Four-rotor suspension system sliding mode control method based on extended state observer

Abstract

The invention discloses a four-rotor suspension system sliding mode control method based on an extended state observer. The four-rotor suspension system sliding mode control method comprises the following steps: constructing a kinetic model of a four-rotor suspension system; analyzing the established kinetic model of the four-rotor suspension system to obtain virtual control moments in one-to-one correspondence with state variables of the four-rotor suspension system, and decomposing the whole four-rotor suspension system into a plurality of subsystems according to the virtual control moments; various uncertain disturbances existing in the four-rotor suspension system are regarded as expansion state variables of the system, and a nonlinear expansion state observer is designed on the basis and used for estimating the disturbance condition of the system in real time; and designing a non-singular fast sliding mode controller for each subsystem based on disturbance estimation provided by a non-linear extended state observer. According to the method, the wobble phenomenon of the load can be effectively and quickly inhibited while the four-rotor suspension system accurately tracks the expected target.

Description

Technical Field

[0001] The present invention relates to the field of automatic control of the position and attitude of a quadrotor suspension system, and in particular to a sliding mode control method of a quadrotor suspension system based on an extended state observer. Background Art

[0002] In the context of the booming low-altitude economy today, the application scope of various types of drones is expanding. Among them, quadcopters are gradually emerging in the field of air transportation and becoming a new trend leading the trend. Traditional ground transportation methods rely on transport vehicles, which are limited by road conditions and terrain conditions, especially in areas with inconvenient transportation such as mountainous areas and dense urban high-rise buildings. Its transportation efficiency is greatly reduced. Traditional air transportation mainly relies on helicopters, which is costly. In contrast, quadcopters significantly reduce their dependence on terrain by virtue of their ability to suspend loads with ropes. Its flight altitude cleverly fills the gap between ground transportation and the flight routes of large passenger aircraft, avoiding the occupation of existing transportation resources. Compared with helicopter transportation, quadcopters show unique advantages in suspension transportation. It is small in size, does not require special take-off and landing facilities, and has higher flexibility. It is especially suitable for transportation operations between urban high-rise buildings and has a high cost-effectiveness. However, during the suspension transportation of quadcopters, the inertia of the load often leads to inevitable swinging, which not only weakens the trajectory tracking ability of the transportation system, but also may bring major safety hazards. Therefore, an important current research direction is to explore how to effectively control the quadrotor suspension system to overcome this challenge.

[0003] Most of the control strategies currently used in quadrotor suspension systems have many limitations. They generally tend to treat the load as a disturbance factor and rely on disturbance suppression methods to reduce the swing angle oscillation. However, given the wide range and diversity of load types, simply treating the load as a disturbance factor is not a good approach.

[0004] 8 / The strategy of simply regarding load swing as a disturbance without deeply exploring the intrinsic impact mechanism of load swing on the dynamic behavior of the system is obviously flawed. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a sliding mode control method for a quadrotor suspension system based on an extended state observer, which enables the quadrotor suspension system to effectively and quickly suppress the swing of the load while accurately tracking the desired target.

[0006] The technical solution adopted by the present invention is:

[0007] The sliding mode control method of a quadrotor suspension system based on an extended state observer comprises the following steps:

[0008] Step 1: Construct a dynamic model of the quadrotor suspension system;

[0009] Step 2: Analyze the dynamic model of the quadrotor suspension system established in step 1, obtain the virtual control torque corresponding to each state variable of the quadrotor suspension system, and decompose the entire quadrotor suspension system into multiple subsystems based on it;

[0010] Step 3: Consider the various uncertain disturbances existing in the quadrotor suspension system as the extended state variables of the system, and on this basis design a nonlinear extended state observer to estimate the disturbance of the system in real time;

[0011] Step 4: Design a non-singular fast sliding mode controller for each subsystem based on the disturbance estimate provided by the nonlinear extended state observer.

[0012] In step 1, the quadrotor suspension system includes a quadrotor drone, a suspension rope used for suspending a load, and a suspended load. The modeling process of the dynamic model of the quadrotor suspension system includes:

[0013] Through the Lagrange equation and the relationship between the coordinates of the center of mass of the quadrotor drone and the center of mass of the suspended load, the system position swing angle dynamic model is obtained to describe the position of the load in space and its swing characteristics.

[0014] According to the Euler equation, the relationship between the rotational torque around the axis and the attitude angular acceleration is obtained, and then the system attitude dynamics model is determined to reflect the attitude changes of the quadrotor suspension system during flight.

[0015] Based on the inertial coordinate system, the system position swing angle dynamic model is established. It is assumed that the center of mass position of the quadrotor drone is expressed as (x, y, z) in the inertial coordinate system, and the load position is expressed as (x p ,y p ,z p ),like Figure 1 The relative relationship between the coordinates of the center of mass of the payload and the coordinates of the center of mass of the quadrotor drone is:

[0016]

[0017] Where: L represents the length of the hanging rope; α represents the swing angle projection on the yz plane, and β represents the swing angle projection on the xz plane;

[0018] The system position swing angle dynamics model established using the Lagrange equation is as follows:

[0019]

[0020] Among them, q=[x, y, z, α, β, φ, θ, ψ] T,[i] T is the transpose of vector[i], is the first-order derivative of q with respect to time, is the second-order derivative of q with respect to time, and u is the driving force of the system in the position swing angle subsystem, which is the lift moment u of the quadrotor suspension system here. 1 .

