A robust control method for quadrotor hoisting system with anti-sway under non-ideal actuator conditions

Abstract

The present invention discloses a robust control method for eliminating the swing of a quad-rotor hoisting system under non-ideal actuator conditions, which is applied to the field of aircraft automatic control. The prior art does not take into account the influence of non-ideal actuators on system performance. The present invention first uses a first-order transfer function to model the non-ideal actuator link, and identifies the parameters in the model through experimental data. Based on the obtained model information, the present invention introduces an additional intermediate loop: a robust dynamic compensator, on the basis of the original quad-rotor position-attitude dual-loop control, to eliminate the influence of non-ideal actuators. This link can be decoupled from the original position and attitude control of the quad-rotor, so the control of the quad-rotor hoisting system and the compensation of non-ideal actuator interference can be achieved simultaneously.

Description

Technical Field

[0001] The invention belongs to the field of aircraft automatic control, and in particular relates to an aircraft anti-sway control technology. Background Art

[0002] In recent years, quadcopters have been widely used in the field of air transportation due to their low energy consumption, strong maneuverability, and the ability to achieve vertical take-off and landing. Their application scenarios include logistics transportation, earthquake relief, agricultural plant protection and other industries and fields. During transportation, using ropes to lift goods has little effect on the maneuverability of the quadcopter, which is a common practice in quadcopter air transportation. However, during the flight transportation process, the swing of the goods may cause damage to the goods themselves, and even affect the stability of the quadcopter itself, so it is necessary to control the goods to eliminate the swing. At the same time, due to the underlying attitude control and physical response, the quadcopter itself also has the problem of non-ideal actuators, and cannot fully execute the acceleration signal generated by the top-level position controller, resulting in a decrease in control performance. However, the existing anti-swing control methods such as the patent "A swing angle observation and anti-swing control system and method for a quadcopter suspension system" (authorization publication number CN115686038B) and "A quadcopter suspension anti-swing control method based on attitude compensation" (publication number CN116243721A) do not take into account the impact of non-ideal actuators on system performance. Therefore, it is very necessary to study how to achieve anti-sway robust control of the quadrotor lifting system under non-ideal actuator conditions. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a robust control method for eliminating the sway of a quad-rotor lifting system under non-ideal actuator conditions, which can simultaneously achieve trajectory tracking of the quad-rotor lifting system and eliminate the sway of suspended cargo.

[0004] The technical solution adopted by the present invention is: a robust control method for eliminating swing of a quad-rotor lifting system under non-ideal actuator conditions, and the application scenarios include: a quad-rotor unmanned aerial vehicle, cargo lifted by the quad-rotor unmanned aerial vehicle, and a control system; the cargo moves under the acceleration response control output by the quad-rotor unmanned aerial vehicle; the control system includes: an outer loop control module, an intermediate loop control module, and an inner loop control module; the inner loop control module and the physical response of the quad-rotor unmanned aerial vehicle are used together as a non-ideal actuator link;

[0005] Model the non-ideal actuator link as a first-order transfer function;

[0006] The acceleration response of the quadrotor is expressed as

[0007]

[0008] Among them, the mark represents the inverse Laplace transform; the symbol “*” represents convolution; u a is the acceleration command of the quadrotor; f a It is the equivalent acceleration disturbance caused by identification error and external disturbance;

[0009] The outer loop control module includes: a trajectory tracking control unit, a sway elimination control unit and an interference cancellation unit; the trajectory tracking control unit takes the reference system and the position information and speed information of the quadrotor as input, the sway elimination control unit takes the spatial sway angle information and rope length information of the cargo as input, and the output of the trajectory tracking control unit, the output of the sway elimination control unit and the speed information of the quadrotor as input of the interference cancellation unit; the output of the outer loop control module serves as the input of the intermediate loop control module;

[0010] The input of the intermediate loop control module also includes the acceleration of the quadrotor drone; the output of the intermediate loop control module is used as the acceleration command u of the quadrotor a .

