Seven-degree-of-freedom tower crane adaptive sliding mode control method and system

Abstract

The application discloses a seven-freedom-degree tower crane adaptive sliding mode control method and system, wherein the method comprises the following steps: establishing an underactuated seven-freedom-degree tower crane dynamic model; the model comprises three driving state variables and four non-driving state variables; the three driving state variables comprise trolley displacement, boom rotation angle and sling length; the four non-driving state variables comprise the swing angle of a hook and a load in a three-dimensional space; the dynamic model is subjected to approximate linearization processing to obtain a dynamic equation; the dynamic equation is optimized into a full-drive system model; state data of the seven-freedom-degree tower crane are acquired; a dynamic sliding mode surface is constructed based on an error signal; an online update rate is determined based on time delay estimation; an adaptive sliding mode controller is constructed based on the full-drive system model, the state data, the dynamic sliding mode surface and the online update rate; and the seven-freedom-degree tower crane is positioned and swing is eliminated based on the adaptive sliding mode controller.

Description

Technical Field

[0001] This invention relates to the field of tower crane control technology, and in particular to an adaptive sliding mode control method and system for a seven-degree-of-freedom tower crane. Background Technology

[0002] The statements in this section merely refer to the background art related to this invention and do not necessarily constitute prior art.

[0003] Tower cranes are lifting equipment widely used in construction sites, factories, docks, and other locations. Currently, the vast majority of tower cranes still rely on traditional manual operation, and efficient and precise lifting places high demands on the technical skills of the operators. Automatic control methods can help tower cranes achieve efficient and precise lifting operations while reducing reliance on operator skill levels. This not only improves work efficiency but also reduces safety accidents caused by human factors. Therefore, research on automatic control methods for tower cranes has significant theoretical research value and practical application value.

[0004] As a typical multi-input multi-output and underactuated electromechanical system, the control inputs of a tower crane are less than the system's output degrees of freedom. When lifting large structural loads during trolley movement and boom rotation, the hook and load exhibit two-stage oscillations in three-dimensional space, displaying complex double-spherical pendulum characteristics. To improve operational efficiency, the length of the lifting rope also changes during trolley movement and boom rotation to complete the load lifting operation. At this point, the tower crane has three control inputs (trolley controller, boom controller, and lifting controller) and seven output degrees of freedom (trolley displacement, boom rotation angle, lifting rope length, and the swing angle of the hook and load in three-dimensional space). Compared to existing simplified tower crane models, the dynamic modeling and anti-sway controller design of a seven-DOF tower crane are more challenging.

[0005] In recent years, the research on automatic control methods for tower cranes has become a hot topic. Domestic scholars have proposed various control methods for tower crane systems. Based on whether or not system motion state feedback signals are included, these methods can be divided into open-loop control and closed-loop control. Open-loop control methods include trajectory planning, input shaping, and smoothers. Closed-loop control methods include neural network control, adaptive control, energy-analysis-based (EAB) control, active disturbance rejection control, and model predictive control.

[0006] The inventors discovered that although tower crane control methods have made significant progress and development, some problems still need to be solved. Existing tower crane control methods consider at most six output degrees of freedom (i.e., trolley displacement, boom slewing angle, and the swing angle of the hook and load in three-dimensional space), while neglecting changes in the length of the lifting rope. The automatic positioning and anti-sway control method for seven-degree-of-freedom tower cranes with variable rope length and double-spherical characteristics needs further improvement. Furthermore, most existing control methods rely on precise tower crane model parameters, neglecting factors such as unknown model parameters and unmodeled dynamics, which seriously affects the accuracy of tower crane operation. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides an adaptive sliding mode control method and system for a seven-degree-of-freedom tower crane. First, a seven-degree-of-freedom dynamic model considering boom rotation, trolley motion, rope length variation, and load / hook spherical oscillation in three-dimensional space is established using the Lagrangian method. Then, a dynamic sliding mode surface is constructed by analyzing the nonlinear coupling relationship between the non-driven and driven states. Time delay estimation techniques are employed to adaptively control unknown system parameters online. For a seven-degree-of-freedom tower crane system with uncertain parameters, an adaptive sliding mode control method based on time delay estimation is designed. The stability of the closed-loop control system is demonstrated in detail using Lyapunov stability theory. Finally, experiments verify that the designed adaptive sliding mode controller has better positioning and anti-sway control performance compared to existing technologies.

