Anti-swing control method for tower crane system based on composite integral complementary sliding mode control

Abstract

The application discloses a tower crane system anti-swing control method based on composite integral complementary sliding mode control, and belongs to the technical field of tower cranes. Step 1, defining a tower crane system error variable: used to represent the difference between the actual operation state of the tower crane and the ideal state, so as to realize the positioning anti-swing control target; step 2, constructing a composite integral complementary sliding mode controller: according to the tower crane system error variable defined in step 1, fully considering the under-actuated characteristics of the tower crane system, a composite integral complementary sliding mode controller is constructed, which can suppress the load swing of the tower crane system and maintain the stability and control accuracy of the system; step 3, controlling the operation of the tower crane system: using the composite integral complementary sliding mode controller constructed in step 2, the operation state of the tower crane system is controlled in real time, and the controller can realize the smooth and accurate handling of the tower crane load according to the current load, position and speed state information of the tower crane, and effectively suppress the swing of the load.

Description

Technical Field

[0001] This invention belongs to the field of tower crane technology, and in particular, it proposes an anti-sway control method based on composite integral complementary sliding mode control to address the problem of load sway control in tower cranes. Background Technology

[0002] In recent years, the field of intelligent manufacturing has experienced strong growth, achieving remarkable results not only in technological innovation but also demonstrating enormous potential in industrial applications. As a crucial piece of equipment in infrastructure construction, the development of intelligent control technology for tower cranes has attracted particular attention.

[0003] Driven by the trends of integration, automation, and green development, the intelligent control technology of tower cranes is constantly being upgraded. To improve construction efficiency and ensure operational safety, anti-sway control technology has become a research and application hotspot. Currently, research in this field mainly focuses on various control strategies such as PID control, adaptive control, fuzzy control, and sliding mode control. Among them, sliding mode control, with its simple structure, strong robustness, and ease of engineering implementation, has received widespread attention from the industry.

[0004] However, the underactuated nature of tower cranes introduces additional complexity to anti-sway control. Since the underactuated state cannot be directly controlled by the actuators but must be indirectly achieved through a series of complex coupling relationships, this undoubtedly increases the difficulty of designing the control algorithm. Furthermore, tower cranes operate in variable environments, often facing interference from external factors such as wind, temperature changes, and uneven ground. These uncertainties further exacerbate hook sway, making precise control even more challenging. Summary of the Invention

[0005] The purpose of this invention is to provide an anti-sway control method based on composite integral complementary sliding mode control, so as to solve the shortcomings of existing controllers in terms of control performance.

[0006] To achieve the above objectives, the following technical solution is adopted: The method of the present invention includes the following steps:

[0007] Step 1, define the tower crane system error variable: used to characterize the difference between the actual operating state and the ideal state of the tower crane, so as to achieve the positioning and anti-sway control target;

[0008] Step 2, Construct a composite integral complementary sliding mode controller: Based on the tower crane system error variables defined in Step 1, and taking into full account the underactuated characteristics of the tower crane system, construct a composite integral complementary sliding mode controller. This controller effectively suppresses the load swing of the tower crane system and can maintain the stability and control accuracy of the system even when faced with complex and variable loads and external environmental disturbances.

[0009] Step 3: Control the tower crane system operation: Using the composite sliding mode controller constructed in Step 2, the operating status of the tower crane system is controlled in real time. Based on the tower crane's current load, position, speed, and other status information, the controller enables smooth and precise handling of the tower crane load, while effectively suppressing load swaying, thus improving the safety and efficiency of tower crane operations.

[0010] Furthermore, in step 1, considering a 4-DOF tower crane system with model uncertainties and external disturbances, according to the Euler-Lagrange principle, the system's dynamic equation is:

[0011]

[0012] in It is a 4-dimensional column vector. Let θ(t) be the rotation angle of the tower crane system boom, x(t) be the displacement of the trolley, θ1(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction, and θ2(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction; M(q)∈R 4×4 It is a 4-dimensional positive definite inertial matrix; This is the matrix of Coriolis force and centrifugal force; This serves as the system control input; furthermore, the system's uncertainties and external disturbances are represented as...

[0013] Tower crane systems have the following properties:

[0014] Property 1: The inertia matrix M(q) is a symmetric positive definite matrix with two positive constants δ. m and δ M Make

[0015]

[0016] Where I is a 4-dimensional identity matrix.

