016] Among them, I=diag(I x ,I y ,I z ) is the inertia tensor matrix, l is the length from the center of mass of the quadrotor drone to the center of the rotor, k f is the air resistance coefficient, φ represents the roll angle, i.e. the rotation angle of the quadrotor drone around the x-axis, θ represents the pitch angle, i.e. the rotation angle of the quadrotor drone around the y-axis, ψ represents the yaw angle, i.e. the rotation angle of the quadrotor drone around the z-axis, and the virtual control variables (U1, U2, U3, U4) are as follows:

[0017]

[0018] Wherein, m is the mass of the quadrotor drone, M i (M1, M2, M3, M4) represents the lift of each rotor motor in the quadrotor drone, b1 is used as the lift coefficient of the drone attitude system, and b2 is used as the anti-torque coefficient of the drone attitude system.

[0019] Preferably, the motion equation is expressed as:

[0020]

[0021] Among them, y represents the output of the second-order control system; u is the control input of the second-order control system; ω represents the external unknown disturbance of the second-order control system; a1 and a2 represent the parameters of the second-order control system; b is the control gain of the second-order control system and is partially known, and the known part is defined as b0.

[0022] Preferably, the state variables of the quadrotor drone are defined as x1, x2, x3, and the state equation is expressed as:

[0023]

[0024] Among them, the definition x1=y, x3=f, x3 is the expanded state variable of the second-order control system.

[0025] Preferably, in the step of estimating multiple state variables of the quadrotor drone in real time by using a linear extended state observer to obtain estimated values ​​of the state variables, the estimated values ​​are expressed as:

[0026]

[0027] Among them, z1, z2, z3 are the estimated values ​​of x1, x2, x3 respectively, and l1, l2, l3 are the observer gains.

[0028] Preferably, in the step of establishing a second-order active disturbance rejection control controller through a PD controller and the linear extended state observer to optimize the control amount of the quadrotor drone, the control amount is expressed as:

[0029]

[0030] Where u0 represents the output of the PD controller, k p , k d Expressed as PD link control parameter, v d is the desired input, and u represents the control variable of the second-order control system.

[0031] Preferably, the tracking differentiator is expressed as:

[0032]

[0033] Where r is the fast factor, h1 is the sampling time, fhan(·) is the fastest control synthesis function, v1(t) is the tracking signal of the initial signal, v2(t) is the tracking signal of the initial signal derivative, t represents a certain state, and t+1 represents the next state relative to t.

[0034] Preferably, the adaptive law is expressed as:

[0035]

[0036]

[0037] in, and represents the estimated value of PD gain in the active disturbance rejection control; and is the estimation error; k p0 and k d0 is a preset constant, χ=[Λ T 1]e, Λ=a1 is the gain vector, so that when χ→0, e→0 is satisfied; γ and ε represent constants.

[0038] Preferably, in the step of establishing an active disturbance rejection control law of a proportional derivative term to optimize the transfer function of the linear extended state observer and outputting the transfer function as a control signal, the optimized transfer function is expressed as:

[0039] G(S)=l4(1+l5s) / [s 3 +l1s 2 +(l2+l4l5)s+l4];

[0040] Where s is a complex variable representing the frequency in the Laplace transform domain, and l4 and l5 represent the observed gains after replacing l3.

