A tower crane self-adaptive sliding mode control method based on improved fruit fly optimization algorithm

Abstract

This invention discloses an adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm, comprising the following steps: Step 1): Designing an extended state observer to observe the load swing angle state; Step 2): Designing an adaptive sliding mode controller, feeding back the observed swing angle state to the adaptive sliding mode controller, which will enable the trolley to be precisely positioned while suppressing load swing angle oscillation; Step 3): Optimizing the parameters of the adaptive sliding mode controller through an improved fruit fly optimization algorithm, thereby improving the controller's control effect. This invention uses a combination of a linear extended observer and an adaptive sliding mode controller, which has the advantages of easy swing angle observation, simple physical implementation of the controller, and good control effect; in terms of parameter tuning, an improved fruit fly algorithm is used to strengthen the cooperation among fruit flies, avoid getting trapped in local optima, and improve the controller's control effect.

Description

Technical Field

[0001] This invention relates to the field of anti-sway control technology for tower cranes, and in particular to an adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm. Background Technology

[0002] Tower cranes, often simply called tower cranes, are widely used for material transportation at high-rise building construction sites. Due to the complex factors at construction sites, their loads often exhibit swaying phenomena. Problems such as difficulty in directly measuring the load sway angle, significant vibration in the system's slipform controller, and complex controller parameter adjustments threaten transportation safety. Therefore, intelligent tower cranes have become an important development direction in the construction machinery field, and positioning and anti-sway control is one of the key issues in the research of intelligent tower crane technology.

[0003] Currently, methods for anti-sway control of tower cranes include PID control, shaping input method, adaptive control, and robust control. Among these, adaptive sliding mode control has been widely used due to its strong robustness and adaptability. However, it suffers from problems such as difficulty in directly measuring the load swing angle, significant system chattering in sliding mode control, and ineffective manual adjustment of controller parameters. To improve the anti-sway control effect, further improvements to the anti-sway controller are needed.

[0004] Based on sliding mode control theory, Liang Huihui et al. designed a proportional-derivative sliding mode controller and a proportional-derivative-integral sliding mode controller to conduct crane control experiments. These controllers can move the trolley from the starting position to the target position while ensuring that the speed of the trolley, the swing angle of the load, and the swing angular velocity tend to 0. However, they did not consider the difficulty in measuring the load swing angle and the controller parameter issues. Furthermore, they did not consider the chattering problem in sliding mode control when conducting numerical simulation experiments. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention aims to provide an adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm. The method employs a combination of a linear extended observer and an adaptive sliding mode controller, which features good observation of the swing angle, simple physical implementation of the controller, and good control effect. In terms of parameter tuning, an improved fruit fly algorithm is used to enhance the cooperation among fruit flies, avoid getting trapped in local optima, and improve the control effect of the controller.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] An adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm includes the following steps;

[0008] Step 1): Design an extended state observer to observe the load swing angle state;

[0009] Step 2): Design an adaptive sliding mode controller to feed back the observed swing angle state to the adaptive sliding mode controller. The controller will enable the trolley to be accurately positioned while suppressing the load swing angle oscillation.

[0010] Step 3): Optimize the parameters of the adaptive sliding mode controller by improving the fruit fly optimization algorithm, thereby improving the control effect of the controller.

[0011] In step 1), designing the extended state observer includes the following steps:

[0012] In the tower crane system, the mass of the luffing trolley and the load mass are represented by M and m, respectively. The origin is taken as the center of the intersection of the tower body, the counterweight boom, and the jib. The driving force of the trolley moving along the luffing direction X on the boom is F. x x and l represent the luffing distance of the trolley and the length of the rope, respectively; θ1 represents the load swing angle when the tower crane is luffing; the Lagrange equation is used to establish the tower crane dynamics model;

[0013] The system's Lagrange operators:

[0014]

[0015] Establish the Lagrange equations corresponding to x and θ1:

[0016]

[0017] F fx This represents the frictional resistance experienced by the luffing trolley during its motion; let...

[0018]

[0019] Where f1 and f2 represent the friction factors in the amplitude direction, respectively.

