Anti-sway control method for variable rope length container crane based on phase plane trajectory planning

Abstract

The application discloses a variable rope length container crane anti-swing control method based on a phase plane trajectory planning, steps: obtaining a constant constant; inputting the constant constant into a lifting control parameter calculation model, the lifting control parameter calculation model outputs acceleration amplitudes a1 and a2, switching times t a1 、 t b 、 t a2 and t c ; determining a control scheme according to the above lifting control parameters, and controlling a trolley according to the control scheme, wherein the lowering control parameters are matched with the lifting control parameters in the control scheme. The method is suitable for any system taking a step acceleration signal as input, performing anti-swing control or relieving oscillation to finally realize zero oscillation, can control the load swing angle within the planned swing angle range, and relieve the residual oscillation of the system, and the residual oscillation is controlled below 4% of the maximum amplitude, which shows the effectiveness of the method and good application prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of trajectory planning of shore cranes, and relates to a variable rope length container crane anti-swing control method, equipment and storage medium based on phase plane trajectory planning, in particular to a method for planning load swing angle through phase plane method, processing variable rope length problem by using phase plane trajectory for linear approximation, realizing crane anti-swing, and the equipment and storage medium. BACKGROUND

[0002] Container cranes are widely used in various working environments such as ports and logistics companies. With the acceleration of social life, the requirement for logistics timeliness is also increasing, so it is necessary to study a crane control scheme with high efficiency. In order to ensure that the goods are quickly and accurately delivered to the target position, it is required to not only improve the transportation efficiency and enhance the safety of the crane system, but also to make the load swing as small as possible during the work process, so as to meet the requirements of the working environment and realize accurate positioning.

[0003] When the rope length changes, this system is a complex multi-input multi-output control system without considering the trolley operation. Not only the trolley operation needs to be controlled, but also the load lifting and lowering need to be controlled, and at the same time, the trolley needs to reach the target position quickly and the load swing angle output needs to be small. For the variable rope length condition, many scholars use feedback control for anti-swing design. For example, the method of designing a state observer to eliminate load swing, fuzzy logic or fuzzy estimation feedback anti-swing control strategy, adaptive control and the application of sliding mode control in anti-swing. These closed-loop control anti-swing methods increase the complexity and cost of the system. In order to reduce the complexity of the system and save the cost, while ensuring that the crane can quickly and efficiently complete the transportation work, many scholars have devoted themselves to the research of open-loop control anti-swing method under variable rope length. For example, the method of using multiple polynomials or multiple linear interpolation to fit the load trajectory for anti-swing control has not achieved good anti-swing effect, and there is a large residual error.

[0004] Therefore, it is of great practical significance to develop a variable rope length container crane anti-swing control method with simple system, low cost, good anti-swing effect and small residual error. SUMMARY

[0005] Since the prior art has the above-mentioned defects, the present application provides a variable rope length container crane anti-swing control method with simple system, low cost, good anti-swing effect and small residual error, specifically, the load has lifting and lowering motion while the trolley moves, the phase plane trajectory of the load swing angle is planned through linear approximation, the load swing is effectively suppressed, the system residual oscillation is relieved, the working efficiency of the crane system is improved, and the defects that the existing variable rope anti-swing control method cannot balance low cost and good anti-swing effect are overcome.

[0006] To achieve the above object, the present application provides the following technical solutions:

[0007] The variable rope length container crane anti-swing control method based on phase plane trajectory planning comprises the following steps:

[0008] (1) Obtain the length of the hoisting rope l, the target distance of the trolley S x , the maximum speed of the trolley v max , the maximum swing angle θ max , the lifting acceleration a vl , and the maximum lifting speed v lmax , and determine the control scheme type, which is lifting-maintaining-lowering or lifting-maintaining;

[0009] (2) Determine whether the control scheme type is lifting-maintaining-lowering. If yes, go to step (3), otherwise go to step (5);

[0010] (3) Input the parameters obtained in step (1) into the lifting control parameter calculation model. The lifting control parameter calculation model outputs the acceleration amplitudes a1 and a2, the switching times t a1 , t b , t a2 , and t c . The calculation formula involved in the lifting control parameter calculation model is as follows:

