A dynamic modeling method and control method for double-bridge lifting equipment

Abstract

The present invention belongs to the field of lifting equipment control technology, and specifically relates to a dynamic modeling method and control method for double-bridge lifting equipment. The dynamic equations of a five-degree-of-freedom double-bridge crane are constructed using the Lagrangian method, and the geometric constraint relationships between trolley I and trolley II in the direction parallel to the bridge and the vertical direction are constructed. The dynamic model of the double-bridge crane is constructed by combining the dynamic equations and the geometric constraint relationships, and the dynamic model is transformed into a general model. Based on the general model, a first error function is constructed based on the difference between the actual position and the expected position, and a virtual controller is constructed based on the first error function. A second error function is constructed based on the virtual controller, and an actual controller is constructed based on the first error function, the virtual controller, and the second error function. This technical solution models the system as a whole through the constraint relationship between the two trolleys, taking the mass of the hook into consideration during the modeling process, and solving the singularity problem.

Description

Technical Field

[0001] The present invention belongs to the technical field of control of under-actuated five-degree-of-freedom double-bridge lifting equipment, and in particular relates to a dynamic modeling method and a control method of the double-bridge lifting equipment. Background Art

[0002] Bridge cranes are important equipment for cargo loading and unloading. In practice, for many large and heavy loads, such as large pipelines and rockets, it is difficult to transport them with a single bridge crane, so double bridge cranes are generally used.

[0003] For dual-bridge cranes, they have nonlinear and under-driven characteristics, so fast and accurate control of the entire system is still a challenge. The control problem of dual-bridge cranes mainly lies in how to ensure the coordination between the two trolleys and control the entire system as a whole. At present, most of the more mature research on dual-bridge cranes is to split the two trolleys into two independent systems and control them separately. This method ignores the coordination between the two trolleys, such as reference [1]: Miller, AS, Sarvepalli, P., & Singhose, W. (2014). Dynamics and control of dual hoist cranes moving triangular payloads. In ASME dynamic systems and control conference. (pp. 1-9). Although some studies have conducted holistic modeling for dual-bridge crane equipment, their models have singularity problems, which can easily lead to system loss of control during the control process, such as reference [2]: [2] Lu, B. Sun, N. (2020). Adaptive Output-FeedbackControl forDual Overhead Crane System With Enhanced Anti-Swing Performance. IEEE Transactions on Control Systems Technology, 28 (6), 2235-2248. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to make up for the deficiencies of the prior art and provide a dynamic model and a control method for a double-bridge lifting equipment.

[0005] To solve the above technical problems, the technical solution of the present invention is:

[0006] A method for modeling a dynamic model of a double-bridge lifting equipment comprises the following steps:

[0007] Step SA1: Construct the dynamic equations of the five-degree-of-freedom double-bridge crane by Lagrangian method;

[0008] Step SA2: Construct the geometric constraint relationship between trolley I and trolley II in the direction parallel to the bridge and in the vertical direction respectively;

[0009] Step SA3: Combining the dynamic equations of the five-degree-of-freedom double-bridge crane in step SA1 and the geometric constraint relationship in step SA2, a dynamic model of the double-bridge crane is constructed.

[0010] Furthermore, in step SA1, the dynamic equation of the five-degree-of-freedom double-bridge crane is:

[0011] (1);

[0012] in, is the state vector of the system, Represents time, and They are About Time The first and second derivatives of ; represents the actual displacement of trolley I, represents the actual displacement of trolley II, and They represent the swing angles of cable I and cable II parallel to the bridge direction respectively; Indicates the tilt angle of the load;

[0013] is the system damping vector, and ; and are the friction coefficients of trolley I and trolley II respectively. and is the friction coefficient between cable I and cable II and the air when they swing parallel to the bridge frame. is the coefficient of friction between the load and the air when it is tilted parallel to the bridge direction; and They represent the moving speeds of trolley I and trolley II respectively, and They represent the speeds of cable I and cable II swinging in the direction parallel to the bridge frame, is the speed at which the load changes in the inclination angle parallel to the bridge direction;

[0014] is the control input vector; and They represent the driving forces of trolley I and trolley II respectively;

[0015] is the gravity matrix, and ; The mass of trolley Ⅰ and trolley Ⅱ are The mass of hook Ⅰ and hook Ⅱ are , the mass of the load is , the lengths of cable I and cable II are ; is the gravitational constant;

[0016] is the inertia matrix, is the centripetal-Coriolis force matrix.