[0021] M(q), G(q) and b are the model parameter matrices defined as follows:

[0022]

[0023] In the above formula, m 11 、m 15 、m 22 、m 24 、m 25 、m 33 、m 34 、m 35 、m 42 、m 43 、m 44 、m 51 、m 52 、m 53 、m 55 They are all model parameters, and the specific expressions are as follows:

[0024] m 11 =m 22 =m 33 =M+m,m 15 =mLcos(β)

[0025] m 24 =mLcos(β)cos(α),m 25 =-mLsin(β)sin(α)

[0026] m 34 =mLcos(β)sin(α),m 35 =mLsin(β)cos(α)

[0027] m 42 =cos(α),m 43 = sin(α),m 44 =cos(β)

[0028] m 51 =cos(β),m 52 = -sin(β)sin(α),m 53 = sin(β)cos(α),m 55 =L

[0029] Where: M and m are the masses of the UAV and the suspended load respectively.

[0030]

[0031] In the above formula, C 15 , C 25 , C 35 , C 24 , C 34 , C 44 , C 54 They are all model parameters, and the specific expressions are as follows:

[0032]

[0033] G(q)=[0 0 g sin(α)g cos(α)sin(β)g] T ;

[0034] b=[b 1 b 2 b 3 0 0] T ;

[0035] In the above formula: g is the acceleration due to gravity. 1 , b 2 , b 3 is the transformation matrix from the drone body coordinate system to the inertial coordinate system. The specific expression is as follows:

[0036] b 1 =cos(φ)sin(θ)cos(ψ)+sin(φ)sin(ψ)

[0037] b 2 =cos(φ)sin(θ)sin(ψ)-sin(φ)cos(ψ)

[0038] b 3 =cos(φ)cos(θ)

[0039] The system attitude dynamics model established using the Euler equation is as follows:

[0040]

[0041] Among them, l is the wheelbase of the quadrotor drone; φ, θ, ψ are the angles of the drone’s counterclockwise rotation around the body’s coordinate axis; are the second-order derivatives of φ, θ, ψ with respect to time; are the first-order derivatives of φ, θ, ψ with respect to time; u φ ,u θ ,u ψThey represent the counterclockwise rotation torque of the drone around the body coordinate axis; I x ,I y ,I z They represent the UAV's counterclockwise rotational inertia around the body's coordinate axis; d φ ,d θ ,d ψ is the uncertainty disturbance of the system.

[0042] The four-rotor suspension system adopts a cross structure, and the speed of the four rotors is ω 1 ,ω 2 ,ω 3 ,ω 4 and the system lift moment u 1 , torque u around three axes φ ,u θ ,u ψ The corresponding relationship is:

[0043]

[0044] Among them, c T is the lift coefficient, c M is the counter torque coefficient.

[0045] In step 2, first, set the virtual control torque u x ,u y ,u z :

[0046]

[0047] Among them, M represents the mass of the drone and m represents the mass of the payload.

[0048] Then the virtual control torque u can be obtained x ,u y ,u z and the system lift moment u 1 and the desired attitude angle φ d ,θ d The relationship between:

[0049]

[0050] The position and swing angle dynamics model of the quadrotor suspension system can be expressed as:

[0051]

[0052] in, Respectively represent the second-order derivatives of x, y, and z with respect to time, are the second and first order derivatives of α and β with respect to time, respectively, d x ,d y,d z ,d α ,d β represents the uncertainty disturbance of the system, and g represents the acceleration of gravity.

[0053] will u x As the main control quantity of the β subsystem, u y As the main control quantity of the α subsystem, u x Decompose to get the control quantity u of the x subsystem x1 and the control quantity u of the β subsystem x2 ,u y Decomposed into the control quantity u of the y subsystem y1 and the control quantity u of the α subsystem y2 , thus we get u x 、u y The expression is:

[0054]

[0055] Let P = [x, y] T , Q = [α, β] T ,Ω=[z,φ,θ,ψ] T , the entire quadcopter suspension system can be redefined as:

[0056]

[0057] in, is the second-order derivative of P, Q, Ω with respect to time; P, Q, Ω represent the state variable vectors of the translation subsystem, the swing angle subsystem, the height and attitude subsystem respectively; f(P), f(Q), f(Ω) are the model variables other than the control quantity in the translation subsystem model, the swing angle subsystem model, the height and attitude subsystem model; g(P), g(Q), g(Ω) are the control quantity coefficients of the translation subsystem model, the swing angle subsystem model, the height and attitude subsystem model respectively. f(P)=[f(x),f(y)] T ,f(Q)=[f(α),f(β)] T , f(Ω)=[f(z),f(φ),f(θ),f(ψ)] T , f(x), f(y), f(α), f(β), f(z), f(φ), f(θ), and f(ψ) represent the model variables other than the items where the control quantities are located in the x, y, α, β, φ, θ, and ψ subsystem models, respectively.

[0058] g(P)=[g(x),g(y)] T ,g(Q)=[g(α),g(β)] T , g(Ω)=[g(z),g(φ),g(θ),g(ψ)]T , g(x), g(y), g(α), g(β), g(z), g(φ), g(θ), and g(ψ) represent the control coefficients of the x, y, α, β, φ, θ, and ψ subsystem models, respectively.

[0059] u P 、u Q 、u Ω They are the control quantities of translation subsystem, swing subsystem, height and attitude subsystem respectively.

