Modeling method and control method for dynamic model of double-bridge type hoisting equipment

Abstract

The invention belongs to the technical field of lifting equipment control, and particularly relates to a modeling method and a control method for a dynamic model of double-bridge type lifting equipment, and a dynamic equation of a five-degree-of-freedom double-bridge type crane is constructed through a Lagrange method. Constructing a geometric constraint relationship between the trolley I and the trolley II in the direction parallel to the bridge frame and the vertical direction, constructing a kinetic model of the double-bridge crane by combining the kinetic equation and the geometric constraint relationship, and converting the kinetic model into a universal model; based on the general model, a first error function is constructed according to the difference between the actual position and the expected position, and a virtual controller is constructed based on the first error function; and constructing a second error function based on the virtual controller, and constructing an actual controller based on the first error function, the virtual controller and the second error function. According to the technical scheme, overall modeling is carried out on the system through the constraint relation between the two trolleys, the quality of the lifting hook is considered during modeling, and the singular problem is solved.

Description

Technical Field

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

[0002] Bridge hoisting equipment is an important device for cargo handling. In practical applications, for many large and heavy loads, such as large pipelines, rockets, etc., it is very difficult to transport them through single-bridge hoisting equipment, and generally double-bridge hoisting equipment is used.

[0003] For double-bridge hoisting equipment, it has the characteristics of non-linearity and under-actuation. Therefore, rapid and precise control of the entire system is still a challenge to be faced. The main problem in the control of double-bridge hoisting equipment lies in how to ensure the coordination between the two trolleys and conduct overall control of the entire system. At present, most of the relatively mature research on double-bridge hoisting equipment is to split the two trolleys into two independent systems for separate control. This method ignores the coordination between the two trolleys. For example, in reference [1]: Miller, A. S., 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). Some research has carried out overall modeling for double-bridge hoisting equipment, but its model has singularity problems, which easily lead to system out-of-control during the control process. For example, in reference [2]: [2] Lu, B., Sun, N. (2020). Adaptive Output-Feedback Control for Dual 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 double-bridge hoisting equipment.

[0005] To solve the above technical problem, the technical solution of the present invention is as follows: A method for modeling the dynamic model of a double-bridge hoisting equipment, comprising the following steps: Step SA1: Construct the dynamic equation of a five-degree-of-freedom double-bridge crane by the Lagrange method; Step SA2: Construct the geometric constraint relationships existing in trolley Ⅰ and trolley Ⅱ in the direction parallel to the bridge and in the vertical direction respectively; Step SA3: Combine the dynamic equation of the five-degree-of-freedom double-bridge crane in Step SA1 and the geometric constraint relationships in Step SA2 to construct the dynamic model of the double-bridge crane.

[0006] Further, in Step SA1, the dynamic equation of the five-degree-of-freedom double-bridge crane is: (1); Wherein, is the state vector of the system, represents time, and are respectively the first derivative and the second derivative of with respect to time represents the actual displacement of trolley Ⅰ, represents the actual displacement of trolley Ⅱ, and represent the swing angles of cable Ⅰ and cable Ⅱ in the direction parallel to the bridge respectively; represents the tilt angle of the load; is the system damping vector, and ; and are the friction coefficients when trolley Ⅰ and trolley Ⅱ move respectively, and are the friction coefficients between cable Ⅰ and cable Ⅱ and the air when swinging in the direction parallel to the bridge, is the friction coefficient between the load and the air when tilting in the direction parallel to the bridge; and represent the moving speeds of trolley Ⅰ and trolley Ⅱ respectively, and represent the swinging speeds of cable Ⅰ and cable Ⅱ at the swing angles in the direction parallel to the bridge respectively, is the speed of change of the tilt angle of the load in the direction parallel to the bridge; is the control input vector; and 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 both , the masses of the hook Ⅰ and the hook Ⅱ are both , the mass of the load is , the lengths of the cable Ⅰ and the cable Ⅱ are both ; is the gravitational constant; is the inertia matrix, is the centripetal-Coriolis force matrix.

[0007] Further, the geometric constraint relationships existing in the trolley Ⅰ and the trolley Ⅱ in the direction parallel to the bridge and the vertical direction in step SA2 are: (2); (3); Among them, represents the distance between the connection point Ⅰ of the load and the cable Ⅰ and the connection point Ⅱ of the load and the cable Ⅱ.

[0008] Further, in step SA3, the dynamic model of the double-girder crane: (4); Among them, , , , , , ; is the constraint matrix, and .