[0008] On the one hand, an adaptive sliding mode control method for a seven-degree-of-freedom tower crane is provided, including:

[0009] A dynamic model of an underactuated seven-degree-of-freedom tower crane is established. The model includes three driven state variables and four non-driven state variables. The three driven state variables include: trolley displacement, boom slewing angle, and hoisting rope length. The four non-driven state variables include: hook and load swing angles in three-dimensional space. The dynamic model of the underactuated seven-degree-of-freedom tower crane is approximated and linearized to obtain the linearized dynamic equations of the seven-degree-of-freedom tower crane. The linearized dynamic equations of the seven-degree-of-freedom tower crane are then optimized into a fully driven system model.

[0010] Acquire state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on error signals; determine the online update rate based on time delay estimation;

[0011] An adaptive sliding mode controller is constructed based on the all-drive system model, state data, dynamic sliding surface, and online update rate.

[0012] A seven-degree-of-freedom tower crane is positioned and its sway is eliminated based on an adaptive sliding mode controller.

[0013] On the other hand, an adaptive sliding mode control system for a seven-degree-of-freedom tower crane is provided, including:

[0014] The model building module is configured to: establish a dynamic model of an underactuated seven-degree-of-freedom tower crane; the model includes three driving state variables and four non-driving state variables; the three driving state variables include: trolley displacement, boom slewing angle, and hoisting rope length; the four non-driving state variables include: the swing angle of the hook and load in three-dimensional space; approximate linearize the dynamic model of the underactuated seven-degree-of-freedom tower crane to obtain the linearized dynamic equations of the seven-degree-of-freedom tower crane; optimize the linearized dynamic equations of the seven-degree-of-freedom tower crane into a fully driven system model;

[0015] The processing module is configured to: acquire the state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on error signals; and determine the online update rate based on time delay estimation.

[0016] The controller construction module is configured to build an adaptive sliding mode controller based on the all-drive system model, state data, dynamic sliding surface, and online update rate.

[0017] The output module is configured to position and eliminate sway of a seven-degree-of-freedom tower crane based on an adaptive sliding mode controller.

[0018] Furthermore, an electronic device is also provided, including:

[0019] Memory, used for non-transitory storage of computer-readable instructions; and

[0020] Processor, for executing the computer-readable instructions,

[0021] When the computer-readable instructions are executed by the processor, they perform the method described in the first aspect above.

[0022] In another aspect, a storage medium is also provided for non-transitory storage of computer-readable instructions, wherein when the non-transitory computer-readable instructions are executed by a computer, the instructions of the method described in the first aspect are executed.

[0023] In another aspect, a computer program product is also provided, including a computer program that, when run on one or more processors, is used to implement the method described in the first aspect above.

[0024] The above technical solution has the following advantages or beneficial effects:

[0025] 1) A dynamic model of an underactuated seven-DOF tower crane was established for the first time. The model contains three driven state variables (trolley displacement, boom slewing angle, and rope length) and four undriven state variables (swing angle of the hook and load in three-dimensional space), and the relationships between them are strongly coupled and nonlinear. Compared with existing models, this invention considers a variable rope length and a double-spherical pendulum, resulting in more system degrees of freedom and more complex dynamic characteristics, thus more accurately describing the full-state dynamic characteristics of the tower crane.

[0026] 2) For an underactuated seven-DOF tower crane system, an adaptive sliding mode controller that simultaneously controls seven system outputs with three inputs is proposed. Through rigorous stability analysis, the finite-time convergence of the designed sliding surface and the stability of the closed-loop control system are proven.

