Variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning

Abstract

The application discloses a variable rope length industrial crane anti-swing control method based on seven-segment trajectory planning. In view of the variable rope length crane anti-swing control problem of coupling of horizontal movement and lifting movement of the crane, a seven-segment trajectory planning variable rope length industrial crane anti-swing control method is designed based on the idea of phase trajectory switching, and the operation efficiency of the crane is greatly improved. Compared with the traditional three-segment trajectory planning, the acceleration selectable domain of the seven-segment trajectory planning is changed from a discrete domain to a continuous domain, and the acceleration size and acceleration duration can be more flexibly planned, so that the performance of the crane driver can be fully utilized. The system hardware device of the seven-segment trajectory planning industrial crane anti-swing control method mainly comprises a PLC controller, a frequency converter, an alternating current asynchronous motor, an angle measuring instrument, a Gray bus ranging cable and an upper computer.

Description

Technical Field

[0001] This invention belongs to the field of industrial crane technology, specifically relating to a method for anti-sway control of variable rope length industrial cranes based on seven-segment trajectory planning. Background Technology

[0002] With the rapid development of my country's manufacturing industry and the continuous expansion of production scale, the role of overhead cranes in industrial production is becoming increasingly important. When using overhead cranes to lift goods, the flexible material of the wire ropes inevitably causes the goods to sway during acceleration and deceleration. This swaying causes wear and tear on mechanical devices and requires repeated manual adjustments, severely impacting work efficiency and even potentially leading to safety accidents. Therefore, researching an anti-sway positioning control method for overhead cranes has significant practical importance and value, and has received considerable attention both domestically and internationally.

[0003] The overhead crane's handling process mainly consists of three parts: lifting goods, horizontal transport, and lowering goods. However, in actual industrial settings, to improve the crane's handling efficiency, there is a need to simultaneously perform horizontal transport and rope lifting, which introduces a new variable: rope length. Since the load's swaying frequency is directly related to the rope length, improper control of the crane's movement and rope lifting will exacerbate load swaying, causing more serious consequences. Because overhead cranes are underactuated, nonlinear, and strongly coupled systems, coupled with the harsh production environment and strong electromagnetic interference, achieving variable rope length industrial-grade crane anti-sway control faces numerous challenges.

[0004] Existing control methods for anti-sway positioning control of cranes with variable rope lengths are scarce. Traditional schemes based on phase-plane three-segment acceleration trajectory planning require a constant rope length, failing to achieve the anti-sway control goal with variable rope lengths. Furthermore, the acceleration and deceleration phase times can only be set to integer multiples of the pendulum period, resulting in underutilization of the crane's drive performance. Currently, control methods such as fuzzy control and neural networks, which do not rely on crane model parameters, are used to address the anti-sway problem with cranes with variable rope lengths. However, these methods require rule readjustment or relearning when faced with different industrial environments or significant variations in model parameters, hindering practical applications in industrial settings.

[0005] Therefore, a variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning is proposed to realize the lifting and lowering of the load during the horizontal transport of the crane, thereby improving the crane operation efficiency; at the same time, it realizes a continuous acceleration selectable domain to give full play to the performance of the crane drive. Summary of the Invention

[0006] Purpose of the invention: In order to overcome the defects and shortcomings of the prior art, this invention proposes a variable rope length industrial crane anti-sway positioning control method based on seven-segment trajectory planning.

[0007] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0008] The anti-sway positioning control method for variable rope length industrial cranes based on seven-segment trajectory planning includes the following steps:

[0009] 1) A dynamic model of the variable rope length trolley system was established based on the Euler-Lagrange method to obtain the phase plane trajectory of angle and angular velocity;

[0010] 2) Based on the concept of switching the phase trajectory of the vehicle load swing angle, let the maximum allowable acceleration of the vehicle drive be a. u At acceleration a = a u Under the control of / 2, after half a pendulum period T / 2, the acceleration becomes a = a u The rope length is changed from l0 to p dl Then switch to acceleration a = a u / 2, plan the acceleration curves, vehicle speed curves and rope length curves for each acceleration stage;

[0011] 3) The deceleration phase is symmetrical to the acceleration phase in step 2), and the acceleration curve, vehicle speed curve and rope length curve for each deceleration phase are planned.