[0017] Furthermore, the geometric constraint relationship between trolley I and trolley II in step SA2 in the direction parallel to the bridge and in the vertical direction is:

[0018] (2);

[0019] (3);

[0020] in, Represents the distance between the connection point I where the load is connected to cable I and the connection point II where the load is connected to cable II.

[0021] Furthermore, in step SA3, the dynamic model of the double bridge crane is:

[0022] (4);

[0023] in, , , , , , ;

[0024] is the constraint matrix, and

[0025] .

[0026] Furthermore, it also includes

[0027] Step SA4: Transform the dynamic model of the double-bridge crane constructed in step SA3 into a general model:

[0028] remember: ;

[0029] ;

[0030] Then formula (4) can be written as

[0031] (5);

[0032] Formula (4) can be transformed into a general model in the following form:

[0033] (6);

[0034] in , ;

[0035] is the system matrix;

[0036] represents the force of the control system, and They represent the driving forces of trolley I and trolley II respectively, and y is the actual output of the system.

[0037] A control method for double-bridge lifting equipment comprises the following steps:

[0038] Step SB1: Based on the above general model, construct the first error function:

[0039] (7);

[0040] in, is the actual position vector, and Can be obtained through position sensors; is the expected position vector; represent the desired positions of trolley I and trolley II respectively;

[0041] Step SB2: Define the control parameter matrix , combined with the desired speed of trolley I and trolley II, the first error function and the control parameter matrix , build a virtual controller :

[0042] (8);

[0043] in, , All are positive numbers;

[0044] , denote the expected speeds of trolley I and trolley II respectively;

[0045] Step SB3: Combine with Virtual Controller , construct the second error function:

[0046] (9);

[0047] in, ;

[0048] Step SB4: Define the control parameter matrix , combined with the first error function and the control parameter matrix , virtual controller , the second error function and the control parameter matrix , construct the actual controller:

[0049] (10);

[0050] in, , All are positive numbers;

[0051] , and They represent the expected displacement acceleration of trolley I and trolley II respectively.

[0052] Furthermore, it also includes

[0053] Step SB5: Obtain the control parameter matrix by pole configuration method and the control parameter matrix .

[0054] Furthermore, in step SB5, Obtained by the following formula:

[0055] ;

[0056] ;

[0057] ;

[0058] ;

[0059] in, yes The dominant point, , , is the expected adjustment time of trolley I, ; yes The dominant point, , , is the expected adjustment time of trolley II, .

[0060] Furthermore, it also includes

[0061] Step SB6: and Assign, obtain ;

[0062] Step SB7: Under the control of the actual controller, the double-bridge crane equipment is operated to perform a lifting test operation, and then the actual position-time curves of trolley I and trolley II are output respectively. The actual position-time curves are curves with time as the horizontal axis and actual position as the vertical axis; the steady-state positions of trolley I and trolley II are found in the corresponding position-time curves. The time corresponding to the steady-state position is the actual control time;

[0063] Step SB8: For trolley I and trolley II, determine whether the error between the actual adjustment time and the expected adjustment time is within ±20%;

[0064] If not satisfied, and The values ​​of are all increased with a step size of 1, and then return to step SB6;

[0065] If satisfied, for trolley I and trolley II, determine whether the error between the steady-state position and the expected position is within ±2%;

[0066] If not satisfied, and The values ​​of are all increased with a step size of 0.1, and then return to step SB7;

[0067] If satisfied, then The optimal value of .

[0068] The beneficial effects that can be achieved by the present invention are:

[0069] (1) This technical solution models the system as a whole by constructing a constraint relationship between trolley I and trolley II. The mass of the hook is fully considered during the modeling. This is because the shape and mass of the load hoisted by the double-bridge crane are usually large, so the mass of the hook is also large. If the mass of the hook is ignored and the mass of the load is only equivalent to its center of mass, this is not only inconsistent with the actual system model, but also the third and fourth rows of the inertia matrix obtained are equal in the initial state, so its determinant is 0, the inertia matrix is ​​irreversible, and the model has a singularity problem. After taking the mass of the hook into account, the third and fourth rows of the inertia matrix in the initial state are different, the determinant is no longer 0, the singularity problem is solved, and the model considered is more consistent with the actual model. The established dynamic model is of great significance for realizing the nonlinear control of the double-bridge crane.