[0027] 3) An adaptive scheme that takes into account parameter uncertainties was implemented by using time delay estimation technology, which effectively reduced the positioning errors of boom rotation, trolley movement and load lifting. Attached Figure Description

[0028] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0029] Figure 1 This is a schematic diagram of the seven-degree-of-freedom tower crane structure described in this embodiment of the invention;

[0030] Figure 2 This is a block diagram of the control system described in the embodiments of the present invention;

[0031] Figure 3 This is a comparison chart of experimental results between the adaptive sliding mode control method (Proposed controller) described in this embodiment of the invention and the energy analysis-based controller (EAB) and smoother (Smoother);

[0032] Figure 4 The load hoisting trajectory diagrams described in this embodiment of the invention are as follows: (a) a side view of the load trajectory under the control of the Energy Analysis-Based Controller (EAB); (b) a side view of the load trajectory under the control of the Smoother; (c) a side view of the load trajectory under the control of the Proposed Controller; and (d) a top view of the load trajectory under the control of the above three control methods. Detailed Implementation

[0033] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0034] Example 1

[0035] This embodiment provides an adaptive sliding mode control method for a seven-degree-of-freedom tower crane, including:

[0036] S101: Establish a dynamic model of an underactuated seven-degree-of-freedom tower crane; the model includes three driving state variables and four non-driving state variables; the three driving state variables include: trolley displacement, boom slewing angle, and hoisting rope length; the four non-driving state variables include: the swing angle of the hook and load in three-dimensional space; approximate linearize the dynamic model of the underactuated seven-degree-of-freedom tower crane to obtain the linearized dynamic equation of the seven-degree-of-freedom tower crane; optimize the linearized dynamic equation of the seven-degree-of-freedom tower crane into a fully driven system model;

[0037] S102: Acquire the state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on the error signal; determine the online update rate based on time delay estimation;

[0038] S103: Construct an adaptive sliding mode controller based on the all-drive system model, state data, dynamic sliding surface, and online update rate;

[0039] S104: Positioning and anti-swaying of a seven-degree-of-freedom tower crane based on an adaptive sliding mode controller.

[0040] Figure 1 This is a schematic diagram of a seven-degree-of-freedom tower crane system in three-dimensional space. The relevant physical parameters and definitions of the tower crane system are shown in Table 1.

[0041] Table 1 Tower Crane System Parameters

[0042]

[0043] Further, S101: Establishing a dynamic model of an underactuated seven-degree-of-freedom tower crane, including:

[0044] Based on the Lagrange method, the dynamic equations of an underactuated seven-degree-of-freedom tower crane are established.

[0045] The nonlinear dynamic equations related to the boom rotation angle φ, which is the driving state variable, are as follows:

[0046]

[0047] The nonlinear dynamic equations related to the trolley displacement r, the driving state variable, are as follows:

[0048]

[0049] The nonlinear dynamic equations related to the driving state variable, the length l1 of the suspension rope, are as follows:

[0050]

[0051] Among them, F φ =F φa -F φf ,F r =F ra -F rf ,F l =F la -F lf F φa ,F ra and F la These represent the driving forces of the boom, trolley, and lifting rope, respectively. F φf ,F rf and F la These represent the frictional forces of the boom, trolley, and suspension rope, respectively.

[0052] The nonlinear dynamic equations related to the non-driven state variable, hook swing angle θ1, are as follows:

[0053]

[0054] The nonlinear dynamic equations related to the non-driven state variable hook swing angle θ2 are as follows:

[0055]

[0056] The nonlinear dynamic equations related to the non-driven state variable load swing angle θ3 are as follows:

[0057]

[0058] The nonlinear dynamic equations related to the non-driven state variable load swing angle θ4 are as follows:

[0059]

[0060] Where, d i (i = 1, 2, 3, 4) represents the swing damping ratio of the hook and the load.

[0061] Based on the small swing angle of the hook and load (usually less than 10 degrees), the above complex nonlinear dynamic model equations (1)-(7) of the seven-degree-of-freedom tower crane can be approximately linearized.

[0062] Further, in S101: the dynamic model of the underactuated seven-degree-of-freedom tower crane is approximated and linearized to obtain the linearized dynamic equations of the seven-degree-of-freedom tower crane, including:

[0063] The linearized dynamic equations relating to the boom rotation angle φ, the driving state variable, are as follows:

[0064]

[0065] The linearized dynamic equations related to the trolley displacement r, the driving state variable, are as follows:

[0066]

[0067] The linearized dynamic equations related to the driving state variable, the length l1 of the suspension rope, are as follows:

[0068]

[0069] The linearized dynamic equations related to the non-driven state variable, hook swing angle θ1, are as follows:

[0070]

[0071] The linearized dynamic equations related to the non-driven state variable, hook swing angle θ2, are as follows:

[0072]

[0073] The linearized dynamic equations related to the non-driving state variable load swing angle θ3 are as follows:

[0074]

[0075] The linearized dynamic equations related to the non-driving state variable load swing angle θ4 are as follows:

[0076]

[0077] Using the elimination method, the linearized dynamic equations (8)-(14) of the seven-degree-of-freedom tower crane can be further rewritten as a full-drive system model.