[0012] 4) Based on the set target speed v d Calculate the maximum allowable acceleration a of the vehicle's drive system. u The range and acceleration can be arbitrarily chosen within a continuous domain;

[0013] 5) Based on the input system model parameters and the maximum acceleration obtained in step 4), calculate the magnitude and duration of acceleration in each stage of acceleration and deceleration;

[0014] 6) Output a seven-segment trajectory planning curve;

[0015] 7) The PLC controls the frequency converter to drive the horizontal conveyor motor and the rope motor;

[0016] 8) Measure the driving angle and position information in real time and feed the data back to the host computer;

[0017] 9) Determine if the vehicle's stopping position is the target position. If yes, end the process; otherwise, proceed to step 7.

[0018] Based on the trajectory of the vehicle load swing angle, at acceleration a = a u Under the control of / 2, the pendulum angle state moves clockwise from the origin O along the elliptical curve Γ1 for half a pendulum period T / 2, and reaches point A(-a) at time t1, at the end of the first acceleration stage. u / g), that is, the swing angle state θ(t1)=-a u / g,ω(t1)=0, at this point the acceleration is doubled to a=a u Substituting this into the mathematical model of the driving system, we can see that the swing angle will remain stable at point A during this period, and the rise and fall of the rope length will have no effect on the swing angle of the load.

[0019] At time t2, the rope length reaches the target length p. dl At this point, the acceleration is switched back to a = a. u / 2, the pendulum state moves clockwise from point A along the ellipse Γ1 for half a pendulum cycle, and reaches the state origin O at time t3; at this time, the acceleration is set to zero, the load pendulum angle will remain at the state origin, and the vehicle will move at a constant speed; the phase trajectory movement process of the deceleration stage is symmetrical with that of the acceleration stage.

[0020] Seven stages of acceleration during driving It can be represented as follows:

[0021]

[0022] Among them, a u For the maximum acceleration, t i (i = 1, 2, ..., 7) represents the end time of each stage.

[0023] Length of hanging rope This can be expressed as,

[0024]

[0025] Where l0 is the initial rope length, f l (t) represents the change in rope length.

[0026] Let the durations of each of the three acceleration stages be T1, T2, and T3, the duration of the constant velocity stage be T4, and the durations of each of the three deceleration stages be T5, T6, and T7. Based on the rope length and symmetry of each stage, the following can be determined:

[0027]

[0028] Where g is the acceleration due to gravity, l0 is the initial rope length, and p dl The target rope length; then based on the target velocity v d The durations T2 and T6 of the variable rope length phase can be calculated as follows:

[0029]

[0030] The duration T4 of the uniform velocity phase can then be expressed as:

[0031]

[0032] Where, p dxFor the target position, v d The target speed.

[0033] Maximum acceleration a u The maximum acceleration 'a' can take any value within a continuous domain, depending on the duration of each stage. u It should meet the following requirements:

[0034]

[0035] a u The value of is derived from the discrete domain ( By transforming n∈{1,2,…}) into any value within a continuous domain, the system performance of the vehicle drive can be fully utilized, allowing for more flexible planning of acceleration magnitude and duration.

[0036] The control system of the variable rope length anti-sway control method for industrial cranes based on seven-segment trajectory planning mainly includes: a PLC controller, a frequency converter, an AC asynchronous motor, an angle measuring instrument, a Gray line bus ranging cable, and a host computer. The variable rope length anti-sway control method based on seven-segment trajectory planning is implemented through the configuration software of the host computer in the DCS system. The output of the host computer is connected to the input of the PLC controller, and the program is written into the PLC controller. The output of the PLC controller is connected to the input of the frequency converter, and the output of the frequency converter is connected to the input of the AC asynchronous motor. The PLC controller controls the frequency converter, which in turn controls the speed of the AC asynchronous motor, realizing the movement of the crane and the change of the suspension rope. The output of the angle measuring instrument and the Gray line bus ranging cable is connected to the PLC signal input, providing real-time feedback of the crane's angle and position information and transmitting it to the database of the host computer.