[0011] S x = a1t a1 2 + a2t a2 2 + t c (a1t a1 + a2t a2 ) + 2a1t a1 t a2 + 2a1t a1 t b

[0012] v max = a1t a1 + a2t a2

[0013] θ max = r2

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] t d =t a1 +t b ;

[0025] (4) Determine the control scheme based on the lifting control parameters and control scheme type obtained in step (3), and control the trolley according to the control scheme, wherein the descent control parameters and the lifting control parameters are matched in the control scheme;

[0026] (5) Input the parameters obtained in step (1) into the boost control parameter calculation model. The boost control parameter calculation model outputs acceleration amplitudes a1 and a2, and the switching time t a1 t b t a2 and t c Then, input the parameters obtained in step (1) into the holding control parameter calculation model, and the holding control parameter calculation model outputs the acceleration amplitude a. 12 and a 22 Switching time t a12 t b2 and t a22 The calculation formulas involved in the control parameter calculation model are basically the same as those in the improvement control parameter calculation model, except that the latter also includes the following formulas:

[0027] ω1=ω2=ω3=ω n ;

[0028] (6) Determine the control scheme based on the lifting control parameters, holding control parameters and control scheme type obtained in step (5), and control the trolley according to the control scheme.

[0029] To improve the working efficiency of quay cranes, the simultaneous lifting and lowering of the load during trolley movement is usually considered. Therefore, an anti-sway scheme for variable rope length container cranes is proposed, which is as follows: Figure 1 According to the dynamic formula, the load swing angle has the following relationship:

[0030]

[0031] in, l i =lv l t

[0032] In the formula: t represents time, and variable (t) represents the change of that variable with respect to time. Expressing the angular acceleration, θ(t) represents the angular acceleration, and ω represents the angular acceleration. n Let g represent the natural oscillation frequency, g represent the gravitational acceleration, l represent the initial length of the rope, and v represent the initial oscillation frequency. l Let a be the lifting speed of the rope. c This indicates the acceleration of the car.

[0033] Analysis of the mathematical model equations of the system reveals that, under time-varying conditions, the phase plane trajectory of the load swing angle exhibits limit cycle behavior. When the lifting speed v... l When < 0, according to the formula, a family of limit cycles is obtained on the phase plane, and the equilibrium solution is an unstable focus, such as Figure 2 As shown. When the acceleration v l When >0, according to the formula, another family of limit cycles is obtained in the phase plane, and the equilibrium solution is a stable focus, such as Figure 3 As shown. When the crane appropriately switches operating conditions during operation, there will be a family of limit cycle combinations, such as... Figure 2 As shown in the entity trajectory OABCO, the load swing angle and the trolley speed should be brought to zero within an appropriate time.

[0034] Studies have found that when using two-step acceleration, the period of large oscillations is so short that the difference between linear and nonlinear frequency approximations does not produce a significant deviation from the desired system dynamics. From the trajectory variation law of the two-step acceleration phase plane in the underactuated crane model formula, a trajectory profile resembling OABCO can be found, such as... Figure 4 As shown, this demonstrates that using a two-step acceleration method for phase plane trajectory planning, linearly approximating the equation is effective and feasible.

[0035]

[0036] During the acceleration phase of the vehicle, the approximation is mainly divided into three segments. In each segment, the natural oscillation frequency is calculated by taking the rope length at the midpoint of the switching time. The deceleration phase is symmetrical to the acceleration phase, and will not be elaborated further here. The phase plane trajectory design is as follows... Figure 4 As shown.

[0037] The acceleration signal obtained by the input shaper, which follows the designed phase plane trajectory, is as follows: Figure 5 As shown, we consider two cases after convolution: acceleration a1 > a2 and acceleration a1 < a2. The expression is as follows:

[0038]

[0039] Among them, t d =t a1 +t b , t g =t b +t a2 , t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

[0040] When 0≤t<t a1 At that time, the first limit cycle trajectory is linearly approximated by circle O1, with the trolley's acceleration being a1 and its lifting speed being v. l The natural oscillation frequency is ω1 during the operation process.