[0009] Further, it also includes Step SA4: Transform the dynamic model of the double-girder crane constructed in step SA3 into a general model: Denote: ; ; Then equation (4) can be written as (5); Equation (4) can be transformed into a general model in the following form: (6); Among them , ; is the system matrix; represents the force of the control system, and represent the driving forces of the trolley Ⅰ and the trolley Ⅱ respectively, and y is the actual output of the system.

[0010] A control method for a double-bridge hoisting equipment, comprising the following steps: Step SB1: Based on the above general model, construct the first error function: (7); Wherein, is the actual position vector, and can be obtained through a position sensor; is the desired position vector; respectively represent the desired positions of trolley Ⅰ and trolley Ⅱ; Step SB2: Define the control parameter matrix , and combine the desired speeds of trolley Ⅰ and trolley Ⅱ, the first error function and the control parameter matrix to construct the virtual controller : (8); Wherein, , are both positive constants; , respectively represent the desired speeds of trolley Ⅰ and trolley Ⅱ; Step SB3: Combine the virtual controller to construct the second error function: (9); Wherein, ; Step SB4: Define the control parameter matrix , and combine the first error function, the control parameter matrix , the virtual controller , the second error function and the control parameter matrix to construct the actual controller: (10); Wherein, , are both positive constants; , and respectively represent the desired displacement accelerations of trolley Ⅰ and trolley Ⅱ.

[0011] Furthermore, it further includes Step SB5: Obtain the control parameter matrix and the control parameter matrix .

[0012] Further, in step SB5, obtained by the following formula: ; ; ; ; wherein, is the dominant pole of, , , is the desired adjustment time of trolley I, ; is the dominant pole of, , , is the desired adjustment time of trolley II, .

[0013] Further, it further includes step SB6: respectively assign values to and to obtain ; step SB7: under the control of the actual controller, make the double-bridge lifting equipment perform a hoisting test operation, and then output the actual position-time curves of trolley I and trolley II respectively. The actual position-time curve is a curve with time as the abscissa and the actual position as the ordinate; find the steady-state positions of trolley I and trolley II in the corresponding position-time curves, and the time corresponding to the steady-state position is the actual control time; step SB8: for trolley I and trolley II, respectively judge whether the error between the actual adjustment time and the desired adjustment time meets within ±20%; if not, then increase the values of and by 1, and then return to step SB6; if satisfied, for trolley I and trolley II, respectively judge whether the error between the steady-state position and the desired position meets within ±2%; if not, then increase the values of and by 0.1, and then return to step SB7; if satisfied, then obtain the optimal value of.

[0014] The beneficial effects that the present invention can achieve are: (1) In this technical solution, the system is globally modeled by constructing the constraint relationship between trolley I and trolley II. When modeling, the mass of the hook is fully considered. This is because the shape and mass of the load lifted by the double-bridge lifting equipment are usually large, so the mass of its hook is also large. If the mass of the hook is ignored and only the mass of the load is equivalent to its centroid, this not only does not conform to the actual system model, but also the third and fourth rows of the inertia matrix are equal in the initial state. Therefore, its determinant is 0, the inertia matrix is irreversible, and the model has a singularity problem. After considering the mass of the hook, there is a difference between the third and fourth rows of the inertia matrix in the initial state, the determinant is no longer 0, the singularity problem is solved, and the considered model 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.

[0015] (2) For the underactuated double-bridge lifting equipment, a nonlinear controller based on the backstepping method is constructed. The proposed control scheme is based on the established model of the double-bridge lifting equipment, fully considering the cooperation between the two trolleys. For the first time, the backstepping method is combined with the underactuated double-bridge lifting equipment, providing a new solution for the nonlinear control of the double-bridge lifting equipment, and solving the deficiencies in past research that did not consider the cooperation between the two trolleys and the control anomalies and model out-of-control problems that may be caused by the singularity problem of the inertia matrix in the model. Description of the Drawings

[0016] Figure 1 is a schematic diagram of the five-degree-of-freedom double-bridge crane in the present invention.

[0017] Figure 2 is the actual position-time curve of trolley I output in Experiment 1 of the embodiment of the present invention.

[0018] Figure 3 is the actual position-time curve of trolley II output in Experiment 1 of the embodiment of the present invention.

[0019] Figure 4 is the actual position-time curve of trolley I output in Experiment 2 of the embodiment of the present invention.