[0037] Seven-segment trajectory planning acceleration curve, vehicle speed curve, and rope length variation curve, as shown below. Figure 4 As shown, the planned speed curve is written into the PLC controller through the host computer configuration software, and the frequency converter drives the crane motor and the rope motor to move according to the planned speed.

[0038] Beneficial Effects: This invention provides a variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning. It enables rope lifting and lowering operations during the acceleration and deceleration phases of horizontal transport, improving operational efficiency. Simultaneously, the selectable domain of crane acceleration changes from a discrete domain to a continuous domain, allowing for more flexible planning of acceleration magnitude and duration to fully utilize the crane's drive performance. This control scheme achieves coupled control of horizontal crane transport and load lifting, improving crane operating efficiency. It suppresses load swaying and achieves precise crane positioning, meeting the accuracy requirements of anti-sway positioning control for industrial cranes. Attached Figure Description

[0039] Figure 1This is a flowchart illustrating the overall process of the seven-segment trajectory planning variable rope length industrial crane anti-sway control method implemented in this invention.

[0040] Figure 2 This is a schematic diagram of a bridge-type vehicle model according to an embodiment of the present invention;

[0041] Figure 3 This is a schematic diagram of the seven-segment acceleration phase plane trajectory according to the present invention;

[0042] Figure 4 This invention provides a seven-segment trajectory planning curve with variable rope length.

[0043] Figure 5 This is a block diagram of the hardware device of the control system implemented in this invention;

[0044] Figure 6 This is a diagram illustrating the effect of the variable rope length seven-segment trajectory planning and control implemented in this invention. Detailed Implementation

[0045] The method of the present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0046] Example 1: A method for anti-sway control of variable rope length industrial cranes based on seven-segment trajectory planning, the method specifically includes the following steps:

[0047] Step 1) Establish a dynamic model of the variable rope length trolley system based on the Euler-Lagrange method to obtain the phase plane trajectory of angle and angular velocity;

[0048] Step 2) Based on the idea of ​​switching the phase trajectory of the vehicle load swing angle, let the maximum allowable acceleration a of the vehicle drive be denoted as . u At acceleration a = a u Under the control of / 2, after half a pendulum period T / 2, the acceleration becomes a = a u The rope length is changed from l0 to p dl Then switch to acceleration a = a u / 2, plan the acceleration curves, vehicle speed curves and rope length curves for each acceleration stage;

[0049] Step 3) The deceleration phase is symmetrical to the acceleration phase in Step 2), and the acceleration curve, vehicle speed curve and rope length curve for each deceleration phase are planned.

[0050] Step 4) Based on the set target speed v d Given the rope length, calculate the maximum allowable acceleration a of the vehicle's drivetrain. u The range and acceleration can be arbitrarily chosen within a continuous domain;

[0051] Step 5) Calculate the magnitude and duration of acceleration in each stage of acceleration and deceleration based on the input system model parameters and the maximum acceleration obtained in step 4).

[0052] Step 6) Output the seven-segment trajectory planning curve;

[0053] Step 7) Use the PLC to control the frequency converter to drive the horizontal conveyor motor and the rope motor;

[0054] Step 8) Measure the driving angle and position information in real time and feed the data back to the host computer;

[0055] Step 9) Determine if the vehicle's stopping position is the target position. If yes, end the process; otherwise, proceed to step 7. Details are as follows:

[0056] The overall process of the method of this invention is as follows: Figure 1 As shown, the specific steps are as follows:

[0057] 1) Two-dimensional driving diagram as follows Figure 2 As shown, the system consists of a track, a trolley, and a load. Using the Euler-Lagrange method, the system's differential equations are modeled, yielding:

[0058]

[0059] Where M and m are the trolley mass and the load mass, respectively; The second derivative of the trolley's displacement, i.e., acceleration; l represents the length of the suspension rope; g is the acceleration due to gravity; θ, This indicates the angle, angular velocity, and angular acceleration of the swinging load; f x These refer to the motor driving force of the crane in the horizontal direction.