[0060] u P =[u x1 ,u y2 ] T ,u Q =[u y2 ,u x2 ] T ,u Ω =[u z ,u φ ,u θ ,u ψ ] T ,u x1 、u y1 、u z 、u y2 、u x2 、u φ 、u θ 、u ψ They represent the control quantities of the x, y, α, β, φ, θ, and ψ subsystems respectively.

[0061] d P =[d x ,d y ] T ,d Q =[d α ,d β ] T ,d Ω =[d z ,d φ ,d θ ,d ψ ] T .d x ,d y ,d z ,d α ,d β ,d φ ,d θ ,d ψ Respectively represent the amount of interference received by each subsystem.

[0062] In step 3, n 1 Represents the observed state variables of the quadrotor suspension system, expressed as dη Represents the system disturbance and serves as the expanded state of the system, let The observed state space expression of the quadrotor suspension system is expressed as:

[0063]

[0064] in, η 2 is the first-order derivative of the system state variable with respect to time, is the second-order derivative of the system state variable with respect to time, η 3 Here we denote the system disturbance, is the third-order expansion state of the system, where is the first-order derivative of the system disturbance with respect to time. f(η) is the model variable in the system model except the term where the control quantity is located, and g(η) is the control quantity coefficient in the system model.

[0065] Let ε be the observation error and introduce the nonlinear feedback function g n (ε):

[0066]

[0067] Among them, n is the system order, and the system in this part is a third-order system, that is, n￡3.

[0068] The nonlinear extended state observer can be designed as:

[0069]

[0070] in, They are η 1 , η 2 , η 3 Observed value of μ 1 , μ 2 , μ 3 is the error feedback gain of the extended state observer. 1 (ε), g 2 (ε), g 3 (ε) are g n (ε) Expression when n=1,2,3.

[0071] In step 4, according to the control objective, combined with the linear sliding mode and non-singular terminal sliding mode theory, the following non-singular fast terminal sliding mode surfaces are designed for the x-β subsystem:

[0072]

[0073] Among them: a x 、c x 、a β 、c β 、px ,q x 、p β ,q β All of them are controller parameters and need to be given in conjunction with the embodiments.

[0074] e x is the deviation between the expected trajectory and the actual trajectory of the x subsystem; for e x Derivative with respect to time.

[0075] a x 、c x 、a β 、c β >0;p x ,q x 、p β ,q β are all positive odd numbers; and p x >q x , p β >q β ;

[0076] Reaching law selection:

[0077]

[0078] in: They represent the reaching laws of x and β subsystems respectively.

[0079] k x , k β , η x , η β , γ x , γ β It is a controller parameter and needs to be given in combination with the embodiment.

[0080] k x , k β , η x , η β >0,0<γ x <1, 0<γ β <1.

[0081] u x1 、u x2 Can be designed as:

[0082]

[0083] in: is the disturbance estimated by the observer. x1 is the control law of the x subsystem, u x2 is the control law of the β subsystem, is the second-order derivative of the expected trajectory of the x subsystem with respect to time; f(x), g(x), f(β), g(β) are model variables, and the specific expressions are as follows.

[0084]

[0085] The swing angle variable of the suspended load cannot be directly controlled, but can only be indirectly controlled through the position control signal. The position control signal can be expressed as:

[0086] u x =u x1 +u x2

[0087] Similarly, the non-singular fast terminal sliding surface of the y-α control subsystem is:

[0088]

[0089] Where: s y 、s α are the sliding surfaces of the y and α subsystems respectively; a y 、c y 、a α 、c α 、p y ,q y 、p α ,q α is the controller parameter, which needs to be given in combination with the embodiment; e y is the deviation between the expected trajectory and the actual trajectory of the y subsystem; for e x Derivative with respect to time.

[0090] The reaching law is:

[0091]

[0092] in: They represent the reaching laws of y and α subsystems respectively.

[0093] k y , k α , η y , η α , γ y , γ α It is a controller parameter and needs to be given in combination with the embodiment.

[0094] k y , k α , η y , η α >0,0<γ y <1, 0<γ α <1.

[0095] u y1 、u y2 Can be designed as:

[0096]

[0097] in: is the disturbance estimated by the observer; u y1 is the control law of the y subsystem; u y2 is the control law of the α subsystem; is the second-order derivative of the expected trajectory of the y subsystem with respect to time. f(y), g(y), f(α), g(α) are model variables, and their specific expressions are as follows.

[0098]

[0099] The position control signal can be expressed as:

[0100] u y =u y1 +u y2

[0101] For the design of the remaining height and attitude subsystems, taking the height z subsystem as an example, the sliding surface can be selected:

[0102]

[0103] Where: s z is the sliding surface of the designed height and attitude subsystem; a z 、c z 、p z ,q z is the controller parameter, which needs to be given in combination with the embodiment; e z is the deviation between the expected trajectory and the actual trajectory of the altitude and attitude subsystem; for e z First derivative with respect to time.

[0104] Convergence law:

[0105]

[0106] in: represents the reaching law of the z subsystem; k z , η z , γ z It is a controller parameter and needs to be given in combination with the embodiment.

[0107] u z Can be designed as:

[0108]

[0109] Where: u Ω It is the designed height and attitude subsystem controller output. is the second-order derivative of the desired trajectory with respect to time for a given height; f(z) and g(z) are model variables, and the specific expressions are as follows.