[0070] (2) For under-actuated double-bridge cranes, a nonlinear controller based on the backstepping method was constructed. The proposed control scheme is based on the established model of the double-bridge crane and fully considers the coordination between the two trolleys. It is the first time that the backstepping method is combined with the under-actuated double-bridge crane, providing a new solution for the nonlinear control of the double-bridge crane. It solves the shortcomings of previous studies that did not consider the coordination between the two trolleys and the control anomalies and model loss of control that may be caused by the singularity of the inertia matrix in the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a schematic diagram of a five-degree-of-freedom double-bridge crane in the present invention.

[0072] Figure 2 This is the actual position-time curve of trolley I outputted in Experiment 1 of the embodiment of the present invention.

[0073] Figure 3 This is the actual position-time curve of trolley II outputted in Experiment 1 of the embodiment of the present invention.

[0074] Figure 4 This is the actual position-time curve of trolley I outputted in Experiment 2 of Example 1 of the present invention.

[0075] Figure 5 This is the actual position-time curve of trolley II outputted in Experiment 2 of Example 1 of the present invention.

[0076] Figure 6 The cable I output from Experiment 1 and Experiment 2 of the embodiment of the present invention is Curves of change over time.

[0077] Figure 7 The cable II output from Experiment 1 and Experiment 2 of the embodiment of the present invention is Curves of change over time.

[0078] Figure 8 The load output of Experiment 1 and Experiment 2 of the embodiment of the present invention is Curves of change over time.

[0079] Figure 9 The driving force of the trolleys I and II in Experiment 1 and Experiment 2 of the embodiment of the present invention is and Curves of change over time.

[0080] Figure 10 This is the actual position-time curve of trolley I and trolley II outputted in Experiment 3 of the embodiment of the present invention.

[0081] Figure 11 The output of cable Ⅰ in experiment 3 of the present invention is 、Cable II and load Curves of change over time.

[0082] Figure 12 The driving force of the trolleys I and II in the third experiment of the embodiment of the present invention is and Curves of change over time.

[0083] In the figure: 1-trolley I, 2-cable I, 3-connection point I, 4-load, 5-connection point II, 6-cable II, 7-trolley II. DETAILED DESCRIPTION

[0084] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] A method for modeling a dynamic model of a double-bridge lifting equipment comprises the following steps:

[0086] Step SA1: Construct the dynamic equations of the five-degree-of-freedom double-bridge crane by Lagrangian method:

[0087] (1);

[0088] in, is the state vector of the system, Represents time, and They are About Time The first and second derivatives of ; represents the actual displacement of trolley I, represents the actual displacement of trolley II, and They represent the swing angles of cable I and cable II parallel to the bridge direction respectively; Indicates the tilt angle of the load;

[0089] is the system damping vector, and ; and are the friction coefficients of trolley I and trolley II respectively. and is the friction coefficient between cable I and cable II and the air when they swing parallel to the bridge frame. is the coefficient of friction between the load and the air when it is tilted parallel to the bridge direction; and They represent the moving speeds of trolley I and trolley II respectively, and They represent the speeds of cable I and cable II swinging in the direction parallel to the bridge frame, is the speed at which the load changes in the inclination angle parallel to the bridge direction;

[0090] is the control input vector; and They represent the driving forces of trolley I and trolley II respectively;

[0091] is the gravity matrix, and ; The mass of trolley Ⅰ and trolley Ⅱ are The mass of hook Ⅰ and hook Ⅱ are , the mass of the load is , the lengths of cable I and cable II are ; is the gravitational constant;

[0092] is the inertia matrix, is the centripetal-Coriolis force matrix;

[0093] ;

[0094] ;

[0095] ;

[0096] ;

[0097] The inventors have conducted intensive research and found that the mass of the hook is generally ignored when modeling in the existing technology, such as in the literature [2]. However, for double-bridge lifting equipment, since the shape and mass of its load are usually large, the mass of its hook is also large. If its mass is ignored, the mass of the load is equivalent to its center of mass, which is inconsistent with the actual system model. The inertia matrix obtained by ignoring the mass of the hook is equal to the third and fourth rows in the initial state, so its determinant is 0, the inertia matrix is ​​irreversible, and the model has a singularity problem. After the hook mass is taken into account in this technical solution, the third and fourth rows of the inertia matrix in the initial state are different, the determinant is no longer 0, the singularity problem is solved, and the model considered is more consistent with the actual model.