[0078] Further, S101: Optimizing the linearized dynamic equations of the seven-degree-of-freedom tower crane into a full-drive system model, including:

[0079]

[0080] Where q a =[φ r l1] T Represents the driving state vector, U = [F φ F r Fl ] T Controller vector, Matrix and The vector representation is as follows:

[0081]

[0082] m 11 =J+Mr 2 +m2θ3rl2+(m1+m2)θ1rl1,

[0083] m 12 =m 21 =-[m2θ4l2+(m1+m2)θ2l1],m 13 =m 31 =(m1+m2)θ2r,m 22 =M,

[0084] m 23 =m 32 =(m1+m2)θ1,m 33 =m1+m2,

[0085]

[0086]

[0087] Where M represents the mass of the trolley, m1 represents the mass of the hook, m2 represents the mass of the load, J represents the moment of inertia of the boom, φ represents the slewing angle of the boom, r represents the displacement of the trolley, l1 represents the length of the lifting rope, l2 represents the length of the rigging rope, θ1 represents the swing angle of the hook, θ2, θ3, θ4 represent the three-dimensional swing angles of the load, and F φ F represents the resultant torque of the boom. r F represents the resultant torque of the trolley. l The torque of the suspension rope is represented by g, and g represents the acceleration due to gravity.

[0088] First, define As matrix M a The nominal matrix, (15) is further rewritten as

[0089]

[0090] Where the matrix sum vector The expression is as follows The gain coefficient is positive. At this point, all state variables related to the system parameters are contained in vector N.

[0091] To more clearly describe the controller design process, Figure 2 A block diagram of the adaptive sliding mode control system is shown.

[0092] Further, step S102: acquiring the status data of the seven-degree-of-freedom tower crane, including:

[0093] The mass of the trolley, the mass of the hook, the mass of the load, the moment of inertia of the boom, the initial and target values ​​of the boom's rotation angle, the initial and target values ​​of the trolley displacement, the initial and target values ​​of the lifting rope length, and the length of the rigging rope.

[0094] Further, S102: Constructing a dynamic sliding surface based on the error signal includes:

[0095] The error vector e is defined as follows:

[0096]

[0097] Where e φ ,e r ,e l The sub-tables represent error signals related to boom rotation angle, trolley displacement, and rope length, φ s ,r s ,l 1s Let these represent the reference trajectories for boom rotation, trolley movement, and rope length variation, respectively, and satisfy the following constraints:

[0098]

[0099] Where φ i φ d Represent the initial and target values ​​of the boom slewing angle, r. i r d These represent the initial and target values ​​of the trolley displacement, respectively. 1i l 1d Let t represent the initial and target values ​​of the suspension rope length, respectively. d This refers to the duration of exercise.

[0100] Based on the error signal (17), the dynamic sliding mode surface vector s is constructed as follows:

[0101]

[0102] Where s φ ,s r ,s l The sub-tables represent the sliding surfaces related to the boom rotation angle, trolley displacement, and rope length, Λ=diag{k φ ,k r ,k l} represents the control gain matrix.

[0103] Taking the first-order time derivative of (19), we get:

[0104]

[0105] in Represented as

[0106] Further, S102: determining the online update rate based on latency estimation includes:

[0107] Based on time delay estimation, design vector The online update rule is:

[0108]

[0109] Where L represents a smaller time delay. Representing vectors respectively The latency value.

[0110] The estimation error vector ε associated with vector N is defined as follows:

[0111]

[0112] Where ε φ ,ε r ,ε l This represents a component vector in the estimation error vector ε.

[0113] Further, S103: Based on the all-drive system model, state data, dynamic sliding surface, and online update rate, an adaptive sliding mode controller is constructed, including:

[0114] Adaptive sliding mode controller:

[0115]

[0116] Where κ = diag{k1,k2,k3} and H = diag{η1,η2,η3} represent the control gain matrix, and must satisfy the following conditions: eta1>0, eta2>0, eta3>0, vector This represents an online estimate of the parameter vector N of an uncertain system.