[0110]

[0111] The controller designs of the remaining φ, θ, ψ subsystems of the altitude and attitude subsystem are similar to those of the altitude z subsystem, and their controller designs are:

[0112]

[0113] Among them, f(φ), f(θ), f(ψ), g(φ), g(θ), and g(ψ) are model variables, and the specific expressions are as follows.

[0114]

[0115] The present invention proposes a sliding mode control method for a quadrotor suspension system based on an extended state observer. Compared with the prior art, the present invention shows many obvious advantages in solving the load swing problem of a quadrotor suspended UAV.

[0116] First, in terms of control strategy, the present invention innovatively introduces a nonlinear extended state observer (NESO) to accurately estimate and compensate for system disturbances and uncertainty parameters in real time. This design significantly enhances the robustness of the system, allowing the drone to maintain stable control performance when facing parameter uncertainties such as moment of inertia, lift coefficient, torque coefficient, and external interference forces and torques. In contrast, traditional control methods often find it difficult to effectively deal with these uncertain factors, resulting in a decrease in system performance.

[0117] Secondly, in controller design, the present invention adopts a non-singular fast terminal sliding mode controller (NFTSM). This controller not only combines non-singularity and fast convergence characteristics, but also effectively solves the singularity problem in traditional terminal sliding mode control by introducing nonlinear terms and fast convergence terms, and improves the convergence speed of the system.

[0118] The control scheme proposed in the present invention regards the output of the swing angle subsystem controller as a compensation of the position control signal when dealing with the problem of mutual coupling between the position subsystem and the swing angle subsystem of the UAV suspension system, and linearly combines the position subsystem with the swing angle subsystem controller to obtain the system position control signal, thereby effectively solving the problem of high coupling of the position and swing angle systems of the quadrotor suspension system.

[0119] In summary, the present invention demonstrates unique innovation and practicality in solving the load swing problem of quadrotor suspension UAVs. Based on the quadrotor suspension system dynamics model established by the Lagrange-Euler equation, by introducing advanced control technologies and strategies such as NESO and NFTSM, the present invention not only improves the robustness and trajectory tracking performance of the system, but also broadens its scope of application and application scenarios, laying a solid foundation for the further development and application of quadrotor suspension UAVs. BRIEF DESCRIPTION OF THE DRAWINGS

[0120] Figure 1 This is a schematic diagram of the structure of the quadrotor suspension system.

[0121] Figure 2 This is the structural block diagram of the control system of the quadrotor suspension system.

[0122] Figure 3 This is the corresponding relationship diagram between the virtual torque and each subsystem after the overall system is decomposed.

[0123] Figure 4 Schematic diagram of the tracking of the desired trajectory in the x and y directions and the suppression effect on the load swing angle.

[0124] Figure 5 This is a schematic diagram of the simulation structure of the attitude control system.

[0125] Figure 6 Schematic diagram of the limiting filtering effect of the limiting filter.

[0126] Figure 7 Schematic diagram of the expected trajectory tracking effect for the altitude and attitude subsystems.

[0127] Figure 8 Schematic diagram of the estimated effect of the extended state observer on the assumed disturbance.

[0128] Fig. 9 Schematic diagram of the jitter amplitude of the controller output when different reaching laws are selected. DETAILED DESCRIPTION

[0129] A sliding mode control method for a quadrotor suspension system based on an extended state observer is proposed to address the common problem of load swing affecting trajectory tracking performance in quadrotor suspension systems. This innovative improvement scheme is based on non-singular fast sliding mode control based on overall system decomposition. Firstly, an accurate mathematical model for the quadrotor suspension system is constructed using the Lagrange-Euler equation, and an advanced nonlinear extended state observer is introduced to accurately estimate the system disturbance in real time. Then, in order to more effectively manage the complexity of the system, a virtual torque is set for each state variable, and the entire system is cleverly decomposed into several subsystems based on this. This step not only simplifies the control design, but also improves the controllability and response speed of the system. Furthermore, a non-singular fast terminal sliding mode control method is designed for each subsystem based on the disturbance estimation. With this method, we can ensure that each subsystem can quickly and stably reach the desired state when facing disturbances. Subsequently, the torque command that meets the actual control requirements is derived using the corresponding relationship between the virtual torques. This step ensures that our control strategy meets both theoretical requirements and can be effectively implemented in practical applications.

[0130] A decomposition method for the overall system and a non-singular fast sliding mode control scheme for a quadrotor suspension system based on disturbance estimation implemented for each decomposed subsystem subsequently include the following steps:

[0131] S1: Using the Lagrange-Euler equation, the dynamic model equation of the quadrotor suspension system was constructed, providing a theoretical basis for subsequent analysis and control.

[0132] S2: In order to achieve precise control of each state variable in the quadrotor suspension system, the established system model was deeply analyzed. The virtual control torque corresponding to each state variable of the system was obtained, and the entire system was decomposed into multiple subsystems based on this, so as to facilitate the subsequent independent control design.

[0133] S3: In view of the various uncertain disturbances that may exist in the system, these disturbances are regarded as the extended state variables of the system. On this basis, a nonlinear extended state observer is designed to estimate the disturbance of the system in real time.

[0134] S4: Non-singular fast sliding mode controllers are designed for each subsystem based on the disturbance estimates provided by the nonlinear extended observer.