[0020] Figure 5 is the actual position-time curve of trolley II output in Experiment 2 of the embodiment of the present invention.

[0021] Figure 6 is the time-varying curve of cable I output in Experiment 1 and Experiment 2 of the embodiment of the present invention.

[0022] Figure 7 is the time-varying curve of cable II output in Experiment 1 and Experiment 2 of the embodiment of the present invention.

[0023] Figure 8 are the curves of the load output from Experiment 1 and Experiment 2 of the embodiments of the present invention changing with time.

[0024] Figure 9 are the driving forces of Trolley Ⅰ and Trolley Ⅱ in Experiment 1 and Experiment 2 of the embodiments of the present invention and changing with time.

[0025] Figure 10 are the actual position-time curves of Trolley Ⅰ and Trolley Ⅱ output from Experiment 3 of the embodiments of the present invention

[0026] Figure 11 are the , and load changing with time in Experiment 3 of the embodiments of the present invention

[0027] Figure 12 are the driving forces of Trolley Ⅰ and Trolley Ⅱ in Experiment 3 of the embodiments of the present invention and changing with time.

[0028] 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. Specific Embodiments

[0029] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0030] A method for modeling the dynamic model of a double-bridge lifting equipment includes the following steps: Step SA1: Construct the dynamic equation of a five-degree-of-freedom double-bridge crane by the Lagrange method: (1); Wherein, is the state vector of the system, represents time, and are respectively the first derivative and the second derivative with respect to time ; represents the actual displacement of Trolley Ⅰ, represents the actual displacement of Trolley Ⅱ, and respectively represent the swing angles of Cable Ⅰ and Cable Ⅱ parallel to the bridge direction; represents the tilt angle of the load; is the system damping vector, and ; and are the friction coefficients of bogie Ⅰ and bogie Ⅱ during movement respectively, and are the friction coefficients of cable Ⅰ and cable Ⅱ with air when swinging in the direction parallel to the bridge; is the friction coefficient of the load with air when tilting in the direction parallel to the bridge; and represent the moving speeds of bogie Ⅰ and bogie Ⅱ respectively, and represent the swinging speeds of cable Ⅰ and cable Ⅱ when swinging at an angle in the direction parallel to the bridge respectively, is the speed of the change in the tilt angle of the load in the direction parallel to the bridge; is the control input vector; and represent the driving forces of bogie Ⅰ and bogie Ⅱ respectively; is the gravity matrix, and ; the masses of bogie Ⅰ and bogie Ⅱ are both , the masses of hook Ⅰ and hook Ⅱ are both , the mass of the load is , and the lengths of cable Ⅰ and cable Ⅱ are both ; is the gravitational constant; is the inertia matrix, is the centripetal-Coriolis force matrix; ; ; ; ;

[0031] The inventor painstakingly studied and found that: when modeling in the prior art, the mass of the hook is generally ignored, such as in Document 【2】. However, for double-bridge lifting equipment, due to the large shape and mass of its load, the mass of its hook is also large. If its mass is ignored and the mass of the load is equivalent to its centroid, this does not conform to the actual system model. And the third row and the fourth row of the inertia matrix obtained by ignoring the mass of the hook are equal in the initial state, so its determinant is 0 and the inertia matrix is irreversible, and there is a singularity problem in the model. After considering the mass of the hook in this technical solution, there is a difference between the third row and the fourth row of the inertia matrix in the initial state, the determinant is no longer 0, the singularity problem is solved, and the considered model is more consistent with the actual model.

[0032] Step SA2: Construct the geometric constraint relationships existing between trolley I and trolley II in the direction parallel to the bridge and in the vertical direction: (2); (3); Among them, represents the distance between connection point I of the load and cable I and connection point II of the load and cable II; Step SA3: Combine the dynamic equation of the five-degree-of-freedom double-bridge crane in step SA1 and the geometric constraint relationships in step SA2 to construct the dynamic model of the double-bridge crane: (4); Among them, , , , , , ; is the constraint matrix, and .

[0033] Furthermore, it also includes Step SA4: Transform the dynamic model of the double-bridge crane constructed in step SA3 into a general model: Denote: ; ; Then equation (4) can be written as (5); Equation (4) can be transformed into a general model in the following form: (6); Among them , ; is the system matrix; represents the force of the control system, and respectively represent the driving forces of trolley I and trolley II, and y is the actual output of the system.