[0020] Furthermore, under the variable luffing condition with a constant rope length, the dynamic equation of the tower crane's simple pendulum system is as follows:

[0021]

[0022]

[0023] After linearization, the tower crane system is converted into a state-space form as follows:

[0024]

[0025]

[0026] Where: M and m represent the mass of the luffing trolley and the load respectively, l represents the length of the rope, g is the gravitational acceleration, x represents the luffing distance of the trolley, θ1 represents the swing angle of the load when the tower crane is luffing, and F represents the luffing control force;

[0027] Let θ1 = α1, and expand equation (2).

[0028]

[0029]

[0030] Write equation (3) in matrix form

[0031]

[0032] in,

[0033] Design a Linear Extended State Observer (LESO) based on equation (4).

[0034]

[0035] Where matrix z represents the estimated value of state α, z = [z1z2] T , Let L be the estimated value of the output y, and L be the observation gain vector. ω0 is the LESO bandwidth, and e is defined as the observation error of α, e = [e1e2] T e1 = α1 - z1, e2 = α2 - z2.

[0036] Furthermore, from equations (4) and (5), the error equation for the observation can be obtained:

[0037]

[0038] Let W1 = e1, W2 = -3ω0e1 + e2, then (6) can be expressed as:

[0039]

[0040] Let a = 3ω0, Right now The characteristic equation of the above equation is: aλ 2 +bλ=0;

[0041] According to the Hurwitz condition, the necessary and sufficient condition for its eigenvalues ​​to have negative real parts is: a>0, b>0. Based on the Barbazin formula, the error equation and the Lyapunov function V are obtained.

[0042]

[0043] From a > 0 and b > 0, we can obtain:

[0044]

[0045] Differentiating the above equation and substituting equation (7) into it, we get:

[0046]

[0047] Then V is positive definite. LESO is asymptotically stable in the range e1=0, e2=0.

[0048] The linear expansion state observer is used for load swing state observation and estimation, which solves the problem that the load swing angle is difficult to measure directly in some operating conditions.

[0049] In step 2), the adaptive sliding mode controller is designed, including the following steps:

[0050] Define the linear sliding surface as:

[0051]

[0052] Where γ1, γ2, and γ3 are coefficients to be tuned, and the position error signal e x =xx p ,x p The target position of the variable amplitude trolley can be obtained by differentiating with respect to the linear sliding surface s.

[0053]

[0054] Substituting equations (1) and (2) into (9) yields

[0055]

[0056] make Find the equivalent driving force F

[0057]

[0058] Adding the hyperbolic tangent function ζtanh(s) based on the sliding surface s to equation (11), the control law is updated as follows:

[0059]

[0060] The hyperbolic tangent function ζtanh(s) used is a continuous function, which to some extent reduces the system chattering caused by the discontinuous sign function that is often used, and allows the controller to be corrected.

[0061] Furthermore, to further suppress chattering in the sliding mode control system and improve its disturbance rejection, adaptive control design is incorporated, and the friction resistance formula is rewritten in vector form:

[0062]

[0063]

[0064] Define the estimated value of the displacement output of the variable amplitude trolley:

[0065]

[0066] Wherein: Γ x ∈R 2×2 It is a positive definite diagonal matrix.

[0067] Furthermore, to improve the transient performance of the tower crane system, the following adaptive control law is proposed.

[0068]

[0069] in:

[0070]

[0071]

[0072] Where, θ 1o The target value for the load swing angle. It is the error value of the load swing angle. The displacement output y of the car x The estimated value enables the recursive realization of the corresponding parameter update rate, simplifying the controller design steps. Combining equations (12) and (15), the tower crane anti-sway controller can be designed as follows:

[0073] F = F xn +F xs (17)

[0074] The adaptive sliding mode controller eliminates load sway while accurately positioning the load trolley, and also solves the problem of chattering in sliding mode control.

[0075] In step 3), the improved fruit fly optimization algorithm adjusts the parameters of the adaptive sliding mode controller, including the following steps:

[0076] The optimization strategy of fruit flies is dynamically adjusted so that 2 / 3 of the fruit flies search along the original evolutionary direction, while the other fruit flies search around the edge of the evolutionary direction in an arc-shaped curve. This enriches the diversity of search paths and accelerates the optimization speed.

[0077] The new position of the individual fruit fly is determined by comparing its position with the linear position along the search direction, considering both global and local factors. The expression is as follows:

[0078]

[0079]

[0080] λ i It represents the straight-line position from the individual's location to the search direction vector, rdom(*) is a random number within the search interval, and μ is the global-local coordination factor (a constant value), whose value is proportional to the search capability. The angle between the direction vectors of two adjacent fruit fly individuals is denoted as .