[0041] Compared with the prior art, the beneficial effects of the present invention are: faster response speed, the transfer function algorithm of the optimized linear extended state observer greatly improves the response speed of the control system, and by adding the proportional derivative term, the transfer function algorithm can more keenly capture the dynamic changes of the control system and quickly make corresponding adjustments, which helps the quad-rotor UAV to respond to the external environment and flight mission requirements more promptly; the control system is more stable, compared with the traditional algorithm, in the control system response process, the amplitude change of the transfer function algorithm of the optimized linear extended state observer is smoother. It helps to reduce the oscillation and instability of the control system and improve the attitude control stability of the quad-rotor UAV; the control accuracy is high, and the present invention significantly reduces the phase lag by optimizing the control algorithm, so that the actual attitude of the quad-rotor UAV is more in line with the expected target attitude, and the control accuracy and stability are improved; the parameters are easy to set, and the difficulty of adjusting the control parameters of the PD link online may cause deviations in parameter selection, thereby generating tracking errors. During the flight, the UAV may be subject to various interferences, resulting in unstable system output. Therefore, the present invention introduces an adaptive control method for real-time adjustment of the PD link control parameters of the PD controller, which can compensate for the tracking error caused by the controller parameter deviation and disturbance, which not only simplifies the parameter setting process, but also improves the control accuracy of the control system and enhances the anti-disturbance performance of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The present invention will be described in detail below in conjunction with the accompanying drawings. The above and other aspects of the present invention will become clearer and easier to understand through the detailed description made in conjunction with the following drawings. In the accompanying drawings:

[0043] Figure 1 Schematic diagram of the coordinate system of the quad-rotor drone provided by an embodiment of the present invention;

[0044] Figure 2 It is a flow chart of an improved second-order active disturbance rejection control method for attitude control of a quad-rotor UAV provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0046] Please refer to Figure 1 and Figure 2 The present invention provides an improved second-order anti-disturbance control method for attitude control of a quad-rotor unmanned aerial vehicle, the attitude control method comprising the following steps:

[0047] S101, establishing an attitude dynamics model of the quadrotor drone;

[0048] In the embodiment of the present invention, in order to achieve the purpose of establishing an accurate description of the dynamic model of the quadcopter UAV system, it is necessary to clarify the reference coordinate system. Determine the fixed coordinate system E and the body coordinate system B. The fixed coordinate system E is a spatial coordinate system used to study the relative position of the quadcopter relative to the ground during flight, and is used to describe its movement relative to the earth and determine its own position. The earth coordinate system and the body coordinate system are as follows: Figure 1 As shown. e represents the origin of the Earth coordinate system, {x e y e z e} is used to indicate the positive direction of each coordinate axis in a fixed coordinate system.

[0049] O b represents the origin of the quadcopter coordinate system, {x b y b z b} is used to indicate the positive direction of each coordinate axis in the quadcopter. Among them, {φθψ} is the angle of rotation around each axis, which is specifically defined as follows: φ represents the roll angle, that is, the rotation angle of the quadcopter around the x-axis. θ represents the pitch angle, that is, the rotation angle of the quadcopter around the y-axis. ψ represents the yaw angle, that is, the rotation angle of the quadcopter around the z-axis.

[0050] Convert the attitude angle in the body coordinate system B to the earth coordinate system E. The rotation matrix is ​​as follows:

[0051]

[0052] In the coordinate system established above, the attitude dynamics model of the quadrotor drone is established using the Newton-Euler equation as follows:

[0053]

[0054] Where T is the moment, I = diag(I x ,I y ,I z ) is the inertia tensor matrix; is the angular velocity of the quadrotor drone rotating around each coordinate axis; N is the pulling torque of the quadrotor drone; O is the reaction torque of the quadrotor drone, is the drag moment, l is the length from the center of mass of the quadrotor drone to the center of the rotor, k f is the air resistance coefficient.

[0055] By analyzing Figure 1 It can be known that the arm direction and pulling direction of the quadcopter drone, the pulling torque N provided by the four rotors can be expressed as:

[0056]

[0057] The reaction force torque O of the UAV rotor is:

[0058]

[0059] Wherein, b1 is the lift coefficient of the UAV attitude system; b2 is the anti-torque coefficient of the UAV attitude system.