[0034] A control method for a double-bridge lifting equipment, including the following steps: Step SB1: Based on the above general model, construct the first error function: (7); Among them, is the actual position vector, and can be obtained by a position sensor; is the desired position vector; respectively represent the desired positions of trolley Ⅰ and trolley Ⅱ.

[0035] Step SB2: Define the control parameter matrix , combine the desired speeds of trolley Ⅰ and trolley Ⅱ, the first error function, and the control parameter matrix , and construct a virtual controller : (8); wherein, , are all positive constants; , respectively represent the desired speeds of trolley Ⅰ and trolley Ⅱ.

[0036] Step SB3: Combine the virtual controller , and construct the second error function: (9); wherein, .

[0037] Step SB4: Define the control parameter matrix , combine the first error function, the control parameter matrix , the virtual controller , the second error function, and the control parameter matrix , and construct an actual controller: (10); wherein, , are all positive constants; , and respectively represent the desired displacement accelerations of trolley Ⅰ and trolley Ⅱ.

[0038] Step SB5: Obtain the control parameter matrix and the control parameter matrix .

[0039] are obtained by the following formula: ; ; ; ; Among them, is the dominant pole of , , is the expected regulation time of trolley Ⅰ, ; is the dominant pole of , , is the expected regulation time of trolley Ⅱ, .

[0040] The expected regulation time of the trolley is obtained by the following formula: ; Among them, is the rated speed of the trolley, which is determined by the rated speed of the motor, is the expected position of the trolley, is the initial position of the trolley.

[0041] Step SB6: Assign values to and respectively to obtain .

[0042] Step SB7: Under the control of the actual controller, make the double-bridge lifting equipment perform a hoisting test operation, and then output the actual position-time curves of trolley Ⅰ and trolley Ⅱ respectively. The actual position-time curve is a curve with time as the abscissa and the actual position as the ordinate; find the steady-state positions of trolley Ⅰ and trolley Ⅱ in the corresponding position-time curves, and the time corresponding to the steady-state position is the actual control time.

[0043] The steady-state position of the trolley is determined by the following formula: ; Among them, is the stable position of the trolley.

[0044] Step SB8: For trolley Ⅰ and trolley Ⅱ, respectively judge whether the error between the actual regulation time and the expected regulation time satisfies within ±20%; If not satisfied, increase the values of and by 1 each, and then return to step SB6; If satisfied, for trolley Ⅰ and trolley Ⅱ, respectively judge whether the error between the steady-state position and the expected position satisfies within ±2%; If not satisfied, increase the values of and by 0.1 each, and then return to step SB7; If satisfied, then obtain the optimal value.

[0045] Simulation experiment analysis: To fully verify the performance of the proposed control method, three groups of experiments were conducted on the designed controller. For all experiments, the initial values of the double-bridge lifting equipment were , and the expected values were set to .

[0046] Experiment 1: To verify the correctness of the established model and the effectiveness of the designed control method, the rated speeds of the two trolleys given by the rated motor speed were both set to . According to , the expected adjustment times of the two trolleys could be calculated as . Then the control parameters could be calculated as . The initial position of trolley I was 0 m, and the expected position was 1.5 m. The initial position of trolley II was 0.9 m, and the expected position was 2.4 m. That is, the steady-state position of trolley I was , and the steady-state position of trolley II was . That is, the actual adjustment time of trolley I should be the time required to travel from the initial position to 1.425 m, and the actual adjustment time of trolley II should be the time required to travel from the initial position to 2.325 m. As shown in Figure 2 and 3 , the actual adjustment times of trolleys I and II were 4.15 seconds, and the error between the actual adjustment time and the expected adjustment time was -17%, which met the requirement within the range of ±20%. The final actual positions of the two trolleys were 1.49998 m and 2.39998 m respectively, and the differences from the expected positions were both 0.00002 m at this time. The errors between the actual positions and the expected positions of the two trolleys met the requirement within the range of ±2%. Figure 6 , Figures 7 and 8 show the swing angles and of the rope, as well as the tilt angle of the load. Among them, the maximum absolute values of and were 5.2° and 5.1° respectively, and both converged to the interval [-1°, 1°] within 28.7 seconds. For , its absolute mean value and variance were 1.0756° and 0.0356 deg 2 ; the absolute mean value and variance were 1.0754° and 0.0355 deg 2 . The maximum absolute value of the tilt angle of the load was 0.005°. Figure 9The driving force curve is given, and its value is bounded and finally converges to 0. Through Experiment 1, it can be shown that the designed nonlinear control method can achieve the positioning control of the established double-bridge hoisting equipment, successfully verifying the correctness of the established model and the effectiveness of the designed control method.