[0081] Furthermore, based on the average taste concentration in the population, the fixed search radius of one-third of the fruit flies in the population, which used an arc-shaped curve to circle the edge, was changed. By using the new search radius method, the division of labor among individual fruit flies was clarified, the differences in the individual search range were increased, and the diversity of the group's search range was expanded.

[0082] The formula for calculating the search radius is as follows:

[0083]

[0084] R min The minimum search radius is Ssmo; the initial average flavor concentration of the population is Ssmo; R1 is the current search radius; t and T are the current iteration number and the maximum iteration number, respectively; Ssmli is the current flavor concentration; R max These are the maximum search radius.

[0085] The beneficial effects of this invention are:

[0086] 1. This invention provides an adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm, wherein the active disturbance rejection controller consists of a linear extended observer and an adaptive sliding mode controller.

[0087] 2. The adaptive sliding mode controller of the present invention has the characteristics of simple physical implementation, strong robustness and strong anti-interference ability.

[0088] 3. This invention proposes an improved fruit fly optimization algorithm. By optimizing the optimization strategy and search radius of the standard fruit fly algorithm, the algorithm's optimization speed and accuracy are improved. It optimizes the typical defect of swarm intelligence algorithms that are prone to getting trapped in local optima as much as possible, reasonably disperses individual competition to enhance population cooperation, delineates the division of labor, improves the individual's escape ability and local development ability, and explores new evolutionary paths.

[0089] 4. This invention improves the efficiency and accuracy of parameter tuning during the fruit fly optimization algorithm tuning process. Attached Figure Description

[0090] Figure 1 A simplified model diagram of a tower crane.

[0091] Figure 2 This is a block diagram of the overall structure of the anti-sway control system for a tower crane.

[0092] Figure 3 These are schematic diagrams showing the simulation results of state extension observer tracking observation under different system parameters.

[0093] Figure 4 The simulation diagrams show the anti-sway control of the tower crane system under three different conditions.

[0094] Figure 5 This diagram illustrates the robustness of controller operation under different conditions.

[0095] Figure 6 This is a schematic diagram of the controller's control effect under interference conditions. Detailed Implementation

[0096] The present invention will now be described in further detail with reference to the accompanying drawings.

[0097] This invention can be used in adaptive sliding mode controllers for various cranes based on an improved fruit fly optimization algorithm, such as gantry cranes, bridge cranes, and truck cranes. The following example uses a tower crane.

[0098] This invention addresses the challenges of directly measuring the load swing angle of tower cranes under certain operating conditions, significant chattering in the system's sliding mode controller, and complex controller parameter adjustment. It proposes an adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm. The overall system structure diagram is shown below. Figure 1 As shown, an extended state observer is first designed to observe the load swing angle state, and the observation results are fed back to the adaptive sliding mode controller. Secondly, the adaptive sliding mode controller is designed to achieve precise positioning while reducing load sway. In the construction of the sliding surface, a hyperbolic tangent function is used instead of the commonly used sign function to increase its continuity and reduce chattering. Finally, the optimization strategy and search radius of the fruit fly optimization algorithm are improved to optimize the parameters of the adaptive sliding mode controller.

[0099] Furthermore, to address the difficulty of directly measuring the load swing angle of tower cranes under certain operating conditions, an extended state observer is designed for load swing state observation and estimation. The linear extended state observer has the advantages of fewer parameters, a simpler linear structure, and easier adjustment. Its parameters are linked to the observer bandwidth, and the system's input and output are used to estimate the extended system state.

[0100] Furthermore, an adaptive sliding mode controller is designed to feed back the tracking observation results to the adaptive sliding mode controller. In the construction of the sliding surface, the hyperbolic tangent function is used instead of the commonly used sign function to increase its continuity and reduce chattering. This enables the tower crane trolley to quickly track the desired position and effectively suppress load swing.

[0101] Furthermore, during the fruit fly-based algorithm implementation, the fixed search radius of one-third of the fruit flies searching along an arc-shaped curve is altered based on the average flavor concentration in the population. This causes two-thirds of the fruit flies to search along their original evolutionary direction, thus creating a new search method. This new method clarifies their roles, increases the diversity of individual search ranges, and expands the diversity of the population's search range. It overcomes the shortcomings of traditional fruit fly optimization algorithms, such as slow convergence, premature convergence, and susceptibility to local optima. In the parameter tuning process, the fruit fly optimization algorithm is used for parameter optimization, improving the efficiency and accuracy of parameter tuning.