[0135] The present invention provides a dynamic model of a quad-rotor suspension system, the structure diagram of which is shown in FIG. Figure 1As shown, the quadcopter suspension system includes a quadcopter drone, a suspension rope used for hanging a load, and a suspended load. The modeling process of the dynamic model of the quadcopter suspension system provided by the present invention is mainly divided into two parts. One is to establish the Lagrange equation and combine the relationship between the center of mass coordinates of the quadcopter drone and the center of mass coordinates of the suspended load to obtain the system position swing angle dynamic model; the other is to obtain the relationship between the rotational torque around the axis and the attitude angular acceleration according to the Euler equation, and then determine the system attitude dynamic model.

[0136] The present invention provides a sliding mode control system based on the established quadcopter suspension system dynamics model, such as Figure 2 As shown, the control system includes the establishment of non-singular fast sliding mode controllers for the x, y, z, α, β, φ, θ, ψ subsystems, the combination of various sliding mode controllers, and the design of nonlinear extended state observers. The corresponding relationship between each controller and each subsystem that needs to be designed is shown in Figure 3 shown.

[0137] The specific implementation details of step S1 of the proposed control scheme are as follows:

[0138] Firstly, the Lagrange equation is used to construct the dynamic model of the position swing angle system, which describes the position of the load in space and its swing characteristics. At the same time, combined with the Euler equation, an attitude dynamic model is established to reflect the attitude changes of the quadrotor suspension system during flight.

[0139] In order to simplify the dynamic model of the system, the following assumptions are made:

[0140] (1) The quadrotor drone is symmetrical and rigid;

[0141] (2) The load is connected to the center of mass of the quadrotor drone through a rope, and the rope is massless, inelastic, and always in a tensioned state;

[0142] (3) The load can be regarded as a point mass, which is always located below the UAV;

[0143] (4) Ignore air resistance.

[0144] The variables used to build the model are shown in Table 1 below:

[0145] Table 1 Meaning of parameters used in model establishment

[0146] symbol meaning symbol meaning x,y,z Quadrotor center of mass position φ,θ,ψ Angle of rotation around the axis M Drone quality m Load quality α Swing angle projection on the yz plane β Swing angle projection on xz plane <![CDATA[u 1 ]]> Quadrotor lift torque <![CDATA[u φ ,in θ ,in ψ ]]> Torque about the axis l The distance from the center of mass of the quadrotor to the rotor axis L Length of hanging rope g Gravity acceleration <![CDATA[I x ,I y ,I z ]]> The moment of inertia of the quadrotor about its axis <![CDATA[x d ,y d ,z d ]]> Position system expected trajectory <![CDATA[φ d ,i d ,ψ d ]]> Expected trajectory of attitude system <![CDATA[e x ,And y ,And z ]]> Position system tracking error <![CDATA[e φ ,And θ ,And ψ ]]> Attitude system tracking error <![CDATA[d x ,d y ,d z ]]> Position system disturbance <![CDATA[d φ ,d θ ,d ψ ]]> Attitude system disturbance

[0147] Firstly, based on the above assumptions, the position swing angle system dynamics model is established with the inertial coordinate system as the reference. The center of mass position of the quadrotor drone can be expressed as (x, y, z), and the load position coordinates can be expressed as (xp ,y p ,z p ), we can get the relationship between the coordinates of the center of mass of the payload and the coordinates of the center of mass of the quadrotor drone:

[0148]

[0149] The dynamic model of the position swing angle system established using the Lagrange equation is as follows:

[0150]

[0151] Among them, q=[x, y, z, α, β, φ, θ, ψ] T , u is the driving force of the system in the position swing angle subsystem, here it is the lift moment u of the quadrotor suspension system 1 .

[0152]

[0153] G(q)=[0 0 g sin(α)g cos(α)sin(β)g] T ;

[0154] b=[b 1 b 2 b 3 0 0] T ;

[0155] The internal parameters of the M(q) matrix are defined as follows:

[0156]

[0157] The internal parameters of the matrix are defined as follows:

[0158]

[0159] The internal parameters of the b matrix are defined as follows:

[0160]

[0161] The attitude system dynamics model established using the Euler equation is as follows:

[0162]

[0163] The four-rotor suspension system adopts a cross structure, and the speed of the four rotors is ω 1 ,ω 2 ,ω 3 ,ω 4 and the system lift moment u 1 , torque u around three axes φ ,uθ ,u ψ The corresponding relationship is:

[0164]

[0165] The specific implementation details of step S2 of the proposed control scheme are as follows:

[0166] First, assume that there is a virtual moment u x ,u y ,u z ,

[0167]

[0168] The corresponding relationship between the position signal and the expected value of the attitude angle is solved:

[0169]

[0170] The position swing angle dynamics model of the quadrotor suspension system can be expressed as:

[0171]

[0172] The present invention will x As the main control quantity of the β subsystem, u y As the main control quantity of the α subsystem, u x Decompose to get the control quantity u of the x subsystem x1 and the control quantity u of the β subsystem x2 ,u y Decomposed into the control quantity u of the y subsystem y1 and the control quantity u of the α subsystem y2 , thus we get u x 、u y The expression is:

[0173] u x =u x1 +u x2

[0174] u y =u y1 +u y2 ;

[0175] In the proposed control scheme, the specific details of step S3 are as follows:

[0176] With η 1 Represents the observed state variables of the quadrotor suspension system, expressed as d η Represents the system disturbance and serves as the expanded state of the system, let The observed state space expression of the quadrotor suspension system is expressed as:

[0177]

[0178] in, η 2 is the first-order derivative of the system state variable with respect to time, is the second-order derivative of the system state variable with respect to time, η 3 Here we denote the system disturbance, is the third-order expansion state of the system, where is the first-order derivative of the system disturbance with respect to time. f(η) is the model variable in the system model except the term where the control quantity is located, and g(η) is the control quantity coefficient in the system model.