[0047] Experiment 2: To test the influence of the coordination of the trolleys on the control performance, the rated speeds of the driving motors of the two trolleys are set to be different. The rated speeds of the two trolleys are respectively , , and according to , the expected adjustment times of the two trolleys can be calculated as . Given , the control parameters can be calculated as . The initial position of trolley I is 0 m, and the expected position is 1.5 m. The initial position of trolley II is 0.9 m, and the expected position is 2.4 m. That is, the steady-state position of trolley I is , and the steady-state position of trolley II is . That is, the actual adjustment time of trolley I should be the time required to travel from the initial position to 1.425 m, and the actual adjustment time of trolley II should be the time required to travel from the initial position to 2.325 m. It can be seen from Figure 4 and 5 that the actual adjustment times of trolleys I and II are 3.54 s and 3.32 s respectively, and the errors between the actual adjustment times of trolleys I and II and the expected adjustment times are -16% and 1% respectively, meeting the requirement within the range of ±20%. The final actual positions of the two trolleys are 1.499999 m and 2.399996 m respectively. At this time, the errors between the actual positions and the expected positions of trolleys I and II are 0.000001 m and 0.000004 m respectively, both meeting the requirement within the range of ±2%. At this time, as shown in Figure 6 and 7 , the maximum absolute values of and are 7.5° and 5.1° respectively, and converge to the interval [-1°, 1°] within 23 s and 21 s. The absolute mean value and variance of 2 are 1.1699° and 0.0453 deg , while the corresponding values of 2 are 1.0838° and 0.0362 deg Figure 8 . As shown in Figure 9 , there is an obvious inclination of the load, and its maximum value is 0.4° (appearing at 3.4 s). Figures 6 - 8 gives the driving force curve, and its value is bounded and finally converges to 0. Through the comparison between Experiment 2 and Experiment 1 in and the inclination angle of the load The maximum absolute value should be less than that in Experiment 2, and the maximum absolute value of the cable swing angle is equal. The comparison between Experiment 2 and Experiment 1 shows that in the control process of the double-bridge lifting equipment, the coordination between the two trolleys plays an important role in reducing the inclination of the load. Therefore, in the actual system, it is best that the models of the drive motors of the two trolleys are the same.

[0048] Experiment 3: The control parameters of Experiment 3 are the same as those of Experiment 1. To verify the robustness of the designed control scheme, at 20 seconds, a step disturbance with a magnitude of 20 N and a duration of 0.1 s is applied to trolley 1. As Figure 10 shown, due to the external disturbance, overshoot occurs in trolley I. Figure 11 shows the swing angles of the rope and the load under the disturbance , and . It can be clearly observed that when the disturbance appears, the cable and the load will swing significantly (the circled area indicated by the arrow in the figure); after the disturbance disappears, all angles will tend to the interval [-1°, 1°] again. Figure 12 shows the driving forces and under the disturbance. The results show that and will change suddenly when the disturbance appears, but as the disturbance gradually disappears, the trolley finally stabilizes at the target position.

Claims

1. A method for modeling the dynamic model of a double-bridge lifting equipment, characterized in that: It includes the following steps: Step SA1: Construct the dynamic equation of the five-degree-of-freedom double-girder crane by the Lagrange method; Step SA2: Construct the geometric constraint relationships existing in trolley Ⅰ and trolley Ⅱ in the direction parallel to the bridge girder and the vertical direction respectively; Step SA3: Combine the dynamic equation of the five-degree-of-freedom double-girder crane in Step SA1 and the geometric constraint relationships in Step SA2 to construct the dynamic model of the double-girder crane.

2. The method for modeling the dynamic model of the double-bridge lifting equipment according to claim 1, characterized in that: In Step SA1, the dynamic equation of the five-degree-of-freedom double-girder crane is: （1）； Among them, is the state vector of the system, represents time, and are respectively the first derivative and the second derivative with respect to time ; represents the actual displacement of trolley Ⅰ, represents the actual displacement of trolley Ⅱ, and respectively represent the swing angles of cable Ⅰ and cable Ⅱ parallel to the bridge direction; represents the tilt angle of the load; is the system damping vector, and ; and are the friction coefficients during the movement of trolley Ⅰ and trolley Ⅱ respectively, and are the friction coefficients between cable Ⅰ and cable Ⅱ and air when swinging in the direction parallel to the bridge,[ is the friction coefficient between the load and air when tilting in the direction parallel to the bridge; and represent the moving speeds of trolley Ⅰ and trolley Ⅱ respectively, and represent the swinging speeds of cable Ⅰ and cable Ⅱ at the swing angle in the direction parallel to the bridge respectively, is the speed of the change in the tilt angle of the load in the direction parallel to the bridge; is the control input vector; and respectively represent the driving forces of trolley Ⅰ and trolley Ⅱ; is the gravity matrix, and ; the masses of trolley Ⅰ and trolley Ⅱ are both , the masses of hook Ⅰ and hook Ⅱ are both , the mass of the load is , and the lengths of cable Ⅰ and cable Ⅱ are both ; is the gravitational constant; is the inertia matrix, is the centripetal-Coriolis force matrix.