[0017] Property 2: For a tower crane system, there exist positive constants c and ρ such that

[0018]

[0019] (1) By simplifying the derivation, we can obtain:

[0020]

[0021] in Represents a known nonlinear term. Represents aggregate uncertainty. Indicates system control input, Given a nonlinear term, and

[0022]

[0023] Define error variables

[0024]

[0025] Where i = 1, 2, 3, 4, q id Let q be the desired position for the tower crane's operation. Without loss of generality, since it is desirable to minimize the load swing angle during tower crane operation, therefore, q 3d =q 4d =0.

[0026] Furthermore, in step 2, the integral complementary sliding surface is defined as:

[0027]

[0028] Where λ is a positive parameter of the sliding surface.

[0029] The composite sliding surface is defined as:

[0030]

[0031] in It is a composite complementary sliding surface, and α1 and α2 are adjustable parameters.

[0032] Setting up a composite integral complementary sliding mode controller:

[0033]

[0034] in, It is a nonlinear control function. and Φ represents the known nonlinear term in the system, sat(·) is the saturation function, K is the controller parameter, and Φ is the boundary layer parameter.

[0035] Differentiating the composite sliding surface (8), we get

[0036]

[0037] Combining (4) and (7), we get

[0038]

[0039] Furthermore, complementary sliding modes S and S c The derivatives are respectively

[0040]

[0041] The following relationship is derived between the coupled sliding surfaces.

[0042]

[0043] From (4), (6)

[0044]

[0045] in, To account for lumped uncertainty and external disturbances, assume There exists an upper bound, that is... D is a positive constant.

[0046] Substituting (9) and (14) into (12) gives us

[0047]

[0048] The Lyapunov candidate function is selected as follows:

[0049]

[0050] Differentiating the Lyapunov candidate function V along the system's trajectory yields:

[0051]

[0052] Choosing K > D, according to the definition of the Lyapunov equation (16) and equation (17), all signals in the tower crane system are bounded, and the composite integral complementary sliding surfaces S and S c It will converge to 0 within a finite time T.

[0053] Therefore, when t > T, S = 0. From (8) we get

[0054]

[0055] make x2 = e4, x5 = e1, but

[0056]

[0057] It can be rewritten in a compact form in

[0058]

[0059]

[0060] Based on (6) and (19), it is not difficult to find

[0061]

[0062] Furthermore, when t≥T, the complementary sliding surfaces S and S of the composite integral... c Converging to 0, the controller (9) simplifies to

[0063] u(t) = -h′ -1 H(e′,t) (24)

[0064] Choose appropriate controller parameters α1 and λ such that matrix A is Hurwitz. Therefore, there exists a unique positive definite matrix P that satisfies... Here, Q is a positive definite symmetric matrix. For further analysis, a Lyapunov candidate function is selected.

[0065]

[0066] The derivative of V′ along the system's trajectory can be expressed as:

[0067]

[0068] Q has a minimum eigenvalue σ. m Therefore, based on properties 1 and 2 of the tower crane system, and (23), (24), it can be deduced that:

[0069]

[0070] in, Given positive parameters, in addition, y=Ω1||X|| 2 +Ω2||X||+D is a quadratic function with opening upwards in ||X||, therefore, when the initial value of ||X|| is in the neighborhood...

[0071]

[0072] At that time, Furthermore, ||X|| will decay over time until ||X|| = 0, that is... Therefore, it can be concluded that

[0073]

[0074] Right now Therefore, from (18),

[0075] Similarly, through a similar analysis of the composite sliding surface S2, it can be concluded that... This completes the proof that all error states of the tower crane system are asymptotically stable.

[0076] In step 3, appropriate parameters for the composite integral complementary sliding mode controller are selected so that the invented composite integral complementary sliding mode controller can control the smooth and precise handling of the tower crane load, while effectively suppressing the swaying of the load.

[0077] The parameters of the composite integral complementary sliding mode controller include:

[0078] (1) λ in formula (7) is used to adjust the convergence speed of the sliding surface. The larger λ is, the faster the convergence speed of the sliding surface.

[0079] (2) In formula (8), α1 and α2 are used to adjust the weight of the driving sliding surface and the underdriven sliding surface in the controller to control the suppression effect on load swing. The larger α1 and α2 are, the more obvious the suppression of load swing angle is, but too large will cause the trolley and cantilever to shake. A balance needs to be struck between them.

[0080] (3) K and Φ in formula (9) are used to suppress the influence of external disturbances on the system. K should be slightly larger than the upper limit of the external disturbances of the system. Φ is the boundary layer thickness of the composite integral complementary sliding surface, which is a small positive parameter. The thicker the boundary layer, the less sensitive it is to disturbances, but the positioning accuracy will be worse. There is a trade-off between the two.

[0081] All parameters are coupled and need to be adjusted according to the actual situation and running results.