[0041]

[0042] When the acceleration is a1, solving the differential equation based on the formula yields:

[0043]

[0044] Taking the first derivative of the equation with respect to time t, we get...

[0045]

[0046] To facilitate the subsequent phase plane trajectory analysis, the following scaled angular velocity signal is introduced:

[0047]

[0048] Based on formula:

[0049]

[0050] It can be seen that when 0≤t<t a1 At that time, the input acceleration is a1, and the phase plane trajectory will follow the path of a1. With the center of the circle, an arc with radius The motion conforms to the planned phase plane trajectory of the swing angle.

[0051] When t a1 ≤t<t d At that time, using the circle O to linearly approximate the second limit cycle trajectory (gliding segment), the car's acceleration is 0, and its lifting speed is v. l The natural oscillation frequency is ω2.

[0052]

[0053] When the acceleration is 0, based on the equation to solve the differential equation:

[0054] θ2(t) = C4cos(ω2t) + C5sin(ω2t) (18)

[0055] The first order derivative of the equation with respect to time t is obtained:

[0056]

[0057] Wherein,

[0058]

[0059]

[0060] Similarly, introduce:

[0061]

[0062] Based on the equation-:

[0063]

[0064] Wherein,

[0065] It can be seen that when t a1 ≤t<t d , the input acceleration is 0, the phase plane trajectory will be along the circular arc Motion with the center as the origin and r2 as the radius, which meets the planned swing angle phase plane trajectory.

[0066] When t d ≤t<t e , the third segment limit ring trajectory is linearly approximated by the circle O2, the trolley acceleration is a2, the lifting speed is v l , and the natural oscillation frequency is ω3.

[0067]

[0068] When the acceleration is a2, based on the equation to solve the differential equation:

[0069]

[0070] The first order derivative of the equation with respect to time t is obtained:

[0071]

[0072] Wherein,

[0073]

[0074]

[0075]

[0076] Similarly, we have:

[0077]

[0078] Based on the formula:

[0079]

[0080] where r3 2 = C b 2 + C7 2

[0081] It can be seen that when t1≤t e , the input acceleration is a2, and the phase plane trajectory will follow a circular arc with r3 as the radius and as the center, which meets the planned swing angle phase plane trajectory.

[0082] Thus, the linear approximation planning of the phase plane trajectory of the load swing angle is completed, and the solution of the acceleration amplitude and switching time will be carried out next.

[0083] Based on the formula, the running distance S x of the trolley is obtained by twice integrating the time t:

[0084] S x = a1t a1 2 + a2t a2 2 + t c (a1t a1 + a2t a2 ) + 2a1t a1 t a2 + 2a1t a1 t b (27)

[0085] Based on the formula, the maximum speed v max of the trolley is:

[0086] v max = a1t a1 + a2t a2 (28)

[0087] Based on Figure 6 , the maximum swing angle θ maxThe amplitude of the line segment OB is equal to the radius of the circle of the swing angle equation of the sliding segment, so:

[0088] θ max = r2 (29)

[0089] The swing angle trajectory equation when the first segment is accelerated can be used to obtain the coordinates of point A:

[0090]

[0091] From the coordinates of point A, we can obtain:

[0092]

[0093] The swing angle trajectory equation of the sliding segment can be used to obtain the coordinates of point C:

[0094]

[0095] From the coordinates of point C, we can obtain:

[0096]

[0097] Based on Figure 6 , the acceleration time t a1 corresponding to the arc is calculated as follows:

[0098]

[0099] Based on Figure 6 , the acceleration time t a2 corresponding to the arc is calculated as follows:

[0100]

[0101] In order to make the swing angle return to zero after the second segment of acceleration, i.e., the load swing angle circle equation of the second segment of acceleration must pass through the origin, we have:

[0102]

[0103] Based on the constraint conditions: distance constraint, speed constraint, swing angle constraint, first segment acceleration time constraint, second segment acceleration time constraint, and zero return constraint, the acceleration amplitudes a1 and a2, the switching times t a1 , t b , t a2 , and t c can be solved. According to the acceleration signal generated by Figure 5 , the corresponding acceleration amplitudes and switching times are provided to the trolley, and the positioning and anti-shake control of the trolley can be completed.