[0011] Beneficial effects of the present invention: First, according to the characteristics of the actuator, the present invention models its complex physical mechanism as a simple first-order transfer function. Then, according to the experimental data, the parameter size in the model is identified to provide model information for subsequent control design. Based on the obtained non-ideal actuator model, the intermediate loop robust dynamic compensator is designed to enable the acceleration instructions generated by the trajectory tracking controller and the anti-sway controller designed in the outer loop to be effectively executed; the present invention has the following advantages:

[0012] (1) Characterize the complex non-ideal actuator link through a simple first-order transfer function;

[0013] (2) It can simultaneously realize the trajectory tracking of the quad-rotor lifting system and the elimination of the sway of the suspended cargo;

[0014] (3) The middle ring robust dynamic compensator proposed in the present invention can be decoupled from the outer ring and the inner ring. It is not only applicable to the quad-rotor lifting system, but can also be used in other scenarios to eliminate the influence of non-ideal actuators. Compared with the prior art, the use of a robust dynamic compensator can broaden the underlying execution bandwidth of the quad-rotor drone and achieve rapid cargo sway elimination. Figure 4 The results show that when the quadrotor lifting system has an initial swing angle λ x When (0) = 0.3 rad, the present invention can quickly stabilize the cargo swing angle and return to the original hovering position. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart for the implementation of the present invention;

[0016] Figure 2 This is the quad-rotor lifting system model targeted by the present invention;

[0017] Figure 3 The control framework proposed for the present invention;

[0018] Figure 4 This is the simulation result of the present invention. DETAILED DESCRIPTION

[0019] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.

[0020] The present invention proposes a sway elimination control algorithm for a quad-rotor lifting system under non-ideal actuator conditions, and the control algorithm is composed of an outer-loop trajectory tracking controller and an sway elimination controller, and an intermediate-loop robust dynamic compensator. The reference system is a preset desired trajectory of a quad-rotor drone, and the outer loop is used to achieve trajectory tracking of the quad-rotor drone and sway elimination of cargo; the intermediate loop achieves compensation for the effects of non-ideal actuators, and the inner-loop attitude control is executed by the firmware of the drone itself to achieve tracking of the drone attitude; the intermediate-loop robust dynamic compensator eliminates the effects of non-ideal actuators, so that the instructions given by the outer loop are effectively executed. In the present invention, the inner-loop control and the physical response of the quad-rotor drone are considered as non-ideal actuator links.

[0021] like Figure 1 As shown, the method of the present invention comprises the following steps:

[0022] S1. To achieve cargo sway control, it is first necessary to model the cargo sway. Figure 2 As shown, the model of cargo sloshing is expressed as

[0023]

[0024] Among them Figure 1 Shown x ,λ y Expressed as two swing angles of the cargo, λ x It is the rope and x s O s z s The angle, λ y For the rope at x s O s z s Projection and z s The angle of the axes; are the angular velocities of the two swing angles; is the angular acceleration of the two swing angles; L is the current length of the rope used to lift the cargo; is the rate of change of rope length; is the acceleration of the rope length change; L 0is the original length of the rope; k and c are the elastic coefficient and damping coefficient of the rope respectively; m p It is the quality of the goods; is the acceleration of the quadcopter in the three axes; g is the acceleration due to gravity; F pdx ,F pdy ,F pdz is the air resistance exerted on the cargo; the symbols S and C represent the sin(·) and cos(·) trigonometric functions respectively.

[0025] The dynamic model of the quadrotor drone can be represented by the following second-order system.

[0026]

[0027] where p = [p x p y p z ] T Indicates the position of the quadrotor drone; u c =[u cx u cy u cz ] T Indicates the acceleration of the quadrotor; f p is the unknown disturbance. Next, we model the non-ideal actuator link of the quadrotor. Considering that the actual underlying attitude control of the quadrotor drone has a very complex physical response, which is not conducive to the design of the subsequent controller, we model the non-ideal actuator link as a simple first-order transfer function to simplify the system. The transfer function is expressed as

[0028]

[0029] Where s is the variable in the complex frequency domain in the Laplace transform; K represents the passband gain; τ is the time constant of the transfer function. Therefore, we can express the acceleration response of the quadrotor as

[0030]

[0031] Among them, the mark represents the inverse Laplace transform; the symbol “*” represents convolution; u a is the acceleration command of the quadrotor; f a It is the equivalent acceleration disturbance caused by identification error and external interference.