[0082] Due to the adoption of the above technical solution, the technical effects achieved by the present invention are as follows:

[0083] This invention proposes an anti-sway control method for tower crane systems based on composite integral complementary sliding mode, which improves the accuracy and stability of the controller without any model simplification or transformation.

[0084] The composite sliding surface simultaneously incorporates both driven and underdriven states, improving the coupling between the driven and underdriven states and enhancing the controller's control over the underdriven state.

[0085] Integral complementary sliding surfaces not only avoid the arrival phase of the sliding surface, but also, by introducing complementary functions and constructing complementary sliding surfaces, make the motion of the system on the sliding surface smoother, thereby reducing chattering and improving the control accuracy of the system.

[0086] The invention is applicable to a class of underactuated systems, such as various crane systems, inverted pendulum systems, and flexible robotic arm systems, and can be easily extended to other systems. Attached Figure Description

[0087] Figure 1 This is a flowchart of the control method of the present invention;

[0088] Figure 2 This is a structural schematic diagram of a tower crane system;

[0089] Figure 3 This is a control block diagram of the present invention;

[0090] Figure 4 The figure shows the experimental results comparing the present invention with other inventions.

[0091] Figure 5 The figure shows the experimental results of the robustness test of the present invention. Detailed Implementation

[0092] The present invention will be further described below with reference to the accompanying drawings:

[0093] like Figure 1-5 As shown, the method of the present invention includes the following steps:

[0094] Step 1, define the tower crane system error variable: used to characterize the difference between the actual operating state and the ideal state of the tower crane, so as to achieve the positioning and anti-sway control target;

[0095] Consider a 4-DOF tower crane system with model uncertainties and external disturbances. According to the Euler-Lagrange principle, the dynamic equation of the system is:

[0096]

[0097] in Let θ(t) be the rotation angle of the tower crane system boom, x(t) be the displacement of the trolley, θ1(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction, and θ2(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction; M(q)∈R 4×4 The system's positive definite inertia matrix; This is the vector of Coriolis force and centrifugal force; This serves as the system control input; furthermore, the system's uncertainties and external disturbances are represented as...

[0098] Tower crane systems have the following properties:

[0099] Property 1: The inertia matrix M(q) is a symmetric positive definite matrix with two positive constants δ. m and δ M Make

[0100]

[0101] Where I is a 4th-order identity matrix.

[0102] Property 2: For a tower crane system, there exist positive constants c and ρ such that

[0103]

[0104] (1) By simplifying the derivation, we can obtain:

[0105]

[0106] in Represents a known nonlinear term. Represents aggregate uncertainty. Indicates system control input, Given a nonlinear term, and

[0107]

[0108] Define error variables

[0109]

[0110] Where i = 1, 2, 3, 4, q id Let q be the desired position for the tower crane's operation. Without loss of generality, since it is desirable to minimize the load swing angle during tower crane operation, therefore, q 3d =q 4d =0,q 1d q represents the desired angle for the cantilever rotation operation. 2d q represents the desired angle for the cantilever rotation operation. 3d and q 4d This refers to the desired offset angle of the load relative to the centerline of the tower crane boom in the horizontal direction, both front-back and left-right.

[0111] Step 2, Construct a composite integral complementary sliding mode controller: Based on the tower crane system error variables defined in Step 1, and taking into full account the underactuated characteristics of the tower crane system, construct a composite integral complementary sliding mode controller. This controller effectively suppresses the load swing of the tower crane system and can maintain the stability and control accuracy of the system even when faced with complex and variable loads and external environmental disturbances.

[0112] The integral complementary sliding surface is defined as:

[0113]

[0114] Where λ is a positive parameter of the sliding surface;

[0115] The composite sliding surface is defined as:

[0116]

[0117] in It is a composite complementary sliding surface, and α1 and α2 are adjustable parameters.

[0118] Setting up a composite integral complementary sliding mode controller:

[0119]

[0120] in, It is a nonlinear control function. and Φ represents the known nonlinear term in the system, sat(·) is the saturation function, K is the controller parameter, and Φ is the boundary layer parameter.

[0121] Differentiating the composite sliding surface (8), we get

[0122]

[0123] Combining (4) and (7), we get

[0124]

[0125] Furthermore, complementary sliding modes S and S c The derivatives are respectively

[0126]

[0127] The following relationship is derived between the coupled sliding surfaces.

[0128]

[0129] From (4), (6)

[0130]

[0131] in, To account for lumped uncertainty and external disturbances, assume There exists an upper bound, that is... D is a positive constant.