[0098] Step SA2: Construct the geometric constraint relationships between trolley I and trolley II in the direction parallel to the bridge and in the vertical direction respectively:

[0099] (2);

[0100] (3);

[0101] in, Represents the distance between the connection point I of the load and cable I and the connection point II of the load and cable II;

[0102] Step SA3: Combine the dynamic equations of the five-degree-of-freedom double-bridge crane in step SA1 and the geometric constraint relationship in step SA2 to construct a dynamic model of the double-bridge crane:

[0103] (4);

[0104] in, , , , , , ;

[0105] is the constraint matrix, and

[0106] .

[0107] Furthermore, it also includes

[0108] Step SA4: Transform the dynamic model of the double-bridge crane constructed in step SA3 into a general model:

[0109] remember: ;

[0110] ;

[0111] Then formula (4) can be written as

[0112] (5);

[0113] Formula (4) can be transformed into a general model in the following form:

[0114] (6);

[0115] in , ;

[0116] is the system matrix;

[0117] represents the force of the control system, and They represent the driving forces of trolley I and trolley II respectively, and y is the actual output of the system.

[0118] A control method for double-bridge lifting equipment comprises the following steps:

[0119] Step SB1: Based on the above general model, construct the first error function:

[0120] (7);

[0121] in, is the actual position vector, and Can be obtained through position sensors; is the expected position vector; Represent the expected positions of trolley I and trolley II respectively.

[0122] Step SB2: Define the control parameter matrix , combined with the desired speed of trolley I and trolley II, the first error function and the control parameter matrix , build a virtual controller :

[0123] (8);

[0124] in, , All are positive numbers;

[0125] , They represent the expected speeds of trolley I and trolley II respectively.

[0126] Step SB3: Combine with Virtual Controller , construct the second error function:

[0127] (9);

[0128] in, .

[0129] Step SB4: Define the control parameter matrix , combined with the first error function and the control parameter matrix , virtual controller , the second error function and the control parameter matrix , construct the actual controller:

[0130] (10);

[0131] in, , All are positive numbers;

[0132] , and They represent the expected displacement acceleration of trolley I and trolley II respectively.

[0133] Step SB5: Obtain the control parameter matrix by pole configuration method and the control parameter matrix .

[0134] Obtained by the following formula:

[0135] ;

[0136] ;

[0137] ;

[0138] ;

[0139] in, yes The dominant point, , , is the expected adjustment time of trolley I, ; yes The dominant point, , , is the expected adjustment time of trolley II, .

[0140] The expected adjustment time of the trolley is obtained by the following formula:

[0141] ;

[0142] in, is the rated speed of the trolley, Determined by the rated speed of the motor, is the desired position of the trolley, is the initial position of the trolley.

[0143] Step SB6: and Assign, obtain .

[0144] Step SB7: Under the control of the actual controller, the double-bridge lifting equipment is operated to perform a lifting test operation, and then the actual position-time curves of trolley I and trolley II are output respectively. The actual position-time curve is a curve with time as the horizontal coordinate and the actual position as the vertical coordinate; the steady-state positions of trolley I and trolley II are found in the corresponding position-time curves, and the time corresponding to the steady-state position is the actual control time.

[0145] The steady-state position of the trolley is determined by the following formula:

[0146] ;

[0147] in, It is the stable position of the trolley.

[0148] Step SB8: For trolley I and trolley II, determine whether the error between the actual adjustment time and the expected adjustment time is within ±20%;

[0149] If not satisfied, and The values ​​of are all increased with a step size of 1, and then return to step SB6;

[0150] If satisfied, for trolley I and trolley II, determine whether the error between the steady-state position and the expected position is within ±2%;

[0151] If not satisfied, and The values ​​of are all increased with a step size of 0.1, and then return to step SB7;

[0152] If satisfied, then The optimal value of .

[0153] Simulation experiment analysis:

[0154] In order to fully verify the performance of the proposed control method, three sets of experiments were conducted on the designed controller. For all experiments, the initial value of the double-bridge crane equipment is , the expected value is set to .