[0117] Furthermore, the method also includes: performing stability analysis on the adaptive sliding mode controller.

[0118] Theorem 1: The adaptive sliding mode controller (21) proposed in this invention can make the sliding surface converge to 0 in a finite time, that is:

[0119]

[0120] Proof: First, construct a positive definite scalar function V(t) as follows:

[0121]

[0122] Combining (16) and (20)-(23), we get:

[0123]

[0124] in

[0125] Differentiating (25) and substituting it into (26), we get:

[0126]

[0127] This indicates Furthermore, we can obtain:

[0128]

[0129] Substituting (25) into (27), we get:

[0130]

[0131] Based on the Bellman-Grangell inequality and (29), we can obtain:

[0132]

[0133] From (30), we can obtain:

[0134]

[0135] This indicates that the sliding surface converges exponentially to 0. Next, this invention will further prove the finite-time convergence of the sliding surface. Based on (27), we can obtain:

[0136]

[0137] in Substituting (25) into (32), we get:

[0138]

[0139] If the sliding surface s is within a finite time t f If V(t) converges to 0 at any time, then V(t) f ) = 0. Therefore, we can obtain from (33):

[0140]

[0141] By combining (27) and (34), we can conclude that:

[0142]

[0143] Thus, Theorem 1 is proved.

[0144] Theorem 2: The adaptive sliding mode controller (21) proposed in this invention can ensure that the boom rotation angle φ, trolley displacement r, rope length l1, hook swing angles θ1, θ2, and load swing angles θ3, θ4 converge to their respective target values, that is:

[0145]

[0146] Proof: Substituting (17)-(19) into (35), we get:

[0147]

[0148] From (37), we can see that as t→∞, we can further obtain the following equation:

[0149]

[0150] Substituting (38) into (11)-(14) and further rearranging, we get:

[0151]

[0152]

[0153] Define a vector with respect to the swing angle of the hook and the load. As shown below:

[0154]

[0155] Based on vector p, (39)-(42) can be further rewritten as follows:

[0156]

[0157] in,

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] The characteristic equation of matrix A is expressed as:

[0164] |λI-A|=0 (45)

[0165] Considering the system parameter values ​​of the tower crane platform, the eigenvalues ​​of matrix A can be calculated as follows:

[0166] λ 1,2 = -2.6023 ± 5.6930i;

[0167] λ 3,4 = -1.7102 ± 2.2453i;

[0168] λ 5,6 = -4.1459 ± 9.1466i

[0169] λ 7,8 = -0.1666 ± 3.0580i.

[0170] Clearly, A is a Herwitz matrix because all its eigenvalues ​​have negative real parts. Therefore, (39)-(42) are asymptotically stable, as expressed below:

[0171]

[0172] Substituting (46) into (38), we get:

[0173]

[0174] Combining (46) and (47), we can see that Theorem 2 is proved.

[0175] Experimental verification: To demonstrate the effectiveness of the adaptive sliding mode control method proposed in this invention, a tower crane experimental platform was used to verify the effectiveness of the control method involved.

[0176] The system of the tower crane test platform is as follows: M = 3kg, m1 = 0.8kg, m2 = 0.5kg;

[0177] J = 5.6 kg·m 2 l² = 0.2m, g = 9.8m / s² 2 ,d i =0.1, i=1,2,3,4.

[0178] The initial and target values ​​for each actuator are set as follows:

[0179] φ i =0deg,φ d =50deg,r i =0.15m,r d =0.65m,l 1i =0.1m,l1d =0.5m.

[0180] The controller gain is selected as follows:

[0181] κ=diag{5,5,5},H=diag{5,5,5},

[0182] k φ =10,k r =10,k l =5, L=0.005s.

[0183] The effectiveness of the proposed adaptive sliding mode controller is verified by comparing this invention with existing energy-analysis-based (EAB) controllers and smoothers. Neither of these existing technologies considers variations in the suspension rope length. For ease of comparison, the smoother shaper uses the average suspension rope length l1 = 0.3m to estimate the natural frequency of load swaying and designs the boom rotation, trolley movement, and rope length variation shapers. The EAB controller adds a traditional proportional-differential (PD) controller to the existing boom and trolley controllers to drive rope length variations. Figure 3 This is a comparison chart of experimental results between the adaptive sliding mode control method (Proposed controller) described in this embodiment of the invention and the energy analysis-based controller (EAB) and smoother (Smoother).