[0032] S2. After completing the modeling of the quadcopter lifting system and the non-ideal actuator, in order to obtain the values ​​of the parameters τ and K in the non-ideal actuator model (3), it is necessary to conduct experiments to identify the parameters. Specifically, let the quadcopter fly and record the acceleration command u generated by the controller. aAnd the actual quadrotor acceleration response u c Next, without considering f a In the case of , we put it into formula (4) and get the specific values ​​of parameters τ and K by fitting method, so as to facilitate the design of controller later. In practical application, we use Matlab's System Identification Toolbox to perform parameter identification and get the specific values ​​of τ and K.

[0033] S3. Observe that the cargo sway model (1) is very complex, and simplify the model through feedback linearization. Let λ = [λ x λ y ] T , where the superscript T represents the transpose of the vector, and the output of the virtual anti-sway controller is

[0034]

[0035] Interference λ =[f λx f λy ] T ,in

[0036]

[0037] Substituting the corresponding parts of the first two lines of formula (1) with formula (5) and (6) respectively, and combining with the acceleration response (4), the quadrotor lifting system with non-ideal actuator links can be expressed as

[0038]

[0039] S4, the overall control framework of the present invention is as follows Figure 3 As shown. For the simplified cargo sloshing model, the first subformula of formula (7) is used to design a robust control algorithm based on uncertainty and disturbance estimator, which is expressed as

[0040]

[0041] where u λd It is the feedforward signal, which can be considered as zero when the swing is eliminated; K pλ =(k pλx ,k pλy ) and K dλ =(k dλx ,k dλy ) are the proportional and differential feedback gains of the anti-sway controller respectively; is the disturbance estimation signal generated by the uncertainty and disturbance estimator UDE, which represents the disturbance f acting on the swing angle. λ Estimates.

[0042] The UDE is designed in the frequency domain as

[0043]

[0044] F λ (s) variable f λ The capital form of represents its representation in the frequency domain, Λ(s) is the frequency domain representation of λ; U λ (s) is u λ The frequency domain representation of . In formula (9) is a strictly regular filter designed as

[0045]

[0046] Where T λx ,T λy is an adjustable parameter of UDE, which is used to determine the bandwidth of the filter. Substituting formula (8) into U in formula (9) λ (s), get

[0047]

[0048] Combining like terms on both sides gives

[0049]

[0050] Among them I 2 =diag(1,1) represents a two-dimensional unit vector. The time domain expression corresponding to formula (11) is

[0051]

[0052] Where T λ =diag(T λx ,T λy ).

[0053] After completing the design of the swing control (8), according to formula (5), use u λx ,u λy express The anti-sway acceleration on the X-axis and Y-axis of the quadrotor can be solved Let the anti-sway acceleration on the Z axis be zero, and the anti-sway acceleration on the three axes can be obtained as follows:

[0054]

[0055] Indicates how much acceleration the quadrotor drone should produce if the cargo sway is to be eliminated.

[0056] S5. Next, we design the quadrotor trajectory tracking controller.

[0057]

[0058] where u pd is the feedforward signal, e p =p d -p is the trajectory tracking error, is the speed tracking error, p d =[p dx p dy p dz ] T is the desired quadrotor trajectory, is the expected speed K of the quadrotor drone pp =diag(k ppx ,k ppy ,k ppz ),K dp =diag(k dpx ,k dpy ,k dpz ) represent the proportional and derivative feedback gains of the trajectory tracking controller.

[0059] In addition, in order to compensate for model uncertainty and external time-varying disturbances, an additional UDE is added to the outer loop. Finally, the expression of the outer loop controller is obtained as follows:

[0060]

[0061] in represents the disturbance f generated by UDE acting on the movement of the quadrotor in three-dimensional space p The estimate of can be expressed in the frequency domain as

[0062]

[0063] P(s) is the representation of the position p of the quadrotor in the frequency domain;

[0064] in

[0065]

[0066] And T px ,T py ,T pz >0 is the parameter of UDE. Substituting formula (16) into U in (17) cd (s), we can get

[0067]

[0068] Combining like terms on both sides gives

[0069]

[0070] The corresponding time domain expression is

[0071]

[0072] S6. After completing the design of the outer loop controller, proceed with the design of the intermediate loop robust dynamic compensator.