[0155] Experiment 1:

[0156] In order to verify the correctness of the established model and the effectiveness of the designed control method, it is assumed that the rated speeds of the two trolleys given by the rated speed of the motor are both ,according to , the expected adjustment time of the two trolleys can be calculated as , then the control parameters can be calculated as The initial position of trolley I is 0m, the expected position is 1.5m, the initial position of trolley II is 0.9m, the expected position is 2.4m, that is, the steady-state position of trolley I , the steady-state position of trolley II That is, the actual adjustment time of trolley I should be the time required to move from the initial position to 1.425m, and the actual adjustment time of trolley II should be the time required to move from the initial position to 2.325m. Figure 2 and 3As shown, the actual adjustment time for trolleys I and II is 4.15 seconds, and the error between the actual adjustment time and the expected adjustment time is -17%, which is within the ±20% range. The final actual positions of the two trolleys are 1.49998m and 2.39998m, respectively, and the difference between the actual and expected positions is 0.00002m, which is within the ±2% range. Figure 6 , 7, 8 show the swing angle of the rope 、 and the tilt angle of the load .in, and The maximum absolute values ​​of are 5.2° and 5.1° respectively, and both converge to the interval [-1°, 1°] within 28.7 seconds. , whose absolute mean and variance are 1.0756° and 0.0356deg respectively 2 ; The absolute mean and variance are 1.0754° and 0.0355deg 2 The tilt angle of the load The maximum absolute value is 0.005°. Figure 9 The driving force curve is given, and its value is bounded and eventually converges to 0. Through Experiment 1, it can be shown that the designed nonlinear control method can realize the positioning control of the established double-bridge lifting equipment, and the correctness of the established model and the effectiveness of the designed control method are successfully verified.

[0157] Experiment 2:

[0158] In order to test the influence of the trolley coordination on the control performance, it is assumed that the rated speeds of the driving motors of the two trolleys are different. The rated speeds of the two trolleys are , ,according to , the expected adjustment time of the two trolleys can be calculated as , given , then the control parameters can be calculated as The initial position of trolley I is 0m, the expected position is 1.5m, the initial position of trolley II is 0.9m, the expected position is 2.4m, that is, the steady-state position of trolley I , the steady-state position of trolley II That is, the actual adjustment time of trolley I should be the time required to move from the initial position to 1.425m, and the actual adjustment time of trolley II should be the time required to move from the initial position to 2.325m. Figure 4 and 5It can be seen that the actual adjustment time of trolleys I and II is 3.54 seconds and 3.32 seconds respectively. The errors between the actual adjustment time and the expected adjustment time of trolleys I and II are -16% and 1% respectively, which are within the range of ±20%. The final actual positions of the two trolleys are 1.499999m and 2.399996m respectively. At this time, the errors between the actual position and the expected position of trolleys I and II are 0.000001m and 0.000004m respectively, which are both within the range of ±2%. Figure 6 and 7 As shown, and The maximum absolute values ​​of are 7.5° and 5.1°, respectively, and they converge to the interval [-1°, 1°] within 23 seconds and 21 seconds. The absolute mean and variance are 1.1699° and 0.0453 deg respectively. 2 ,and The corresponding values ​​are 1.0838° and 0.0362 deg 2 .like Figure 8 There is a clear tilt in the load shown, with a maximum value of 0.4° (occurring at 3.4 seconds). Figure 9 The driving force curve is given, its value is bounded and eventually converges to 0. Figure 6-8 Comparison between Experiment 2 and Experiment 1, the cable swing angle in Experiment 1 and the tilt angle of the load The maximum absolute value of the cable swing angle is smaller than that of Experiment 2. The comparison between Experiment 2 and Experiment 1 shows that in the control process of the double-bridge crane, the coordination between the two trolleys plays an important role in reducing the tilt of the load. Therefore, in the actual system, the models of the drive motors of the two trolleys are preferably the same.

[0159] Experiment 3:

[0160] The control parameters of Experiment 3 are the same as those of Experiment 1. In order to verify the robustness of the designed control scheme, a step disturbance of 20N and 0.1s is applied to Car 1 at 20 seconds. Figure 10 As shown in Figure 1, due to external disturbance, overshoot occurs in trolley I. Figure 11 Shows the swing angle of the rope and the load under disturbance 、 and It can be clearly observed that when a disturbance occurs, the cable and the load will swing significantly (the circle indicated by the arrow in the figure); and after the disturbance disappears, all angles will return to the interval [-1°, 1°]. Figure 12 Shows the driving force under disturbance and The results show that when the disturbance occurs and The disturbance will change suddenly, but as the disturbance gradually disappears, the trolley will eventually stabilize to the target position.