[0104] As a preferred technical solution:

[0105] The variable rope length container crane anti-swing control method based on phase plane trajectory planning as described above, the lifting control parameters include acceleration amplitude a1 and a2, switching time t a1 , b , a2 And t c ;

[0106] The holding control parameters include acceleration amplitude a 12 And a 22 , switching time t a12 , b2 And t a22 .

[0107] The variable rope length container crane anti-swing control method based on phase plane trajectory planning as described above, the control scheme in step (4) is specifically that the trolley acceleration is kept at a1 during 0~t a1 ; The trolley acceleration is 0 during t a1 ~t d ; The trolley acceleration is a2 during t d ~t e ; The trolley acceleration is 0 during t e ~t f ; The trolley acceleration is-a2 during t f ~t f +t a2 ; The trolley acceleration is 0 during t f +t a2 ~t f +t g ; The trolley acceleration is kept at-a1 during t f +t g ~t f +t e , wherein t g =t b +t a2 , t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

[0108] The variable rope length container crane anti-swing control method based on phase plane trajectory planning as described above, the control scheme in step (6) is specifically that the trolley acceleration is kept at a1 during 0~t a1 ; The trolley acceleration is 0 during t a1 ~t dwhen the trolley acceleration is a2; t d ~t e when the trolley acceleration is a2; t e ~t f when the trolley acceleration is a2; t f ~t f +t a22 when the trolley acceleration is -a 22 ; t f +t a22 ~t f +t a22 +t b2 when the trolley acceleration is 0; t f +t a22 +t b2 ~t f +t a22 +t b2 +t a12 when the trolley acceleration remains at -a 12 , wherein t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

[0109] The application further provides a computer device, which comprises:

[0110] at least one processor; and

[0111] a memory in communication connection with the at least one processor; wherein

[0112] the memory stores computer readable instructions, and the processor executes the computer readable instructions to realize the phase plane trajectory planning based variable rope length container crane anti-swing control method as described above.

[0113] In addition, the application further provides a computer readable storage medium, which stores computer readable instructions, and the computer readable instructions are executed by a processor to realize the phase plane trajectory planning based variable rope length container crane anti-swing control method as described above.

[0114] The above technical solution is only one feasible technical solution of the application, and the protection scope of the application is not limited to this. Those skilled in the art can reasonably adjust the specific design according to actual needs.

[0115] The above application has the following advantages or beneficial effects:

[0116] (1) The variable rope length container crane anti-swing control method based on phase plane trajectory planning of the present application uses a method combining phase plane trajectory planning and input shaping, which is simple in structure and easy to implement;

[0117] (2) The variable rope length container crane anti-swing control method based on phase plane trajectory planning of the present application adopts the phase plane method, which can clearly see the change of the swing angle size in the phase plane, and then use the swing angle phase plane trajectory planning swing angle change to effectively control the swing angle size;

[0118] (3) The variable rope length container crane anti-swing control method based on phase plane trajectory planning of the present application analyzes the change of the load swing angle trajectory under variable rope length through the phase plane method, linearizes the time-varying system into a time-invariant system, and realizes the effective anti-swing effect under the condition of convenient calculation;

[0119] (4) The variable rope length container crane anti-swing control method based on phase plane trajectory planning of the present application is suitable for any system with step acceleration signal as input for anti-swing control or oscillation mitigation to ultimately realize zero oscillation;

[0120] (5) The variable rope length container crane anti-swing control method based on phase plane trajectory planning of the present application can obtain a control scheme with small residual oscillation, realize linear approximation, and has good application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0121] The present application and its features, shapes and advantages will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The same reference signs indicate the same parts throughout the drawings. The drawings are not necessarily drawn to scale, the emphasis being on illustrating the main idea of the present application.