[0102] An adaptive sliding mode control method for tower cranes based on an improved fruit fly optimization algorithm includes the following steps;

[0103] Step 1): Design an extended state observer to observe the load swing angle state;

[0104] Step 2): Design an adaptive sliding mode controller to feed back the observed swing angle state to the adaptive sliding mode controller. The controller will enable the trolley to be accurately positioned while suppressing the load swing angle oscillation.

[0105] Step 3): Improve the fruit fly optimization algorithm to optimize the parameters of the adaptive sliding mode controller, thereby improving the controller's control effect.

[0106] In step 1), designing the extended state observer includes the following steps:

[0107] like Figure 1 As shown, in the tower crane system of the expansion state observer, the mass of the luffing trolley and the load mass are represented by M and m, respectively. The origin is taken as the center of the intersection of the tower body of the tower crane with the counterweight boom and the jib. The driving force of the trolley moving along the luffing direction X on the boom is F. x x and l represent the luffing distance of the trolley and the length of the rope, respectively; θ1 represents the load swing angle when the tower crane is luffing; the Lagrange equation is used to establish the tower crane dynamics model;

[0108] The system's Lagrange operators:

[0109]

[0110] Establish the Lagrange equations corresponding to x and θ1:

[0111]

[0112] F fx This represents the frictional resistance experienced by the luffing trolley during its motion; let...

[0113]

[0114] Where f1 and f2 represent the friction factors in the amplitude direction, respectively.

[0115] The dynamic equations of the tower crane's simple pendulum system under the condition of constant rope length and variable amplitude are as follows:

[0116]

[0117]

[0118] After linearization, the tower crane system is converted into a state-space form as follows:

[0119]

[0120]

[0121] Where: M and m represent the mass of the luffing trolley and the load respectively, l represents the length of the rope, g is the gravitational acceleration, x represents the luffing distance of the trolley, θ1 represents the swing angle of the load when the tower crane is luffing, and F represents the luffing control force;

[0122] Let θ1 = α1, and expand equation (2).

[0123]

[0124]

[0125] Write equation (3) in matrix form

[0126]

[0127] in,

[0128] Design a Linear Extended State Observer (LESO) based on equation (4).

[0129]

[0130] Where matrix z represents the estimated value of state α, z = [z1z2] T , Let L be the estimated value of the output y, and L be the observation gain vector. ω0 is the LESO bandwidth, and e is defined as the observation error of α, e = [e1e2] T e1 = α1 - z1, e2 = α2 - z2.

[0131] From equations (4) and (5), the error equation for the observation can be obtained:

[0132]

[0133] Let W1 = e1, W2 = -3ω0e1 + e2, then (6) can be expressed as:

[0134]

[0135] Let a = 3ω0, Right now The characteristic equation of the above equation is: aλ 2 +bλ=0;

[0136] According to the Hurwitz condition, the necessary and sufficient condition for its eigenvalues ​​to have negative real parts is: a>0, b>0

[0137] Based on the Barbazin formula, the error equation and the Lyapunov function V are obtained.

[0138]

[0139] From a > 0 and b > 0, we can obtain:

[0140]

[0141] Differentiating the above equation and substituting equation (7) into it, we get:

[0142]

[0143] Then V is positive definite. LESO is asymptotically stable in the range e1=0, e2=0.

[0144] The linear expansion state observer is used for load swing state observation and estimation, which solves the problem that the load swing angle is difficult to measure directly in some operating conditions.

[0145] In step 2), the adaptive sliding mode controller is designed, including the following steps:

[0146] Define the linear sliding surface as:

[0147]

[0148] Where γ1, γ2, and γ3 are coefficients to be tuned, and the position error signal e x =xx p ,x p The target position of the variable amplitude trolley can be obtained by differentiating with respect to the linear sliding surface s.

[0149]

[0150] Substituting equations (1) and (2) into (9) yields

[0151]

[0152] make Find the equivalent driving force F

[0153]

[0154] Adding the hyperbolic tangent function ζtanh(s) based on the sliding surface s to equation (11), the control law is updated as follows:

[0155]

[0156] The hyperbolic tangent function ζtanh(s) used is a continuous function, which to some extent reduces the system chattering caused by the discontinuous sign function that is often used, and allows the controller to be corrected.