[0184] The experimental results of the proposed controller and two comparison controllers are as follows: Figure 4 As shown in the sub-figure, the open-loop smoother struggles to eliminate positioning errors in the boom, trolley, and lifting rope. The closed-loop controller described in this invention can estimate unknown system parameters online by using time delay estimation, thereby improving positioning accuracy. The transport times of the smoother, EAB controller, and the adaptive sliding mode controller proposed in this invention are 6.55s, 7.42s, and 6.44s, respectively. Under the condition of achieving the same target displacement, the control method designed in this invention has a shorter transport time than other comparative methods. The maximum swing angles of the smoother, EAB controller, and the adaptive sliding mode controller designed in this invention are 3.92°, 4.25°, and 2.27°, respectively, showing that the swing angle of this invention is the smallest. When the trolley and boom reach the target position, significant residual swing still exists in the hook and load when using the open-loop smoother and EAB controller, while the control method of this invention can eliminate all residual swing within 6.89s.

[0185] Figure 4 (a) Figure 4 (b) and Figure 4 (c) shows the transport trajectories of loads being lifted using the adaptive sliding mode controller, smoother, and EAB controller designed according to this invention. Figure 4 As can be seen from (d) in the figure, compared with the prior art, the adaptive sliding mode controller designed in this invention has a smaller positioning error at the target point.

[0186] Experimental results show that the adaptive sliding mode controller designed in this invention is superior to existing technologies in both sway suppression and precise positioning control.

[0187] A dynamic model of an underactuated seven-degree-of-freedom tower crane system was established and analyzed using the Lagrange method. The model includes three driving state variables: trolley displacement, boom slewing angle and rope length, and four non-driving state variables: hook and load swing angle in three-dimensional space. The above underactuated model was transformed into a fully driven system model using the elimination method.

[0188] Based on the nonlinear coupling relationship between the driving state and the non-driving state variables, a set of dynamic sliding surfaces containing all state variables is constructed. Using time delay estimation technology, adaptive online estimation of unknown system parameters is realized. An adaptive sliding controller is designed by combining sliding mode technology and time delay estimation technology.

[0189] Using Lyapunov stability theory, the finite-time convergence of dynamic sliding surfaces and the asymptotic stability of closed-loop control systems were rigorously proved.

[0190] A seven-degree-of-freedom (DOF) dynamic model considering boom rotation, trolley motion, rope length variation, and load / hook spherical oscillation in three-dimensional space was established using the Lagrange method. Then, a dynamic sliding mode surface was constructed by analyzing the nonlinear coupling relationship between the non-driven and driven states. Time delay estimation techniques were employed to adaptively handle unknown system parameters online. An adaptive sliding mode control method was designed by combining sliding mode control and time delay estimation techniques. The stability of the closed-loop control system was demonstrated in detail using Lyapunov stability theory. This effectively solved the control problems of positioning, anti-swaying, and parameter uncertainty in a seven-DOF tower crane.

[0191] The tower crane described has three control inputs (boom controller, trolley controller, and rope controller) and seven output degrees of freedom (boom slewing angle, trolley displacement, rope length, and the swing angle of the hook and load in three-dimensional space). These seven output degrees of freedom exhibit complex dynamic relationships that are nonlinear and strongly coupled.

[0192] The controller incorporates two technologies: sliding mode control and time delay estimation. It can simultaneously control seven output degrees of freedom from three control inputs, eliminate non-driven sway angles, and achieve precise positioning of the driven actuator.

[0193] The controller has an adaptive mechanism that can dynamically estimate unknown parameters and unmodeled parameters in the tower crane system online, thereby improving the accuracy of control.

[0194] The controller utilizes Lyapunov stability theory to rigorously prove the finite-time convergence of the dynamic sliding surface and the asymptotic stability of the closed-loop control system.