[0122] Figure 1 is a trolley motion model schematic diagram;

[0123] Figure 2 is a v l is a load dynamic trajectory schematic diagram when <0;

[0124] Figure 3 is a v l is a load dynamic trajectory schematic diagram when >0;

[0125] Figure 4 is a phase plane trajectory approximate planning design schematic diagram;

[0126] Figure 5 is an acceleration signal shaping schematic diagram;

[0127] Figure 6 is a load swing angle phase plane trajectory planning geometric relationship schematic diagram;

[0128] Figure 7 for S x = 50 m, θ max = 4°, v max = 2.8 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0129] Figure 8 for S x = 50 m, θ max = 3°, v max = 2.2 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0130] Figure 9 for S x = 50 m, θ max = 2°, v max = 1.4 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0131] Figure 10 for S x = 30 m, θ max = 4°, v max = 2.2 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0132] Figure 11 for S x = 30 m, θ max = 3°, v max = 1.8 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0133] Figure 12 for S x = 30 m, θ max = 2°, v max = 1.2 m / s, where a is the trolley velocity, trolley acceleration and hoist acceleration trajectories, b is the load position trajectory, c is the swing angle trajectory, and d is the swing angle phase plane trajectory;

[0134] Figure 13 is a schematic diagram of the computer device of Example 2. DETAILED DESCRIPTION

[0135] The structure of the present application will be further described below in combination with the drawings and specific examples, but not as a limitation of the present application.

[0136] Example 1

[0137] A variable rope length container crane anti-swing control method based on phase plane trajectory planning, comprising the following steps:

[0138] (1) Obtain the length of the hoisting rope l, the trolley target distance S x , the maximum trolley speed v max , the maximum swing angle θ max , the lifting acceleration a vl , and the maximum lifting speed v lmax , and determine the control scheme type, which is lifting-holding-descending or lifting-holding;

[0139] (2) Determine whether the control scheme type is lifting-holding-descending. If yes, go to step (3), otherwise go to step (5);

[0140] (3) Input the parameters obtained in step (1) into the lifting control parameter calculation model. The lifting control parameter calculation model outputs the acceleration amplitude a1 and a2, the switching time t a1 , t b , t a2 , and t c . The calculation formula involved in the lifting control parameter calculation model is as follows:

[0141] S x = a1t a1 2 + a2t a2 2 + t c (a1t a1 + a2t a2 ) + 2a1t a1 t a2 + 2a1t ai t b

[0142] v max = a1t a1 + a2t a2

[0143] θ max = r2

[0144]

[0145]

[0146]

[0147]

[0148]

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] t d =t a1 +t b ;

[0155] (4) determining a control scheme according to the lifting control parameters (including acceleration amplitudes a1 and a2, switching times t a1 , t b , t a2 and t c ) and the control scheme type obtained in step (3), and controlling the trolley according to the control scheme, wherein the control scheme matches the lifting control parameters with the lowering control parameters, and the control scheme is specifically that the trolley acceleration is kept at a1 during 0~t a1 , the trolley acceleration is 0 during t a1 ~t d , the trolley acceleration is a2 during t d ~t e , the trolley acceleration is 0 during t e ~t f , the trolley acceleration is -a2 during t f ~t f +t a2 , the trolley acceleration is 0 during t f +t a2 ~t f +t g , the trolley acceleration is kept at -a1 during t f +t g ~t f +t e , wherein t g =t b +t a2 , t e =t a1 +t b +t a2 , t f =t a1 +tb +t a2 +t c ;

[0156] (5) input the parameters obtained in step (1) into the boost control parameter calculation model, the boost control parameter calculation model outputs acceleration amplitudes a1 and a2, switching times t a1 , t b , t a2 and t c , and input the parameters obtained in step (1) into the hold control parameter calculation model, the hold control parameter calculation model outputs acceleration amplitudes a 12 and a 22 , switching times t a12 , t b2 and t a22 , the calculation formula involved in the hold control parameter calculation model is basically the same as that of the boost control parameter calculation model, except that it further includes the following formula:

[0157] ω1 = ω2 = ω3 = ω n ;