[0073]

[0074] where u ad is a feedforward term used to track external signals; K pa e c is the feedback term, which is used to improve the stability margin of the system; is the disturbance estimation term generated by UDE, which is used to improve the robustness of the controller. In addition, the combination of feedforward and feedback terms u a0 It is called the nominal controller, K pa =(k pax ,k pay ,k paz ) represents the proportional feedback gain of the robust dynamic compensator, e c is the error in the acceleration response of the quadrotor.

[0075] Considering the actual acceleration response u of the quadrotor c Cannot be measured directly, use interference estimation signal To replace the interference f a , the acceleration response of the quadrotor is estimated as

[0076]

[0077] The acceleration response error of the quadrotor can be expressed as Feedforward signal u ad Can be

[0078]

[0079] Calculated. UDE estimation term Indicates the disturbance f on the system in the actuator link a The estimate is designed to

[0080]

[0081] in for Represented in the frequency domain,

[0082]

[0083] And T ax ,T ay ,T az >0 is an adjustable parameter of UDE. Substituting formula (22) into (25) U a (s), we get The expression is

[0084]

[0085] Combining like terms on both sides gives

[0086]

[0087] The corresponding time domain expression is

[0088]

[0089] Where T a =diag(T ax ,T ay ,T az ).

[0090] S7. After completing the control design, analyze the stability of the system using the Lyapunov method

[0091] The reference system of the quadrotor can be expressed as First consider the x-axis, y-axis and two swing angles λ x ,λ y In order to distinguish the actual control signal acting on the system from the virtual control input in the design process, we λ and u p A superscript “*” is added to indicate the actual control signal.

[0092]

[0093] In formula (30), Substitute u into (7) respectively λx ,u λy ,u px ,u py , and subtract it from the reference system to obtain the error response of the outer loop system:

[0094]

[0095] Since we want to prove the stability of the system itself, we ignore the terms related to external interference here, and formula (31) can be transformed into

[0096]

[0097] Considering the strong nonlinearity of the error system, the system (32) is simplified to

[0098] g i (X)=0,i∈{1,2,3,4} (33)

[0099] Where X = [X 1 ,X 2 ,X 3 ] T ,X 1 =[e px ,e py ,λ x ,λ y ] T , Next, Taylor expansion is performed on formula (33) at the equilibrium point X = 0 and the high-order terms are removed. The error system obtained satisfies

[0100]

[0101] in represents the first-order partial derivative operation of the row vector. Substituting formula (32) into (34) and writing it in the form of state space, we get

[0102]

[0103] in

[0104]

[0105] Observed Formula (35) can be reduced to

[0106]

[0107] in

[0108]

[0109] In order to verify the stability of the outer loop system, the Lyapunov function is designed as

[0110] V 1 =e 3 T P 1 e 3 +e 4 T P 2e 4 (40)

[0111] Where P 1 ,P 2 Defined as

[0112]

[0113] is in k ppx +k pλy ,k ppy +k pλx ,k dpx +k dλy ,k dpy +k dλx >0. Therefore, the function V 1 is also positive definite. Derivative (40) with respect to time along (38) yields

[0114]

[0115] Substitute e in formula (42) 3 、e 4 , P 1 , P 2 , N 11 、N 22 Substituting formula (36), (39), (41) respectively, we get

[0116]

[0117] is a semi-negative definite matrix. Therefore, we can get e 3 ,e 4 is bounded. Considering that all variables are bounded, the Russell invariant set theorem gives

[0118]

[0119] For formula (38) Regarding the time derivative, we can get

[0120]

[0121] is bounded because its components are bounded.

[0122] According to Barbara's lemma, because and is bounded. Finally, It can be concluded that e px ,e py →0. At the same time, we can also get λ x ,λ yare stable because they and e px ,e py There is a proportional relationship between them.

[0123] Next, we prove the stability of the intermediate ring. Substituting formula (22) into the third sub-formula in (7), we can get the error system of the intermediate ring:

[0124]

[0125] To prove the stability of the intermediate ring system, we remove the external signal get

[0126]

[0127] Choose a non-negative Lyapunov function V 2 for

[0128]

[0129] V 2 Taking the derivative about time, we get

[0130]

[0131] In formula (46), Substituting into (49) we get

[0132]

[0133] Among them, K,τ are positive constants. Therefore, it can be proved that the intermediate ring system is in k pax ,k pay >-1 / K is asymptotically stable.