[0195] This invention establishes a dynamic model of an underactuated seven-DOF tower crane considering a double-ball pendulum and variable rope length. The model includes three driven state variables (trolley displacement, boom slewing angle, and rope length) and four undriven state variables (swing angle of the hook and load in three-dimensional space). In the controller design, an adaptive sliding mode anti-swing control method is designed by combining sliding mode control and time delay estimation techniques, enabling simultaneous control of the tower crane's seven output degrees of freedom from three control inputs. This controller has an adaptive mechanism, allowing for online estimation of unknown parameters and unmodeled dynamics in the tower crane system. Finally, experimental results show that the positioning control performance and anti-swing control performance of this invention are superior to existing control technologies.

[0196] Example 2

[0197] This embodiment provides an adaptive sliding mode control system for a seven-degree-of-freedom tower crane, including:

[0198] The model building module is configured to: establish a dynamic model of an underactuated seven-degree-of-freedom tower crane; perform approximate linearization on the dynamic model of the underactuated seven-degree-of-freedom tower crane to obtain the linearized dynamic equations of the seven-degree-of-freedom tower crane; and optimize the linearized dynamic equations of the seven-degree-of-freedom tower crane into a fully driven system model.

[0199] The processing module is configured to: acquire the state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on error signals; and determine the online update rate based on time delay estimation.

[0200] The controller construction module is configured to build an adaptive sliding mode controller based on the all-drive system model, state data, dynamic sliding surface, and online update rate.

[0201] The output module is configured to position and eliminate sway of a seven-degree-of-freedom tower crane based on an adaptive sliding mode controller.

[0202] It should be noted that the model building module, processing module, controller construction module, and output module described above correspond to steps S101 to S104 in Embodiment 1. The examples and application scenarios implemented by these modules and their corresponding steps are the same, but they are not limited to the content disclosed in Embodiment 1. It should also be noted that these modules, as part of the system, can be executed in a computer system, such as a set of computer-executable instructions.

[0203] The descriptions of each embodiment in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0204] The proposed system can be implemented in other ways. For example, the system embodiments described above are merely illustrative, and the division of modules described above is only a logical functional division. In actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed.

[0205] Example 3

[0206] This embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein, the processor is connected to the memory, and the one or more computer programs are stored in the memory. When the electronic device is running, the processor executes the one or more computer programs stored in the memory to cause the electronic device to perform the method described in Embodiment 1.

[0207] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0208] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0209] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.

[0210] The method in Embodiment 1 can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, a detailed description is not provided here.

[0211] Those skilled in the art will recognize that the units and algorithm steps described in connection with the various examples of this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0212] Example 4

[0213] This embodiment also provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the method described in Embodiment 1.

[0214] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An adaptive sliding mode control method for a seven-degree-of-freedom tower crane, characterized by: include: Establish a dynamic model of an underactuated seven-degree-of-freedom tower crane; The model includes three driving state variables and four non-driving state variables; The three driving state variables include: trolley displacement, boom slewing angle, and rope length; the four non-driving state variables include: hook and load swing angle in three-dimensional space; the underdriven seven-degree-of-freedom tower crane dynamic model is approximated and linearized to obtain the linearized dynamic equation of the seven-degree-of-freedom tower crane; the linearized dynamic equation of the seven-degree-of-freedom tower crane is optimized into a fully driven system model. Acquire state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on error signals; determine the online update rate based on time delay estimation; An adaptive sliding mode controller is constructed based on the all-drive system model, state data, dynamic sliding surface, and online update rate. A seven-degree-of-freedom tower crane is positioned and its sway is eliminated based on an adaptive sliding mode controller.

2. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, The linearized dynamic equations of the seven-degree-of-freedom tower crane are optimized into a full-drive system model, including: Where q a =[φ r l1] T Represents the driving state vector, U = [F φ F r F l ] T Controller vector, Matrix and The vector representation is as follows: m 11 =J+Mr 2 +m2θ3rl2+(m1+m2)θ1rl1, m 12 =m 21 =-[m2θ4l2+(m1+m2)θ2l1],m 13 =m 31 =(m1+m2)θ2r,m 22 =M, m 23 =m 32 =(m1+m2)θ1,m 33 =m1+m2, Where M represents the mass of the trolley, m1 represents the mass of the hook, m2 represents the mass of the load, J represents the moment of inertia of the boom, φ represents the slewing angle of the boom, r represents the displacement of the trolley, l1 represents the length of the lifting rope, l2 represents the length of the rigging rope, θ1 represents the swing angle of the hook, θ2, θ3, θ4 represent the three-dimensional swing angles of the load, and F φ F represents the resultant torque of the boom. r F represents the resultant torque of the trolley. l The torque of the suspension rope is represented by g, and g represents the acceleration due to gravity. First, define As matrix M a The nominal matrix, (15) is further rewritten as in and The expression is as follows The gain coefficient is positive; at this time, the state variables related to the system parameters are all contained in the vector N.

3. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, Obtain the status data of a seven-degree-of-freedom tower crane, including: The mass of the trolley, the mass of the hook, the mass of the load, the moment of inertia of the boom, the initial and target values ​​of the boom's rotation angle, the initial and target values ​​of the trolley displacement, the initial and target values ​​of the lifting rope length, and the length of the rigging rope.

4. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, Based on the error signal, a dynamic sliding surface is constructed, including: The error vector e is defined as follows: Where e φ ,e r ,e l These represent the error signals related to the boom rotation angle, trolley displacement, and rope length, respectively. φ s ,r s ,l 1s Let these represent the reference trajectories for boom rotation, trolley movement, and rope length variation, respectively, and satisfy the following constraints: Where φ i φ d These represent the initial and target values ​​of the boom rotation angle, r. i r d These represent the initial and target values ​​of the trolley displacement, respectively. 1i l 1d Let t represent the initial and target values ​​of the suspension rope length, respectively. d For exercise time; Based on the error signal (17), the dynamic sliding mode surface vector s is constructed as follows: Where s φ ,s r ,s l These represent the sliding surfaces related to the boom rotation angle, trolley displacement, and rope length, respectively, Λ=diag{k φ ,k r ,k l } represents the control gain matrix; Taking the first-order time derivative of (19), we get: in Represented as 5. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, Based on latency estimation, the online update rate is determined, including: Based on time delay estimation, design vector The online update rule is: Where L represents a smaller time delay, N t-L U t-L , Let N and U represent vectors respectively. The delay value; The estimation error vector of vector N is defined as follows: Where ε φ ,ε r ,ε l This represents a component vector in the estimation error vector ε.

6. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, Based on the all-drive system model, state data, dynamic sliding surface, and online update rate, an adaptive sliding mode controller is constructed, including: Adaptive sliding mode controller: Where κ = diag{k1,k2,k3} and H = diag{η1,η2,η3} represent the control gain matrix, and must satisfy the following conditions: eta1>0, eta2>0, eta3>0, vector This represents an online estimate of the parameter vector N of an uncertain system.

7. The adaptive sliding mode control method for a seven-degree-of-freedom tower crane as described in claim 1, characterized in that, The method further includes: performing stability analysis on the adaptive sliding mode controller.

8. An adaptive sliding mode control system for a seven-degree-of-freedom tower crane, characterized in that... include: The model building module is configured to: build a dynamic model of an underactuated seven-degree-of-freedom tower crane; The model includes three driving state variables and four non-driving state variables; The three driving state variables include: trolley displacement, boom slewing angle, and rope length; the four non-driving state variables include: hook and load swing angle in three-dimensional space; the underdriven seven-degree-of-freedom tower crane dynamic model is approximated and linearized to obtain the linearized dynamic equation of the seven-degree-of-freedom tower crane; the linearized dynamic equation of the seven-degree-of-freedom tower crane is optimized into a fully driven system model. The processing module is configured to: acquire the state data of a seven-degree-of-freedom tower crane; construct a dynamic sliding surface based on error signals; and determine the online update rate based on time delay estimation. The controller construction module is configured to build an adaptive sliding mode controller based on the all-drive system model, state data, dynamic sliding surface, and online update rate. The output module is configured to position and eliminate sway of a seven-degree-of-freedom tower crane based on an adaptive sliding mode controller.

9. An electronic device, characterized in that it comprises: Memory is used to store computer-readable instructions in a non-transitory manner. as well as Processor, for executing the computer-readable instructions, When the computer-readable instructions are executed by the processor, they perform the method described in any one of claims 1-7.

10. A storage medium, characterized in that, Non-transitory storage of computer-readable instructions, wherein, when executed by a computer, the instructions of the method according to any one of claims 1-7 are executed.

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