[0158] (6) determine the control scheme according to the boost control parameters (including acceleration amplitudes a1 and a2, switching times t a1 , t b , t a2 and t c ) and the hold control parameters (including acceleration amplitudes a 12 and a 22 , switching times t a12 , t b2 and t a22 ) obtained in step (5) and the control scheme type, and control the trolley according to the control scheme, the control scheme is specifically that the acceleration of the trolley is kept at a1 during 0~t a1 , the acceleration of the trolley is 0 during t a1 ~t d , the acceleration of the trolley is a2 during t d ~t e , the acceleration of the trolley is 0 during t e ~t f , the acceleration of the trolley is -a f during t f ~t a22 , the acceleration of the trolley is 0 during t 22 +t f ~t a22 +t f +t a22 , the acceleration of the trolley is 0 during t b2 +t f +t a22 +t b2~t f +t a22 +t b2 +t a12 so that the trolley acceleration is kept at -a 12 where t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

[0159] In order to verify the anti-swing control performance of the above method on the crane, according to the theoretical analysis above, the present application uses Matlab to carry out numerical simulation, and analyzes the anti-swing effectiveness after linear approximation of the phase plane trajectory. In the simulation, the system parameters are determined as follows: the length of the hoisting rope is 30 m, the acceleration of lifting is 0.75 m / s 2 , the maximum lifting speed is 1.5 m / s, the trolley target is 30 m and 50 m, the maximum swing angle of the load is respectively constrained to be about 4°, 3° and 2°, and the maximum speed of the trolley is 2.8 m / s, 2.2 m / s, 1.8 m / s, 1.4 m / s and 1.2 m / s.

[0160] The simulation is divided into two cases. The first case is the lifting-keeping-lowering case. After accelerating for 2 s, the trolley starts to accelerate, the load is lifted from 30 m to 13.5 m, then the load is kept unchanged for a fixed rope length, and then the load is lowered when the trolley moves to the target position. The second case is the lifting-keeping case. After accelerating for 2 s, the trolley starts to accelerate, the load is lifted from 30 m to 13.5 m, then the load is kept unchanged for a fixed rope length, and the trolley stops when it moves to the target position.

[0161] Scheme one: lifting-keeping-lowering scheme

[0162] According to the constraint conditions obtained by the linear approximation planning scheme of the phase plane trajectory: distance constraint, speed constraint, swing angle constraint, first segment acceleration time constraint, second segment acceleration time constraint and zero return constraint, the acceleration amplitude and switching time of the lifting stage can be obtained. The specific acceleration amplitude and switching time are shown in Table 1. The data in Table 1 is provided to the trolley according to the Figure 5 generated acceleration signal, so that the positioning and anti-swing control of the trolley can be completed, and the simulation results are as follows Figures 7 to 9 .

[0163] Table 1: Acceleration amplitude and switching time of lifting-keeping-lowering

[0164]

[0165] from Figures 7 to 9 It can be seen that the phase plane trajectory conforms to the planned trajectory, and the maximum swing angle, load increase, and target distance all meet the design requirements. However, since the time-varying system is approximately a time-invariant system, there is a small amount of residual oscillation in the load swing.

[0166] exist Figure 7 The simulation parameters are designed as follows: the target distance of the car is 50m, the maximum speed is 2.8m / s, the maximum swing angle is 4°, and the lifting acceleration is 0.75m / s². 2 The maximum lifting speed is 1.5 m / s. From Figure 7 (c) shows that the system has a small residual oscillation, which is suppressed to less than 1.7% of its maximum amplitude.

[0167] exist Figure 8 In the middle, the maximum speed decreased to 2.2 m / s, and the maximum swing angle decreased to 3°. From Figure 8 (c) From the swing angle trajectory, the system exhibits a small residual oscillation, which is suppressed to below 1.6% of its maximum amplitude. As the speed decreases, the trolley's running time increases.

[0168] exist Figure 9 In the middle, the maximum speed further decreased to 1.4 m / s, and the maximum swing angle further decreased to 2°. From Figure 9 (c) From the swing trajectory, the system exhibits a small residual oscillation, which is suppressed to below 1.5% of its maximum amplitude. The speed is lower, and the trolley travels for a longer period.