[0060] From formulas (2)-(4), the attitude dynamics of the quadrotor drone can be expressed as follows:

[0061]

[0062] Introduce virtual control variables (U1, U2, U3, U4), as shown below:

[0063]

[0064] Wherein, m is the mass of the quadrotor drone, M i is the lift of each motor. From (5) and (6), the attitude dynamics model of the UAV can be as follows:

[0065]

[0066] S102, establishing the motion equation and state equation of the second-order control system of the quadrotor drone to obtain multiple state variables of the quadrotor drone; estimating the multiple state variables of the quadrotor drone in real time by using a linear extended state observer to obtain estimated values ​​of the state variables; and compensating the total disturbance of the quadrotor drone by using the linear extended state observer;

[0067] In an embodiment of the present invention, the motion equation of the second-order control system of the quadrotor drone can be expressed as:

[0068]

[0069] Where: y is the system output; u is the control input of the system; ω is the external unknown disturbance of the system; a1, a2 are system parameters; b is the system control gain and is partially known, assuming that the known part is b0. Formula (8) can be transformed into the following formula:

[0070]

[0071] make Formula (9) can be rewritten as:

[0072]

[0073] Define x1=y, x3=f, x3 is the expanded state variable of the second-order control system, then the state equation expression of formula (10) can be obtained as follows:

[0074]

[0075] Among them, x1, x2, x3 are state variables, Transform equation (9) into the extended state space equation:

[0076]

[0077] in, C=[1 0 0].

[0078] The corresponding linear extended state observer in formula (12) is:

[0079]

[0080] Where L = [l1 l2 l3] T is the gain vector of the linear extended state observer (LESO). The gain of the linear extended state observer can be parameterized by placing all eigenvalues ​​in the observation bandwidth. The gain of the linear extended state observer can be expressed by its characteristic equation as shown in Equation (13):

[0081] λ(s)=s 3 +l1s 2 +l2s+l3=(s+ω0) 3 (14)

[0082] The gain matrix can be obtained:

[0083]

[0084] After arranging and simplifying formula (13), we can get:

[0085]

[0086] In formula (16), z1, z2, z3 are the estimated values ​​of x1, x2, x3, respectively, and l1, l2, l3 are the observer gains. It can be concluded that when the appropriate observer gains l1, l2, l3 are determined, the linear extended state observer can estimate the various state variables of the original second-order control system in real time.

[0087] S103, defining the control quantity of the second-order control system of the quadrotor drone;

[0088] S104, establishing a second-order active disturbance rejection controller through a PD controller and the linear extended state observer to optimize the control amount of the quadrotor drone;

[0089] In the embodiment of the present invention, the control quantity of the second-order control system is defined as shown in (17):

[0090] u=(-z3+u0) / b0 (17)

[0091] Ignoring the estimation error of z3 on f, the original uncertain control system can be transformed into The original nonlinear control system becomes a linear integrator series control system, which can be simplified into a mathematical model of the controlled object and improve the control performance of the system.

[0092] The use of linear extended state observer in the control system can estimate and compensate the total disturbance, and the use of PD controller can meet the control requirements. Therefore, based on equation (17), a second-order active disturbance rejection controller (LADRC) is designed as shown in equation (18):

[0093]

[0094] Where u0 is the output of the PD controller, k p , k d is the PD link control parameter, v d Expected input.

[0095] S105, establishing an adaptive control method by defining an algorithm of a tracking differentiator, defining a filter tracking error, and defining an adaptive law, wherein the adaptive control method is used to adjust the PD link control parameters in the PD controller in real time;

[0096] In an embodiment of the present invention, the algorithm of the tracking differentiator is as follows:

[0097]

[0098] Where r is the fast factor, h1 is the sampling time, fhan(·) is the fastest control synthesis function, v1(t) is the tracking signal of the initial signal, v2(t) is the tracking signal of the initial signal differential, t represents a certain state, and t+1 represents the next state relative to t. A certain state can be the current state at a certain sampling time.