[0132] Substituting (9) and (14) into (12) gives us

[0133]

[0134] The Lyapunov candidate function is selected as follows:

[0135]

[0136] Differentiating the Lyapunov candidate function V along the system's trajectory yields:

[0137]

[0138] Choosing K > D, according to the definition of the Lyapunov equation (16) and equation (17), all signals in the tower crane system are bounded, and the composite integral complementary sliding surfaces S and S c It will converge to 0 within a finite time T.

[0139] Therefore, when t > T, S = 0. From (8) we get

[0140]

[0141] make x2 = e4, x5 = e1, but

[0142]

[0143] It can be rewritten in a compact form in

[0144]

[0145] Based on (6) and (19), it is not difficult to find

[0146]

[0147] Furthermore, when t≥T, the complementary sliding surfaces S and S of the composite integral... c Converging to 0, the controller (9) simplifies to

[0148] u(t) = -h′ -1 H(e′,t) (24)

[0149] Choose appropriate controller parameters α1 and λ such that matrix A is Hurwitz. Therefore, there exists a unique positive definite matrix P that satisfies... Here, Q is a positive definite symmetric matrix. For further analysis, a Lyapunov candidate function is selected.

[0150]

[0151] The derivative of V′ along the system's trajectory can be expressed as:

[0152]

[0153] Q has a minimum eigenvalue σ. m Therefore, based on properties 1 and 2 of the tower crane system, and (23), (24), it can be deduced that:

[0154]

[0155] in, Given positive parameters, in addition, y=Ω1||X|| 2 +Ω2||X||+D is a quadratic function with opening upwards in ||X||, therefore, when the initial value of ||X|| is in the neighborhood...

[0156]

[0157] At that time, Furthermore, ||X|| will decay over time until ||X|| = 0, that is... Therefore, it can be concluded that

[0158]

[0159] Right now Therefore, from (18),

[0160] Similarly, through a similar analysis of the composite sliding surface S2, it can be concluded that... This completes the proof that all error states of the tower crane system are asymptotically stable.

[0161] Step 3: Control the tower crane system operation: Using the composite sliding mode controller constructed in Step 2, the operating status of the tower crane system is controlled in real time. Based on the tower crane's current load, position, speed, and other status information, the controller enables smooth and precise handling of the tower crane load, while effectively suppressing load swaying, thus improving the safety and efficiency of tower crane operations.

[0162] The parameters of the composite integral complementary sliding mode controller include:

[0163] (1) λ in formula (7) is used to adjust the convergence speed of the sliding surface. The larger λ is, the faster the convergence speed of the sliding surface.

[0164] (2) In formula (8), α1 and α2 are used to adjust the weight of the driving sliding surface and the underdriven sliding surface in the controller to control the suppression effect on load swing. The larger α1 and α2 are, the more obvious the suppression of load swing angle is, but too large will cause the trolley and cantilever to shake. A balance needs to be struck between them.

[0165] (3) K and Φ in formula (9) are used to suppress the influence of external disturbances on the system. K should be slightly larger than the upper limit of the external disturbances of the system. Φ is the boundary layer thickness of the composite integral complementary sliding surface, which is a small positive parameter. The thicker the boundary layer, the less sensitive it is to disturbances, but the positioning accuracy will be worse. There is a trade-off between the two.

[0166] All parameters are coupled and need to be adjusted according to the actual situation and running results.

[0167] This invention eliminates the need for model simplification or transformation, thus improving controller accuracy and stability. The composite sliding surface integrates driven and underactuated states, strengthening their coupling and enhancing the controller's control over underactuated states. The integral complementary sliding surface design avoids arrival phases, and the complementary function makes system motion smoother, reducing chattering and improving control accuracy. This method is applicable to underactuated systems such as cranes, inverted pendulums, and flexible robotic arms, and is easily extended to other systems.