[0169] Option 2: Improvement-Maintainment Plan

[0170] Based on the constraints obtained from the phase plane trajectory approximation planning scheme—velocity constraint, swing angle constraint, first-stage acceleration time constraint, second-stage acceleration time constraint, and zero-return constraint—the acceleration amplitude and switching time of the lifting phase can be calculated. In the fixed rope length phase, we can let ω1=ω2=ω3=ω n Based on the constraints, the acceleration amplitude and switching time can be obtained. During the fixed rope length stage, this paper adopts two different schemes: two cases where the acceleration amplitude and acceleration time are equal, and two cases where the acceleration amplitude and acceleration time are unequal. The specific acceleration amplitude and switching time are shown in Table 2. The data in Table 2 are then processed according to... Figure 5 The generated acceleration signal is provided to the vehicle, which can then perform positioning and anti-sway control. The simulation results are as follows: Figures 10 to 12 .

[0171] Table 2: Boost-fixed acceleration amplitude and switching time

[0172]

[0173] S in Table 2x , v max , θ max , a1, a2, t a1 , t b , t a2 , t c , a 12 , a 22 , t a12 , t b2 , t a22 in m, m / s, deg, m / s 2 , m / s 2 , s, s, s, s, m / s 2 , m / s 2 , s, s, s.

[0174] It can be seen from Figures 10 to 12 that the phase plane trajectory agrees with the planned trajectory, and the maximum swing angle, load lifting and target distance all meet the design requirements. However, due to the approximation of the time-varying system as a time-invariant system, there is a small amount of residual oscillation in the load swing.

[0175] In Figure 10 , the simulation parameters are designed as follows: the target distance of the trolley is 30 m, the maximum speed is 2.2 m / s, the maximum swing angle is 4°, the lifting acceleration is 0.75 m / s 2 , and the maximum lifting speed is 1.5 m / s. From the swing angle trajectory of Figure 10 (c), it can be seen that the system has a small residual oscillation, which is suppressed below 3.9% of its maximum amplitude.

[0176] In Figure 11 , the maximum speed is reduced to 1.8 m / s, and the maximum swing angle is reduced to 3°. From the swing angle trajectory of Figure 11 (c), it can be seen that the system has a small residual oscillation, which is suppressed below 2.9% of its maximum amplitude. The speed is smaller, and the trolley running time is longer.

[0177] In Figure 12 , the maximum speed is further reduced to 1.2 m / s, and the maximum swing angle is further reduced to 2°. From the swing angle trajectory of Figure 12 (c), it can be seen that the system has a small residual oscillation, which is suppressed below 2.8% of its maximum amplitude. The speed is smaller, and the trolley running time is longer.

[0178] From Figures 7 to 12It can be seen that the larger the swing angle constraint is, the greater the maximum speed is, the shorter the total running time is, and the higher the transportation efficiency is. It is possible that no solution can be found to satisfy the conditions when trying to solve a large speed constraint and a small swing angle constraint. Because the constraint of the maximum swing angle and the constraint of the maximum speed are mutually restricted, it is impossible to have the advantages of both at the same time. It can be known from the residual oscillation calculation that the residual oscillation is small when the swing angle constraint is small. The simulation results show that the residual oscillation of the load swing angle is small, which can be accepted or even ignored. This proves the effectiveness and practicability of the linear approximation method proposed in the present application.

[0179] Embodiment 2

[0180] A computer device, as shown in Figure 13 includes at least one processor and a memory connected with the at least one processor in communication;

[0181] The memory stores computer readable instructions, and the processor executes the computer readable instructions to implement the variable rope length container crane anti-swing control method based on the phase plane trajectory planning as described in Embodiment 1.

[0182] Embodiment 3

[0183] A computer readable storage medium, which stores computer readable instructions, and the computer readable instructions are executed by a processor to implement the variable rope length container crane anti-swing control method based on the phase plane trajectory planning as described in Embodiment 1.

[0184] Those skilled in the art should understand that those skilled in the art can make changes in combination with the prior art and the above embodiments, which are not described here. Such changes do not affect the essential content of the present application, which are not described here.

[0185] The preferred embodiments of the present application are described above. It should be understood that the present application is not limited to the above specific embodiments, and the devices and structures not described in detail should be understood as being implemented in the ordinary way in the art; any person skilled in the art can make many possible changes and modifications to the technical solutions of the present application, or modify them as equivalent embodiments, without departing from the scope of the technical solutions of the present application, which does not affect the essential content of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, without departing from the technical solutions of the present application, are still within the scope of protection of the technical solutions of the present application.