[0157] To further suppress chattering in the sliding mode control system and improve its disturbance rejection, adaptive control design is incorporated. The frictional resistance formula is rewritten in vector form:

[0158]

[0159]

[0160] Define the estimated value of the displacement output of the variable amplitude trolley:

[0161]

[0162] Wherein: Γ x ∈R 2×2 It is a positive definite diagonal matrix.

[0163] To improve the transient performance of the tower crane system, the following adaptive control law is proposed.

[0164]

[0165] in:

[0166]

[0167]

[0168] Where, θ 1o The target value for the load swing angle. It is the error value of the load swing angle. The displacement output y of the car x The estimated value enables the recursive realization of the corresponding parameter update rate, simplifying the controller design steps. Combining equations (12) and (15), the tower crane anti-sway controller can be designed as follows:

[0169] F = F xn +F xs (17)

[0170] The adaptive sliding mode controller eliminates load sway while accurately positioning the load trolley, and also solves the problem of chattering in sliding mode control.

[0171] In step 3), the improved fruit fly optimization algorithm adjusts the parameters of the adaptive sliding mode controller, including the following steps:

[0172] The main steps of traditional FOA are as follows:

[0173] Initialize the parameters related to the fruit fly population. When individual i searches for food using its sense of smell, its location is:

[0174]

[0175] In the above formula, X axis and Y axis To randomly initialize the fruit fly colony locations, R domvalue The random search distance for a single fruit fly individual.

[0176] The taste concentration value S at the location of the individual fruit fly was obtained. smell .

[0177] S smell =fitness(S i (19)

[0178] Among them, S i Let be the taste concentration judgment value for an individual fruit fly, and fitness represent the taste concentration judgment function.

[0179] Other fruit flies in the swarm use their vision to fly towards the optimal current taste concentration S. bestSmell The corresponding location of the fruit fly individual will form a new fruit fly population center after the location is updated. This process continues through iterative optimization until the optimal parameters are output.

[0180] Comparative analysis revealed that various improvements to the standard FOA consistently emphasize competition among individuals while neglecting the importance of population cooperation. Therefore, this application dynamically adjusts the Drosophila optimization strategy, causing 2 / 3 of the Drosophila to search along the original evolutionary direction, while the other Drosophila search around the edge of the evolutionary direction in an arc-shaped curve. This enriches the diversity of search paths and accelerates the optimization speed.

[0181] The new position of the individual fruit fly is determined by comparing its position with the linear position along the search direction, considering both global and local factors. The expression is as follows:

[0182]

[0183]

[0184] λi It represents the straight-line position from the individual's location to the search direction vector, rdom(*) is a random number within the search interval, and μ is the global-local coordination factor (a constant value), whose value is proportional to the search capability. The angle between the direction vectors of two adjacent fruit fly individuals is denoted as .

[0185] Furthermore, to address the issue of significant randomness in the search radius, this application modifies the fixed search radius of one-third of the fruit flies in the population, which involves circling the perimeter in an arc shape, based on the average flavor concentration in the population. By employing a new search radius method, the division of labor among individual fruit flies is clarified, the differences in individual search ranges are increased, and the diversity of the population's search range is expanded.

[0186] The new formula for calculating the search radius is as follows:

[0187]

[0188] R min The minimum search radius is Ssmo; the initial average flavor concentration of the population is Ssmo; R1 is the current search radius; t and T are the current iteration number and the maximum iteration number, respectively; Ssmli is the current flavor concentration; R max These refer to the maximum search radius. By optimizing the standard FOA optimization strategy and search radius, the aim is to improve the algorithm's optimization speed and accuracy, minimize the typical defects of the FOA algorithm that easily get trapped in local optima, reasonably disperse individual competition to enhance population cooperation, clarify the division of labor, improve the individual's escape ability and local development ability, and explore new evolutionary paths.

[0189] By using the mutant fruit fly algorithm to optimize controller parameters, the problems of large workload and insignificant effect of manual parameter tuning are reduced, thereby improving parameter accuracy and making the control effect more obvious.

[0190] The overall structural block diagram of the tower crane anti-sway control system is as follows: Figure 2 As shown.