[0099] Define the initial signal v d (t) is smooth and bounded, and the tracking error is defined as e = vv d , then the filter tracking error is defined as:

[0100] χ=[Λ T 1]e (20)

[0101] Where Λ=a1 is an appropriate gain vector, so that when χ→0, e→0 is satisfied. Taking the derivative of χ, we get:

[0102]

[0103] in,

[0104]

[0105] The approximation is achieved by defining a tracking control of the input signal, It is pseudo-control. for Any approximation of , adding or subtracting The following formula can be obtained:

[0106]

[0107] because for is an approximate value of Converges to near zero. The design of pseudo control input is as follows:

[0108] α=-τχ+u0-[0 Λ T ]e (24)

[0109] Where τ is an arbitrary positive parameter. Substituting (18), (23) and (24) into equation (21), we obtain:

[0110]

[0111] Assuming that equation (22) is selected as the control scheme, the following adaptive law is used to make the assumption valid:

[0112]

[0113]

[0114] To eliminate and To solve the singularity problem that may exist in the adaptive law when is zero, the above adaptive law can be changed to:

[0115]

[0116]

[0117] in, and represents the estimated value of the PD gain in the ADRC; and is the estimation error; k p0 and k d0is a properly selected constant; γ and ε represent appropriate constants. The signal of the entire control system is smooth and bounded, and the control system is uniformly stable.

[0118] S106: Establish an active disturbance rejection control law of proportional derivative term to optimize the transfer function of the linear extended state observer, and output the transfer function as a control signal.

[0119] In the embodiment of the present invention, the linear extended state observer (LESO) is the core of the active disturbance rejection control (LADRC). Therefore, we improve the linear extended state observer LESO to make the control system more stable and have better control performance. The transfer function can be obtained from formula (14):

[0120] G(s)=l3 / (s 3 +l1s 2 +l2s+l3) (30)

[0121] The transfer function in the above formula is a third-order system. The frequency characteristics of the system are difficult to analyze theoretically. Therefore, the above formula can be approximated to a second-order system, and the third-order system can be approximated to the following second-order system for analysis:

[0122]

[0123] From (31), we can see that l1, l2, and l3 can affect the response speed of the system at the same time. Compared with l1 and l2, l3 has a greater impact. Therefore, l3 is improved here, and an ADRC based on proportional derivative terms is designed. The improvement of l3 is as follows:

[0124] l3=l4(1+l5s) (32)

[0125] l4 and l5 represent the observed gain after replacing l3, and the transfer function can be transformed into the following formula:

[0126] G(S)=l4(1+l5s) / [s 3 +l1s 2 +(l2+l4l5)s+l4] (33)

[0127] From equation (33), it can be seen that the transfer function of the optimized observer adds zero to the closed loop, which not only improves the response speed of the control system but also reduces the amplitude drop and phase lag of the control signal.

[0128] Compared with the prior art, the beneficial effects of the present invention are: faster response speed, the transfer function algorithm of the optimized linear extended state observer greatly improves the response speed of the control system, and by adding the proportional derivative term, the transfer function algorithm can more keenly capture the dynamic changes of the control system and quickly make corresponding adjustments, which helps the quad-rotor UAV to respond to the external environment and flight mission requirements more promptly; the control system is more stable, compared with the traditional algorithm, in the control system response process, the amplitude change of the transfer function algorithm of the optimized linear extended state observer is smoother. It helps to reduce the oscillation and instability of the control system and improve the attitude control stability of the quad-rotor UAV; the control accuracy is high, and the present invention significantly reduces the phase lag by optimizing the control algorithm, so that the actual attitude of the quad-rotor UAV is more in line with the expected target attitude, and the control accuracy and stability are improved; the parameters are easy to set, and the difficulty of adjusting the control parameters of the PD link online may cause deviations in parameter selection, thereby generating tracking errors. During the flight, the UAV may be subject to various interferences, resulting in unstable system output. Therefore, the present invention introduces an adaptive control method for real-time adjustment of the PD link control parameters of the PD controller, which can compensate for the tracking error caused by the controller parameter deviation and disturbance, which not only simplifies the parameter setting process, but also improves the control accuracy of the control system and enhances the anti-disturbance performance of the controller.