[0179] Let ε be the observation error and introduce the nonlinear feedback function g n (ε):

[0180]

[0181] Among them, n is the system order, and the system in this part is a third-order system, that is, n￡3.

[0182] The nonlinear extended state observer can be designed as:

[0183]

[0184] in, They are η 1 , η 2 , η 3 Observed value of μ 1 , μ 2 , μ 3 is the error feedback gain of the extended state observer. 1 (ε), g 2 (ε), g 3 (ε) are g n (ε) Expression when n=1,2,3.

[0185] In the proposed control scheme, the specific details of step S4 are as follows:

[0186] According to the control objective, combined with the linear sliding mode and non-singular terminal sliding mode theory, the following non-singular fast terminal sliding mode surfaces can be designed for the x-β subsystem:

[0187]

[0188] Among them: a x 、c x 、a β 、c β >0,p x ,q x 、p β ,qβ are all positive odd numbers, and p x >q x , p β >q β .

[0189] Reaching law selection:

[0190]

[0191] Where: k x , k β , η x , η β >0,0<γ x <1, 0<γ β <1.

[0192] u x1 、u x2 Can be designed as:

[0193]

[0194] Where: d x is the disturbance estimated by the observer.

[0195] Similarly, the non-singular fast terminal sliding surface of the y-α control subsystem is:

[0196]

[0197] The reaching law is:

[0198]

[0199] u y1 、u y2 Can be designed as:

[0200]

[0201] The design of the height and attitude subsystem controller, taking the height z subsystem as an example, can select the sliding surface:

[0202]

[0203] Where: s z is the sliding surface of the designed height and attitude subsystem; a z 、c z 、p z ,q z is the controller parameter, which needs to be given in combination with the embodiment; e z is the deviation between the expected trajectory and the actual trajectory of the altitude and attitude subsystem; for e z First derivative with respect to time.

[0204] Convergence law:

[0205]

[0206] in: represents the reaching law of the z subsystem; k z , η z , γ z It is a controller parameter and needs to be given in combination with the embodiment.

[0207] u z Can be designed as:

[0208]

[0209] Where: u Ω It is the designed height and attitude subsystem controller output. is the second-order derivative of the desired trajectory with respect to time, f(z) and g(z) are model variables, and the specific expressions are as follows.

[0210]

[0211] The controller designs of the remaining φ, θ, ψ subsystems of the altitude and attitude subsystem are similar to those of the altitude z subsystem, and their controller designs are:

[0212]

[0213] Among them, f(φ), f(θ), f(ψ), g(φ), g(θ), and g(ψ) are model variables, and the specific expressions are as follows.

[0214]

[0215] The effectiveness of the proposed control scheme is verified by simulation results. In the process of simulation experiment, the initial state of the system is first set to zero, and the simulation time is set to 20 seconds. In order to comprehensively evaluate the effectiveness of the proposed algorithm in trajectory tracking and the effect of suppressing the swing angle, the α, β change curves under its action are compared with the control system without swing angle suppression (i.e., removing the α, β subsystem controller mentioned in the present invention).

[0216] The parameters of the system model, each controller and the extended state observer are shown in Tables 2 to 5.

[0217] Table 2 Quadrotor suspension system model parameters

[0218]

[0219]

[0220] Table 3 Parameters of the x-β, y-α, z subsystem controllers

[0221]

[0222] Table 4 φ, θ, ψ subsystem controller parameters

[0223]

[0224] Table 5 Parameters of the third-order extended state observer

[0225]

[0226] In order to further verify whether the algorithm can accurately track the expected position and effectively suppress the swing angle during the system movement, a set of expected trajectories is designed: d =5,y d = sin(t)+5, z d =10+t, and set the desired yaw angle to ψ d =π / 6. In addition, assume that each subsystem of the system is subject to the following disturbances: d x =0.2sin(t),d y =0.2cos(t),d z =0.5sin(t),d φ =cos(t),d θ = sin(t), d ψ =1.

[0227] Figure 4 The simulation results in the x and y directions are shown in detail, which intuitively demonstrates the performance of the algorithm. When the system performs intermittent point-to-point motion, the algorithm can quickly and accurately guide the system to the target position, while quickly and effectively suppressing the load's swing angle swing. When the system performs reciprocating motion, the swing suppressor also demonstrates excellent control capabilities, strictly limiting the load's swing within the preset safety range, thereby effectively avoiding potential safety hazards.

[0228] In the actual simulation experiment of the attitude system, it can be found that the result φ obtained by the attitude solution d and θ d The rate of change is quite rapid. When using this data to design a sliding mode controller, it is found that the required high-order derivatives and At some point, it approaches infinity, which brings difficulties to the design of attitude control law. d and θ dIn order to ensure that this processing does not interfere with the normal operation of the position angle controller, a filtering process is added to the simulation process.

[0229] Specifically, a fourth-order Butterworth low-pass filter is used in the simulation structure, and the edge filter frequency is set to 30 rad / s to effectively filter out high-frequency noise signals, such as Figure 5 In addition, in order to further enhance flight safety, a limiter is added at the output end of the attitude solution, and the edge amplitude is set to 0.3, so as to ensure that the expected attitude angle of the drone is limited to within 20°, effectively preventing the safety risks that may be caused by excessive attitude angles. The effect of the limiting filter is shown in Figure 6 shown.