[0134] At this point, after completing the stability proof of the outer loop and the middle loop, in order to prove the stability of the entire system, define the Lyapunov function

[0135] V=V 1 +V 2 (51)

[0136] According to the above analysis, we can conclude that the whole system is stable. Similarly, the stability of the Z axis can also be proved by the same steps.

[0137] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A robust control method for eliminating sway in a quadrotor hoisting system under non-ideal actuator conditions, characterized in that: Application scenarios include: quad-rotor drones, cargo lifted by quad-rotor drones, and control systems; cargo moves under the control of the acceleration response output by the quad-rotor drone; the control system includes: an outer loop control module, an intermediate loop control module, and an inner loop control module; the inner loop control module and the physical response of the quad-rotor drone are used together as a non-ideal actuator link; The non-ideal actuator link is modeled as a first-order transfer function H(s); Then the acceleration response output by the quadrotor drone is expressed as: Among them, the mark represents the inverse Laplace transform; the symbol "*" represents convolution; u a is the acceleration command of the quadrotor drone; f a It is the equivalent acceleration disturbance caused by identification error and external disturbance; The outer loop control module includes: a trajectory tracking control unit, a sway elimination control unit and an interference cancellation unit; the trajectory tracking control unit takes the reference system and the position information and speed information of the quad-rotor drone as input, the sway elimination control unit takes the spatial sway angle information and rope length information of the cargo as input, and the output of the trajectory tracking control unit, the output of the sway elimination control unit and the speed information of the quad-rotor drone as input of the interference cancellation unit; the output of the outer loop control module serves as the input of the intermediate loop control module; The outer loop control module is designed as follows: in, It represents the external interference f acting on the position loop generated by the interference cancellation unit p Estimation of u p represents the output of the trajectory tracking control unit; Indicates the anti-sway acceleration in three axes; The trajectory tracking control unit is designed as: Among them, u pd is the feedforward signal, e p is the trajectory tracking error, is the speed tracking error, K pp ,K dp represents feedback gain; The interference cancellation unit is designed in the frequency domain as Where s is the variable in the complex frequency domain in Laplace transform, F λ (s) Representative Represented in the frequency domain, is the interference estimation signal generated by the interference cancellation unit, Λ(s) is the frequency domain representation of λ, and U λ (s) is u λ The frequency domain representation of is a strictly regular filter; The anti-sway control unit is designed as follows: Among them, u λd It is the feedforward signal, which is considered to be zero when the swing is eliminated; K pλ and K dλ are the proportional and differential feedback gains of the controller, respectively, λ=[λ x λ y ] T , the superscript T represents the transpose of the vector, λ x is the angle between the rope used to lift the cargo and the xOz plane, λ y is the angle between the projection of the rope in xOz and the z-axis; The input of the intermediate loop control module also includes the acceleration of the quadrotor drone; the output of the intermediate loop control module is used as the acceleration command u of the quadrotor drone. a ; The intermediate ring control module is designed as follows: Among them, u ad is a feedforward term used to track external signals; K pa e c is the feedback term, K pa is the feedback gain, e c is the error in the acceleration response of the quadrotor; is the interference estimation term generated by the interference cancellation unit; the combination of feedforward and feedback terms u a0 It is called the nominal controller.

2. According to claim 1, a robust control method for eliminating sway of a quadrotor hoisting system under non-ideal actuator conditions is characterized in that: The transfer function is expressed as Where s is the transformation parameter of the Laplace transform; K represents the passband gain; and τ is the time constant of the transfer function.

3. The method for controlling the sway resistance of a quadrotor hoisting system under non-ideal actuator conditions according to claim 2 is characterized in that: The process of determining the values ​​of the parameters τ and K in the transfer function is as follows: let the quadrotor drone fly and record the acceleration command u of the quadrotor a And the actual quadrotor acceleration response u c ; Without considering f a In the case of The specific values ​​of parameters τ and K are obtained by fitting method.

4. The method for controlling the sway resistance of a quadrotor hoisting system under non-ideal actuator conditions according to claim 3 is characterized in that: The acceleration response error of the quadrotor is expressed as Represents an estimate of the acceleration response of the quadrotor.

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