3. The method for modeling the dynamic model of the double-bridge lifting equipment according to claim 2, characterized in that: In Step SA2, the geometric constraint relationships existing in trolley Ⅰ and trolley Ⅱ in the direction parallel to the bridge girder and the vertical direction respectively are: （2）； （3）； Among them, represents the distance between connection point Ⅰ of the load and cable Ⅰ and connection point Ⅱ of the load and cable Ⅱ.

4. The dynamic model modeling method of the double-bridge lifting equipment according to claim 3, characterized in that: In Step SA3, the dynamic model of the double-girder crane is: （4）； Among them, , , , , , ; is a constraint matrix, and 。 5. The method for modeling the dynamic model of the double-bridge lifting equipment according to claim 4, characterized in that: It also includes Step SA4: Transform the dynamic model of the double-girder crane constructed in Step SA3 into a general model: Note: ; ； Then Equation (4) can be written as （5）； Equation (4) can be transformed into a general model in the following form: （6）； Among them , ; is the system matrix; represents the force of the control system, and respectively represent the driving forces of trolley Ⅰ and trolley Ⅱ, and y is the actual output of the system.

6. A control method for a double-bridge lifting equipment, characterized in that: It includes the following steps: Step SB1: Based on the general model described in Claim 2, construct the first error function: （7）； Among them, is the actual position vector, and can be obtained by a position sensor; is the desired position vector; respectively represent the desired positions of trolley Ⅰ and trolley Ⅱ; Step SB2: Define the control parameter matrix , combine the desired speeds of trolley I and trolley II, the first error function, and the control parameter matrix , and construct a virtual controller : （8）； Among them, , are all normal constants; , respectively represent the desired speeds of trolley Ⅰ and trolley Ⅱ; Step SB3: Combine the virtual controller , and construct the second error function: （9）； Among them, ; Step SB4: Define the control parameter matrix , combine the first error function, the control parameter matrix , the virtual controller , the second error function, and the control parameter matrix , to construct the actual controller: （10）； Among them, , are all positive constants; , and respectively represent the expected displacement accelerations of bogie Ⅰ and bogie Ⅱ.

7. The control method of the double-bridge type lifting equipment according to claim 6, characterized in that: It also includes Step SB5: Obtain the control parameter matrix through the pole placement method and the control parameter matrix .

8. The control method of the double-bridge lifting equipment according to claim 7, characterized in that: In step SB5, Obtained by the following formula: ； ； ； ； Among them, is the dominant pole of, , , is the expected adjustment time of trolley Ⅰ, ; is the dominant pole of, , , is the expected adjustment time of trolley Ⅱ, .

9. The control method of the double-bridge lifting equipment according to claim 8, characterized in that: It also includes Step SB6: Assign values to and respectively to obtain ; Step SB7: Under the control of the actual controller, make the double-girder lifting equipment perform a hoisting test operation, and then output the actual position-time curves of trolley Ⅰ and trolley Ⅱ respectively. The actual position-time curve is a curve with time as the abscissa and the actual position as the ordinate; find the steady-state positions of trolley Ⅰ and trolley Ⅱ in the corresponding position-time curves, and the time corresponding to the steady-state position is the actual control time; Step SB8: For trolley Ⅰ and trolley Ⅱ, respectively judge whether the error between the actual adjustment time and the expected adjustment time satisfies within ±20%; If not satisfied, then increase the values of and by 1, and then return to step SB6; If it is satisfied, for trolley Ⅰ and trolley Ⅱ, respectively judge whether the error between the steady-state position and the expected position satisfies within ±2%; If not satisfied, then increase the values of and by 0.1, and then return to step SB7; If satisfied, then obtain the optimal value of.

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