Claims

1. A control method for a double-bridge crane, characterized by: Based on the dynamic model of the double bridge crane, the method includes steps SB1-SB5; The modeling method of the dynamic model of the double bridge crane includes the following steps: Step SA1: Construct the dynamic equations of the five-degree-of-freedom double-bridge crane by Lagrangian method; Step SA2: Construct the geometric constraint relationship between trolley I and trolley II in the direction parallel to the bridge and in the vertical direction respectively; Step SA3: Combining the dynamic equations of the five-degree-of-freedom double-bridge crane in step SA1 and the geometric constraint relationship in step SA2, a dynamic model of the double-bridge crane is constructed; In step SA1, the dynamic equation of the five-degree-of-freedom double-bridge crane is: （1）； in, is the state vector of the system, Represents time, and They are About Time The first and second derivatives of ; represents the actual displacement of trolley I, represents the actual displacement of trolley II, and They represent the swing angles of cable I and cable II parallel to the bridge direction respectively; Indicates the tilt angle of the load; is the system damping vector, and ; and are the friction coefficients of trolley I and trolley II respectively. and is the friction coefficient between cable I and cable II and the air when they swing parallel to the bridge frame. is the coefficient of friction between the load and the air when it is tilted parallel to the bridge direction; and They represent the moving speeds of trolley I and trolley II respectively, and They represent the speeds of cable I and cable II swinging in the direction parallel to the bridge frame, is the speed at which the load changes in the inclination angle parallel to the bridge direction; is the control input vector; and They represent the driving forces of trolley I and trolley II respectively; is the gravity matrix, and ; The masses of trolley Ⅰ and trolley Ⅱ are The mass of hook Ⅰ and hook Ⅱ are , the mass of the load is , the lengths of cable I and cable II are ; is the gravitational constant; is the inertia matrix, is the centripetal-Coriolis force matrix; In step SA2, the geometric constraint relationship between the trolley I and trolley II in the direction parallel to the bridge and in the vertical direction is: （2）； （3）； in, Represents the distance between the connection point I of the load and cable I and the connection point II of the load and cable II; In step SA3, the dynamic model of the double bridge crane is: （4）； in, , , ， ， ， ； is the constraint matrix, and ； The step SA4 is also included: transforming the dynamic model of the double bridge crane constructed in the step SA3 into a general model: remember: ; ； Then formula (4) can be written as （5）； Formula (4) can be transformed into a general model in the following form: （6）； in , ; is the system matrix; represents the force of the control system, and denote the driving forces of trolley I and trolley II respectively, and y is the actual output of the system; Step SB1: Based on the general model formula (6), construct the first error function: （7）； in, is the actual position vector, and Can be obtained through position sensors; is the expected position vector; represent the desired positions of trolley I and trolley II respectively; Step SB2: Define the control parameter matrix , combined with the desired speed of trolley I and trolley II, the first error function and the control parameter matrix , build a virtual controller : （8）； in, , All are positive numbers; , denote the expected speeds of trolley I and trolley II respectively; Step SB3: Combine with Virtual Controller , construct the second error function: （9）； in, ; Step SB4: Define the control parameter matrix , combined with the first error function and the control parameter matrix , virtual controller , the second error function and the control parameter matrix , construct the actual controller: （10）； in, , All are positive numbers; , and denote the expected displacement accelerations of trolley I and trolley II respectively; Step SB5: Obtain the control parameter matrix by pole configuration method and the control parameter matrix ; In step SB5, Obtained by the following formula: ； ； ； ； in, yes The dominant point, , , is the expected adjustment time of trolley I, ; yes The dominant point, , , is the expected adjustment time of trolley II, .

2. The control method of double-bridge crane equipment according to claim 1, characterized in that: Also includes Step SB6: and Assign, obtain ; Step SB7: Under the control of the actual controller, the double-bridge crane equipment is operated to perform a lifting test operation, and then the actual position-time curves of trolley I and trolley II are output respectively. The actual position-time curves are curves with time as the horizontal axis and actual position as the vertical axis; the steady-state positions of trolley I and trolley II are found in the corresponding position-time curves. The time corresponding to the steady-state position is the actual control time; Step SB8: For trolley I and trolley II, determine whether the error between the actual adjustment time and the expected adjustment time is within ±20%; If not satisfied, and The values ​​of are all increased with a step size of 1, and then return to step SB6; If satisfied, for trolley I and trolley II, determine whether the error between the steady-state position and the expected position is within ±2%; If not satisfied, and The values ​​of are all increased with a step size of 0.1, and then return to step SB7; If satisfied, then The optimal value of .

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