[0129] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only the preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation manner. The above-mentioned specific implementation manner is only illustrative rather than restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. An improved second-order anti-disturbance control method for attitude control of a quadrotor drone, characterized in that: The posture control method comprises the following steps: Establishing an attitude dynamics model of the quadrotor drone; Establishing the motion equation and state equation of the second-order control system of the quadrotor drone to obtain multiple state variables of the quadrotor drone; estimating the multiple state variables of the quadrotor drone in real time by using a linear extended state observer to obtain estimated values ​​of the state variables; and compensating the total disturbance of the quadrotor drone by using the linear extended state observer; Defining the control quantity of the second-order control system of the quadrotor drone; A second-order active disturbance rejection controller is established through a PD controller and the linear extended state observer to optimize the control amount of the quadrotor drone; An adaptive control method is established by defining an algorithm of a tracking differentiator, defining a filter tracking error, and defining an adaptive law, wherein the adaptive control method is used to adjust a PD link control parameter in the PD controller in real time; Establishing an auto-disturbance rejection control law of proportional derivative term to optimize the transfer function of the linear extended state observer, and outputting the transfer function as a control signal; The posture dynamics model is expressed as the following relationship: ； in, is the inertia tensor matrix, is the length from the center of mass of the quadrotor drone to the center of the rotor, is the air resistance coefficient, represents the roll angle, i.e., the rotation angle of the quadrotor drone around the x-axis, represents the pitch angle, i.e., the rotation angle of the quadrotor drone around the y-axis, represents the yaw angle, i.e., the angle at which the quadcopter rotates around the z-axis. The virtual control variable ( ), as follows: ； in, m is the mass of the quadrotor drone, ( ) is represented by the lift of each rotor motor in the quadrotor drone, As the lift coefficient of the UAV attitude system, As the anti-torque coefficient of the UAV attitude system; The equation of motion is expressed as: ； in, y is represented as the output of the second-order control system; u is the control input of the second-order control system; is represented as the external unknown disturbance of the second-order control system; , is represented by the parameters of the second-order control system; b is the control gain of the second-order control system and is partially known, and the known part is defined as ; Define the state variables of the quadrotor drone as , , , the state equation is expressed as: ； Among them, the definition , , , , is the expanded state variable of the second-order control system; In the step of estimating multiple state variables of the quadrotor drone in real time by using a linear extended state observer to obtain estimated values ​​of the state variables, the estimated values ​​are expressed as: ； in, , , They are , , The estimated value of , , is the observer gain; In the step of establishing an active disturbance rejection control law of a proportional derivative term to optimize the transfer function of the linear extended state observer and outputting the transfer function as a control signal, the optimized transfer function is expressed as: ； Where s is a complex variable representing the frequency in the Laplace transform domain, Indicates replacement The subsequent observation gain.

2. The improved second-order ADRC attitude control method for a quadrotor drone as claimed in claim 1, characterized in that: In the step of establishing a second-order active disturbance rejection control controller through the PD controller and the linear extended state observer to optimize the control amount of the quadrotor drone, the control amount is expressed as: ； in, Expressed as the output of the PD controller, , It is expressed as the PD link control parameter, Expected input.

3. The improved second-order ADRC attitude control method for a quadrotor drone as claimed in claim 1, characterized in that: The tracking differentiator is expressed as: ； in, r is the fast factor, h 1 is the sampling time, For the fastest control synthesis function, is the tracking signal of the initial signal, It is the tracking signal of the differential of the initial signal, t represents a certain state, and t+1 represents the next state relative to t.

4. The improved second-order ADRC attitude control method for a quadrotor drone as claimed in claim 3, characterized in that: The adaptive law is expressed as: ； ； in, and represents the estimated value of PD gain in the active disturbance rejection control; and is the estimation error; and is a preset constant, , is the gain vector, so that when When, meet ; Represents a constant.

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