[0230] After the attitude angle expected signal is processed by limiting filtering, Figure 7 It can be clearly seen from the (a), (b) and (c) sub-figures in Figure 1 that the designed controller can track the expected value of the attitude angle after filtering. In addition, Figure 7 Subfigure (d) in Figure 3 further demonstrates the excellent performance of the height controller in trajectory tracking.

[0231] Nonlinear extended state observers are designed for the six key subsystems: position x, y, z and attitude angles φ, θ, ψ. These observers can estimate the amount of disturbance suffered by each subsystem quite accurately. Figure 8 The estimation results of these perturbations are presented intuitively.

[0232] While the controller achieves the control target, the system chattering is significantly suppressed thanks to the specially designed reaching law. Fig. 9 As shown, compared with the traditional reaching law s = -ks-ηsign(s), the nonlinear reaching law adopted in the present invention makes u x and u y The trend of change is more stable.

[0233] The present invention includes a decomposition method of the overall system, and a non-singular fast sliding mode control strategy for a quadrotor suspension system based on disturbance estimation designed for each subsystem after decomposition. This control scheme aims to achieve the quadrotor suspension system to effectively and quickly suppress the swing of the load while accurately tracking the desired target.

Claims

1. A sliding mode control method for a quadrotor suspension system based on an extended state observer, characterized in that The following steps are involved: Step 1: Construct a dynamic model of the quadrotor suspension system; Step 2: Analyze the dynamic model of the quadrotor suspension system established in step 1, obtain the virtual control torque corresponding to each state variable of the quadrotor suspension system, and decompose the entire quadrotor suspension system into multiple subsystems based on it; Step 3: Consider the various uncertain disturbances existing in the quadrotor suspension system as the extended state variables of the system, and on this basis design a nonlinear extended state observer to estimate the disturbance of the system in real time; Step 4: Design a non-singular fast sliding mode controller for each subsystem based on the disturbance estimate provided by the nonlinear extended state observer.

2. The sliding mode control method for a quadrotor suspension system based on an extended state observer according to claim 1, characterized in that: In step 1, the quadrotor suspension system includes a quadrotor drone, a suspension rope used for suspending a load, and a suspended load. The modeling process of the dynamic model of the quadrotor suspension system includes: Through the Lagrange equation and the relationship between the coordinates of the center of mass of the quadrotor drone and the center of mass of the suspended load, the system position swing angle dynamic model is obtained to describe the position of the load in space and its swing characteristics. According to the Euler equation, the relationship between the rotational torque around the axis and the attitude angular acceleration is obtained, and then the system attitude dynamics model is determined to reflect the attitude changes of the quadrotor suspension system during flight.

3. The sliding mode control method for a quadrotor suspension system based on an extended state observer according to claim 2, characterized in that: Based on the inertial coordinate system, the system position swing angle dynamic model is established. It is assumed that the center of mass position of the quadrotor drone is expressed as (x, y, z) in the inertial coordinate system, and the load position is expressed as (x p ,y p ,z p ), the relative relationship between the coordinates of the center of mass of the payload and the center of mass of the quadrotor drone is obtained as follows: Where: L represents the length of the hanging rope; α represents the swing angle projection on the yz plane, and β represents the swing angle projection on the xz plane; The system position swing angle dynamics model established using the Lagrange equation is as follows: Among them, q=[x, y, z, α, β, φ, θ, ψ] T ,[i] T is the transpose of vector[i], is the first-order derivative of q with respect to time, is the second-order derivative of q with respect to time, u is the driving force of the system in the position swing angle subsystem, here it is the lift moment u1 of the quadrotor suspension system; M(q), G(q) and b are the definitions of the model parameter matrix; The system attitude dynamics model established using the Euler equation is as follows: Among them, l is the wheelbase of the quadrotor drone; φ, θ, ψ are the angles of the drone’s counterclockwise rotation around the body’s coordinate axis; are the second-order derivatives of φ, θ, ψ with respect to time; are the first-order derivatives of φ, θ, ψ with respect to time; u φ ,u θ ,u ψ They represent the counterclockwise rotation torque of the drone around the body coordinate axis; I x ,I y ,I z They represent the UAV's counterclockwise rotational inertia around the body's coordinate axis; d φ ,d θ ,d ψ is the uncertainty disturbance of the system; The four-rotor suspension system adopts a cross structure. The speeds of the four rotors ω1, ω2, ω3, ω4 are related to the system lift moment u1 and the torque u around the three axes. φ ,u θ ,u ψ The corresponding relationship is: Among them, c T is the lift coefficient, c M is the counter torque coefficient.