[0191] The present invention will be further described in detail below through specific embodiments:

[0192] Example 1:

[0193] To verify the tracking and observation effect of the extended state observer, simulation was performed using Matlab / Simulink. The parameters of the first set of tower crane anti-sway system were selected as follows: M = 8 kg, m = 6 kg, l = 3 m. The simulation results of the tracking and observation are as follows. Figure 3The diagram on the left shows that the designed state observer can track speed relatively quickly, with the tracking error converging to near zero within 2 seconds, and the tracking error being less than 0.7% after 2 seconds. To verify the impact of system parameter changes on the observation results, a second set of simulations was conducted. The system parameters were selected as follows: M = 6 kg, m = 4 kg, l = 5 m. The tracking observation results of the tower crane system are as follows. Figure 3 The diagram on the right shows that under the conditions of changes in the amplitude-changing trolley and load mass, as well as changes in the rope length, the tracking accuracy is higher and the error convergence speed is faster due to the decrease in speed. Although periodic oscillations occur near the convergence to 0, the error remains within 1.3%, indicating that the extended state observer can still maintain a good tracking speed when the system parameters change.

[0194] Example 2:

[0195] To verify the control effect of the adaptive sliding mode controller after fully optimizing parameters using the Improved Fruit Fly Optimization Algorithm (IMFOA), three cases were selected: the adaptive sliding mode controller with standard FOA optimized parameters, without optimized parameters, and with IMFOA optimized parameters. Anti-sway control simulations of the tower crane system were conducted, and the control effects under different conditions were compared. Relevant parameters were selected: M = 8 kg, m = 6 kg, l = 3 m, g = 9.8 m / s², λ = 0.5, ε x =-0.01, γ1=0.54, γ2=0.62, γ3=-2.65, target position x of the luffing trolley p =1m. Simulation results comparing the control effects of the tower crane anti-sway controller are as follows: Figure 4 It can be seen that after reconstructing the sliding surface, the adaptive sliding mode controller can suppress the load swing angle in a short time even without parameter optimization. However, the controller after parameter optimization using the improved fruit fly optimization algorithm significantly increases the suppression effect on the peak load swing angle and accelerates the convergence speed of the residual load swing angle. At the same time, the accuracy of the trolley reaching the target position is improved without significant overshoot. This shows that IMFOA has good optimization ability and good applicability for controller parameter optimization.

[0196] Example 3

[0197] To verify the robustness of the adaptive sliding mode controller after parameter optimization via IMFOA, three sets of simulation experiments were designed, such as... Figure 5(a) Group A: varying load mass; (b) Group B: varying rope length; (c) Group C: varying initial load angle. It can be seen that when the load mass, rope length, and initial load angle increase, although the peak load swing is higher, it still remains at 1.5 degrees, and the residual swing angle converges to near 0 degrees within 5 seconds. When the load mass is small, the rope length is short, and the initial swing angle is close to 0 degrees, the peak load swing angle is controlled within 0.5 degrees. This demonstrates that the adaptive sliding mode controller with parameters fully optimized by IMFOA has excellent robustness.

[0198] Example 4

[0199] To verify the anti-interference capability of the adaptive sliding mode controller after parameter optimization via IMFOA, simulations were performed with different disturbance signals applied only during and after the swing, without changing any parameters. The simulation results... Figure 6 It can be seen that when the swing angle basically converges to around 0 degrees after 5 seconds, applying sinusoidal perturbations at 6 seconds, 11 seconds, and 16 seconds causes the swing angle amplitude to fluctuate within a small range before quickly stabilizing. After the swing angle has completely converged to 0 degrees, applying three pulse perturbations respectively results in fluctuation values ​​of less than 2 degrees, and the swing angle stabilizes quickly.

[0200] Although the present invention has been described in detail with reference to the above embodiments, the above embodiments are not intended to limit the present invention. Any additions, modifications, or substitutions of technical features made without departing from the technical features and structural scope given in the present invention should be within the protection scope of the present invention.