Claims

1. A method for anti-sway control of variable rope length container cranes based on phase plane trajectory planning, characterized in that... The steps include: (1) Obtain the length l of the suspension rope and the target distance S of the trolley. x The maximum speed of the car, v max Maximum swing angle θ max Increase acceleration a vl and maximum speed v lmax And determine the control scheme type, which is either lift-hold-descent or lift-hold; (2) Determine whether the control scheme type is lift-hold-decline. If so, proceed to step (3); otherwise, proceed to step (5). (3) Input the parameters obtained in step (1) into the boost control parameter calculation model. The boost control parameter calculation model outputs acceleration amplitudes a1 and a2, and the switching time t a1 t b t a2 and t c The calculation formulas involved in improving the control parameter calculation model are as follows: S x =a1t a1 2 +a2t a2 2 +t c (a1t a1 +a2t a2 )+2a1t a1 t a2 +2a1t a1 t b v max =a1t a1 +a2t a2 i max =r2 t d =t a1 +t b ; (4) Determine the control scheme based on the lifting control parameters and control scheme type obtained in step (3), and control the trolley according to the control scheme, wherein the descent control parameters and the lifting control parameters are matched in the control scheme; (5) Input the parameters obtained in step (1) into the boost control parameter calculation model. The boost control parameter calculation model outputs acceleration amplitudes a1 and a2, and the switching time t a1 t b t a2 and t c Then, input the parameters obtained in step (1) into the holding control parameter calculation model, and the holding control parameter calculation model outputs the acceleration amplitude a. 12 and a 22 Switching time t a12 t b2 and t a22 The calculation formulas involved in the control parameter calculation model are basically the same as those in the improvement control parameter calculation model, except that the latter also includes the following formulas: ω1=ω2=ω3=ω n ; (6) Determine the control scheme based on the lifting control parameters, holding control parameters and control scheme type obtained in step (5), and control the trolley according to the control scheme.

2. The anti-sway control method for variable rope length container cranes based on phase plane trajectory planning according to claim 1, characterized in that, The boost control parameters include acceleration amplitudes a1 and a2, and switching time t. a1 t b t a2 and t c ; The holding control parameters include the acceleration amplitude a. 12 and a 22 Switching time t a12 t b2 and t a22 .

3. The anti-sway control method for variable rope length container cranes based on phase plane trajectory planning according to claim 2, characterized in that, The control scheme in step (4) is specifically as follows: from 0 to t a1 The acceleration of the t vehicle is kept constant at a1; t a1 ~t d When the acceleration of the car is 0; t d ~t e When the acceleration of the t-car is a2; e ~t f When the acceleration of the car is 0; t f ~t f +t a2 When the acceleration of the car is -a2; t f +t a2 ~t f +t g When the acceleration of the car is 0; t f +t g ~t f +t e The acceleration of the car is kept at -a1, where t g =t b +t a2 , t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

4. The anti-sway control method for variable rope length container cranes based on phase plane trajectory planning according to claim 2, characterized in that, The control scheme in step (6) is specifically as follows: from 0 to t a1 The acceleration of the t vehicle is kept constant at a1; t a1 ~t d When the acceleration of the car is 0; t d ~t e When the acceleration of the t-car is a2; e ~t f When the acceleration of the car is 0; t f ~t f +t a22 When the acceleration of the car is -a 22 ;t f +t a22 ~t f +t a22 +t b2 When the acceleration of the car is 0; t f +t a22 +t b2 ~t f +t a22 +t b2 +t a12 This keeps the car's acceleration at -a 12 , where t e =t a1 +t b +t a2 , t f =t a1 +t b +t a2 +t c .

5. A computer device, characterized in that, The computer device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores computer-readable instructions, and when the processor executes the computer-readable instructions, it implements the anti-sway control method for variable rope length container cranes based on phase plane trajectory planning as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, implement the anti-sway control method for variable rope length container cranes based on phase plane trajectory planning as described in any one of claims 1 to 4.

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