4. The sliding mode control method for a quadrotor suspension system based on an extended state observer according to claim 1, characterized in that: In step 2, first, set the virtual control torque u x ,u y ,u z : Among them, M represents the mass of the drone, and m represents the mass of the payload; Then the virtual control torque u can be obtained x ,u y ,u z With the system lift moment u1 and the desired attitude angle φ d ,θ d The relationship between: The position and swing angle dynamics model of the quadrotor suspension system can be expressed as: in, Respectively represent the second-order derivatives of x, y, and z with respect to time, are the second and first order derivatives of α and β with respect to time, respectively, d x ,d y ,d z ,d α ,d β represents the uncertainty disturbance of the system, and g represents the acceleration of gravity; will u x As the main control quantity of the β subsystem, u y As the main control quantity of the α subsystem, u x Decompose to obtain the control quantity u of the x subsystem x1 and the control quantity u of the β subsystem x2 ,u y Decomposed into the control quantity u of the y subsystem y1 and the control quantity u of the α subsystem y2 , thus we get u x 、u y The expression is: Let P = [x, y] T , Q = [α, β] T ,Ω=[z,φ,θ,ψ] T , the entire quadcopter suspension system can be redefined as: in, is the second-order derivative of P, Q, Ω with respect to time; P, Q, Ω represent the state variable vectors of the translation subsystem, the swing angle subsystem, the height and attitude subsystem respectively; f(P), f(Q), f(Ω) are the model variables other than the control quantity in the translation subsystem model, the swing angle subsystem model, the height and attitude subsystem model; g(P), g(Q), g(Ω) are the control quantity coefficients of the translation subsystem model, the swing angle subsystem model, the height and attitude subsystem model respectively; u P 、u Q 、u Ω They are the control quantities of translation subsystem, swing subsystem, height and attitude subsystem respectively.

5. The sliding mode control method for a quadrotor suspension system based on an extended state observer according to claim 1, characterized in that: In step 3, η1 represents the observed state variable of the quadrotor suspension system, and d η Represents the system disturbance and serves as the expanded state of the system, let The observed state space expression of the quadrotor suspension system is expressed as: in, η2 is the first-order derivative of the system state variable with respect to time, is the second-order derivative of the system state variable with respect to time, η3 here represents the system disturbance, is the third-order expansion state of the system, where is the first-order derivative of the system disturbance with respect to time; f(η) is the model variable in the system model except the term where the control quantity is located, and g(η) is the control quantity coefficient in the system model; Let ε be the observation error and introduce the nonlinear feedback function g n (ε): Where n is the system order; The nonlinear extended state observer can be designed as: in, are the observed values ​​of η1, η2, and η3 respectively; μ1, μ2, and μ3 are the error feedback gains of the extended state observer; g1(ε), g2(ε), and g3(ε) are g n (ε) Expression when n=1,2,3.

6. The sliding mode control method for a quadrotor suspension system based on an extended state observer according to claim 1, characterized in that: In step 4, the following non-singular fast terminal sliding mode surfaces are designed for the x-β subsystem: Among them: a x 、c x 、a β 、c β 、p x ,q x 、p β ,q β All are controller parameters; e x is the deviation between the expected trajectory and the actual trajectory of the x subsystem; for e x Derivatives with respect to time; a x 、c x 、a β 、c β >0;p x ,q x 、p β ,q β are all positive odd numbers; and p x >q x , p β >q β ; Reaching law selection: in: They represent the reaching laws of x and β subsystems respectively; k x , k β , η x , η β , γ x , γ β is the controller parameter; k x ,k β ,or x ,or β >0,0<γ x <1,0<γ β <1; u x1 、u x2 Can be designed as: in: is the disturbance estimated by the observer; u x1 is the control law of the x subsystem, u x2 is the control law of the β subsystem, is the second-order derivative of the expected trajectory of the x subsystem with respect to time; f(x), g(x), f(β), g(β) are model variables, and the specific expressions are as follows; The swing angle variable of the suspended load cannot be directly controlled, but can only be indirectly controlled through the position control signal. The position control signal is expressed as: in x =in x1 +in x2 Similarly, the non-singular fast terminal sliding surface of the y-α control subsystem is: Where: s y 、s α are the sliding surfaces of the y and α subsystems respectively; a y 、c y 、a α 、c α 、p y ,q y 、p α ,q α is the controller parameter, which needs to be given in combination with the embodiment; e y is the deviation between the expected trajectory and the actual trajectory of the y subsystem; for e x Derivatives with respect to time; The reaching law is: in: They represent the reaching laws of the y and α subsystems respectively; k y , k α , η y , η α , γ y , γ α is the controller parameter; k y ,k α ,or y ,or α >0,0<γ y <1,0<γ α <1; u y1 、u y2 Can be designed as: in: is the disturbance estimated by the observer; u y1 is the control law of the y subsystem; u y2 is the control law of the α subsystem; is the second-order derivative of the expected trajectory of the y subsystem with respect to time; f(y), g(y), f(α), g(α) are model variables, and the specific expressions are as follows; The position control signal is expressed as: in y =in y1 +in y2 For the design of the remaining height and attitude subsystems, for the height z subsystem, select the sliding surface: Where: s z is the sliding surface of the designed height and attitude subsystem; a z 、c z 、p z ,q z is the controller parameter; e z is the deviation between the expected trajectory and the actual trajectory of the altitude and attitude subsystem; for e z The first derivative with respect to time; Convergence law: in: represents the reaching law of the z subsystem; k z , η z , γ z is the controller parameter; u z Designed for: Where: u Ω It is the designed height and attitude subsystem controller output; is the second-order derivative of the given height desired trajectory with respect to time; f(z) and g(z) are model variables, and the specific expressions are as follows; The controller designs of the remaining φ, θ, ψ subsystems of the altitude and attitude subsystem are similar to those of the altitude z subsystem, and their controller designs are: Among them, f(φ), f(θ), f(ψ), g(φ), g(θ), g(ψ) are model variables, and the specific expressions are as follows;

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