Claims

1. A tower crane self-adaptive sliding mode control method based on an improved fruit fly optimization algorithm, characterized in that, Includes the following steps; Step 1): Design an extended state observer to observe the load swing angle state; Step 2): Design an adaptive sliding mode controller to feed back the observed swing angle state to the adaptive sliding mode controller. The controller will enable the trolley to be accurately positioned while suppressing the load swing angle oscillation. Step 3): Optimize the parameters of the adaptive sliding mode controller by improving the fruit fly optimization algorithm, thereby improving the controller's control effect; In step 3), the improved fruit fly optimization algorithm adjusts the parameters of the adaptive sliding mode controller, including the following steps: The optimization strategy of fruit flies is dynamically adjusted so that 2 / 3 of the fruit flies search along the original evolutionary direction, while the other fruit flies search around the edge of the evolutionary direction in an arc-shaped curve. This enriches the diversity of search paths and accelerates the optimization speed. The new position of the individual fruit fly is determined by comparing its position with the linear position along the search direction, considering both global and local factors. The expression is as follows: （20） （21） It is the straight-line position from the individual's location to the search direction vector. It is a random number within the search range. It is a global-local coordination factor, the value of which is proportional to the search capability. The angle between the directional vectors of two adjacent fruit fly individuals; , Individual fruit flies Location when using the sense of smell to search for food; The search radius; Based on the average taste concentration in the population, the fixed search radius of 1 / 3 of the fruit flies in the population, which is used to circle the edge in an arc, is changed. By using the new search radius method, the division of labor among individual fruit flies is clarified, the difference in the individual search range is increased, and the diversity of the group search range is expanded. The formula for calculating the search radius is as follows: （22） Minimum search radius; It is the average flavor concentration value of the initial population; The current search radius is t; t and T are the current iteration number and the maximum iteration number, respectively. This is the current flavor concentration value; It is the maximum search radius; The current optimal flavor concentration value.

2. The tower crane adaptive sliding mode control method based on the improved fruit fly optimization algorithm according to claim 1, characterized in that, In step 1), designing the extended state observer includes the following steps: In the tower crane system, the mass of the luffing trolley and the load mass are represented by M and m, respectively. The origin is taken as the center of the intersection of the tower body, the counterweight jib, and the jib of the tower crane. The trolley moves along the luffing direction on the jib. The driving force during movement is ; and These represent the luffing distance of the trolley and the length of the rope, respectively. This represents the load swing angle when the tower crane is undergoing luffing motion; a dynamic model of the tower crane is established using the Lagrange equation; The system's Lagrange operators: Establish and The corresponding Lagrange equation: , This represents the frictional resistance experienced by the luffing trolley during its movement; make ， Where: f1 and f2 represent the friction factors in the amplitude direction, respectively; After linearization, the tower crane system is converted into a state-space form as follows: （1） （2） Where M and m represent the mass of the luffing trolley and the load being lifted, respectively. Indicates the length of the rope. It is the acceleration due to gravity. Indicates the distance the car makes a U-turn. This indicates the swing angle of the load being lifted when the tower crane is performing luffing motion. Indicates amplitude control force; make Expanding equation (2) （3） Write equation (3) in matrix form （4） in, , , , , , ; Design a Linear Extended State Observer (LESO) based on equation (4). （5） Where the matrix For state The estimated value, , For output The estimated value, For the observation gain vector, , Define the LESO bandwidth. for Observation error, , , ; From equations (4) and (5), the error equation for the observation can be obtained: （6） make , Then (6) can be expressed as: （7） make , , Right now The characteristic equation of the above equation is: ; According to the Hurwitz condition, the necessary and sufficient condition for its eigenvalues ​​to have negative real parts is: The error equation and Lyapunov function are derived from the Barbazin formula. Depend on , We can obtain: Differentiating the above equation and substituting equation (7) into it, we get: but Zhengding, LESO in It gradually stabilizes within the range.

3. The tower crane adaptive sliding mode control method based on the improved fruit fly optimization algorithm according to claim 1, characterized in that, In step 2), designing an adaptive sliding mode controller includes the following steps: Define the linear sliding surface as: （8） in, The coefficients to be tuned are the position error signal. , The target position of the luffing trolley; for the linear sliding surface Differentiation yields the result; （9） Substituting equations (1) and (2) into (9), we get （10） make Find the equivalent driving force （11） Add a sliding surface to equation (11) Hyperbolic tangent function based on Then the control law is updated to （12） The hyperbolic tangent function used It is a continuous function, which allows the controller to be corrected; Rewrite the frictional resistance formula in vector form: （13） Define the estimated value of the displacement output of the variable amplitude trolley: （14） in: It is a positive definite diagonal matrix; The following adaptive control law is proposed. （15） in: （16） in, The target value for the load swing angle. It is the error value of the load swing angle. It is the displacement output of the small car. The estimated value, combined with equations (12) and (15), is the tower crane anti-sway controller. （17）。

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