[0168] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for anti-sway control of a tower crane system based on composite integral complementary sliding mode control, characterized in that... Includes the following steps: Step 1, define the tower crane system error variable: used to characterize the difference between the actual operating state and the ideal state of the tower crane, in order to achieve the positioning and anti-sway control target; in Step 1, the position error variable of the 4-DOF tower crane system is defined. e i (t)=q i (t)-q id (6) Among them, e i (t) represents the position error variable, t represents the system running time, and i = 1, 2, 3, 4 represents the four degrees of freedom. Represents a 4-dimensional column vector. Let θ(t) be the rotation angle of the tower crane system boom, x(t) be the displacement of the trolley, θ1(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction, and θ2(t) be the angle of offset of the load relative to the centerline of the tower crane boom in the horizontal direction; q 1d q represents the desired angle for the cantilever rotation operation. 2d q represents the desired angle for the cantilever rotation operation. 3d and q 4d The desired offset angle of the load relative to the centerline of the tower crane boom in the horizontal direction (front-back and left-right) is set as: q 3d =q 4d =0; Step 2, Constructing a Composite Integral Complementary Sliding Mode Controller: Based on the tower crane system error variables defined in Step 1, and fully considering the underactuated characteristics of the tower crane system, a composite integral complementary sliding mode controller is constructed. This controller suppresses the load sway of the tower crane system, maintaining system stability and control accuracy. The integral complementary sliding surface in Step 2 is defined as follows: Where λ is a positive parameter of the sliding surface; In step 2, the composite sliding surface is defined as: Where S = [S1, S2] T S c =[S c1 ,S c2 ] T For composite complementary sliding surfaces, α1 and α2 are adjustable parameters; Setting up a composite integral complementary sliding mode controller: Where, e′=[e1+α1e4,e2+α2e3] T ∈R 2 , The nonlinear control function is f′=[f1+α1f4,f2+α2f3]. T ∈R 2 and h′ -1 =[(h1+α1h4) -1 ,(2+α2h3) -1 ] T ∈R 2×2 Here, is the known nonlinear term in the system, sat(·) is the saturation function, K is the controller parameter, and Φ is the boundary layer parameter; Step 3, control the operation of the tower crane system: using the composite integral complementary sliding mode controller constructed in step 2, the operating status of the tower crane system is controlled in real time. The controller realizes the smooth and precise handling of the tower crane load based on the current load, position and speed status information of the tower crane, while effectively suppressing the swaying of the load.

2. The anti-sway control method for a tower crane system based on composite integral complementary sliding mode control according to claim 1, characterized in that: In step 2, Lyapunov candidate functions are selected: Differentiating the Lyapunov candidate function V along the system's trajectory yields: Choosing K > D, where D > 0 is the upper bound of the unknown disturbance, then according to the definition of the Lyapunov equation (16) and equation (17), all signals in the tower crane system are bounded, and the composite integral complementary sliding surfaces S and S c It will converge to 0 within a finite time T.

3. The anti-sway control method for a tower crane system based on composite integral complementary sliding mode control according to claim 2, characterized in that: In step 2, the composite integral complementary sliding surfaces S and S c After convergence to 0, a Lyapunov candidate function is selected. V′=X T PX (25) The derivative of V′ along the system's trajectory is expressed as: Where X represents the system state and A is the system state matrix, we choose appropriate parameters α1 and λ such that there exists a unique positive definite matrix P satisfying PA+A T P = -Q, therefore when the initial value of ||X|| is in the neighborhood At that time, Furthermore, ||X|| will decay over time until ||X|| = 0, that is... Therefore, it is concluded that Therefore, all position error states of the system are asymptotically stable.

4. The anti-sway control method for a tower crane system based on composite integral complementary sliding mode control according to claim 1, characterized in that: In step 3, appropriate parameters for the composite integral complementary sliding mode controller are selected so that the composite integral complementary sliding mode controller can control the smooth and precise handling of the tower crane load and suppress the swaying of the load. The parameters of the composite integral complementary sliding mode controller include: the positive parameter λ of the sliding surface, the adjustable parameters α1 and α2, the controller parameter K and the boundary layer parameter Φ. There are coupling characteristics between all parameters, and they need to be adjusted according to the actual situation and the operating effect.

5. The anti-sway control method for a tower crane system based on composite integral complementary sliding mode control according to claim 4, characterized in that: λ is used to adjust the convergence speed of the sliding surface. The larger λ is, the faster the convergence speed of the sliding surface. α1 and α2 are used to adjust the weights of the driving and underactuated sliding surfaces in the controller to control the suppression effect on load sway. The larger α1 and α2 are, the more obvious the suppression of load sway angle. However, if they are too large, it will cause the trolley and cantilever to shake. A trade-off needs to be made. K and Φ are used to suppress the influence of external disturbances on the system. K should be slightly larger than the upper limit of the external disturbance of the system. Φ is the boundary layer thickness of the composite integral complementary sliding surface. It is a small positive parameter. The thicker the boundary layer, the less sensitive it is to disturbances, but the positioning accuracy will be worse. There is a trade-off between the two.

6. A computer device, characterized in that: The computer device includes a memory and a processor. The memory stores a computer program. When the computer program is executed by the processor, the processor performs the anti-sway control method for a tower crane system based on composite integral complementary sliding mode as described in any one of claims 1-5.

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