[0060] In this example, the trolley mass M = 6.5 kg, the load mass m = 0.5 kg, the gravitational acceleration g = 9.8 m / s², and the initial rope length l0 = 2.5 m.

[0061] The system differential equations show that the bridge gantry crane has only one input variable, f. x The output variables are angle θ and displacement x, making it a single-input, multiple-output nonlinear underactuated system.

[0062] Researching and designing controllers for nonlinear systems is quite difficult; therefore, linearization is considered near the equilibrium point to further simplify the model. Since the vehicle's sway angle is very small, generally less than 10°, we can assume sinθ≈θ and cosθ≈1. Additionally, we also have:

[0063]

[0064] The original system's differential equation can then be linearized as follows:

[0065]

[0066] Where M and m are the trolley mass and the load mass, respectively; The second derivative of the trolley's displacement, i.e., acceleration; l represents the length of the suspension rope; g is the acceleration due to gravity; θ, This indicates the angle and angular acceleration of the swinging load being hoisted; f x These refer to the motor driving force of the crane in the horizontal direction.

[0067] Increase the acceleration of the vehicle Let angular velocity By selecting the initial conditions θ(t) = θ(t0) and ω(t) = ω(t0), the solution to the differential equation can be derived as follows:

[0068]

[0069] The sorted-out results are as follows:

[0070]

[0071] Where θ(t) and ω(t) represent the angle and angular velocity of the load sway. For any initial state, the relevant trajectory lines of θ(t) and ω(t) are centered at the point (- The concentric ellipse with center point 0) has a specific relationship curve related to θ(t0), ω(t0), and a.

[0072] 2) Based on the concept of switching the phase trajectory of the vehicle load swing angle, the load swing angle state under the seven-segment trajectory planning control with load lifting is analyzed, and its phase plane trajectory is as follows: Figure 3 As shown. Assume the maximum allowable acceleration of the vehicle's drive is a. u At acceleration a = a u Under the control of / 2, the pendulum angle state moves clockwise from the origin O along the elliptical curve Γ1 for half a pendulum period T / 2, and reaches point A(-a) at time t1, at the end of the first acceleration stage. u / g), that is, the swing angle state θ(t1)=-a u / g,ω(t1)=0, at this point the acceleration is doubled to a=a u Substituting this into the differential equation of the driving system, we can see that the swing angle will remain stable at point A during this period, and the rise and fall of the rope length will have no effect on the load swing angle.

[0073] At time t2, the rope length reaches the target length p. dl At this point, the acceleration is switched back to a = a. u / 2, the pendulum state moves clockwise from point A along the ellipse Γ1 for half a pendulum cycle, and reaches the state origin O at time t3; at this time, let the acceleration be zero, the load pendulum angle will remain at the state origin, and the vehicle will move at a constant speed; the phase trajectory movement process of the deceleration stage is symmetrical with that of the acceleration stage, and will not be described in detail here.

[0074] Seven stages of acceleration during driving It can be represented as follows:

[0075]

[0076] Among them, a u For the maximum acceleration, t i (i = 1, 2, ..., 7) represents the end time of each stage.

[0077] Length of hanging rope This can be expressed as,

[0078]

[0079] Where l0 is the initial rope length.

[0080] Let the durations of each of the three acceleration stages be T1, T2, and T3, the duration of the constant velocity stage be T4, and the durations of each of the three deceleration stages be T5, T6, and T7. Based on the rope length and symmetry of each stage, the following can be determined:

[0081]

[0082] Where g is the acceleration due to gravity, l0 is the initial rope length, and p dl Let p be the target rope length. In this example, let p be the target rope length. dl =0.5m.

[0083] Based on the target velocity v d The durations T2 and T6 of the variable rope length phase can be calculated as follows:

[0084]

[0085] The duration T4 of the uniform velocity phase can then be expressed as:

[0086]

[0087] Where, p dx For the target position, v d Let p be the target velocity. In this example, let p. dx =8m, v d =1.2m / s.

[0088] 3) Maximum acceleration can be a uGiven any value within a continuous domain, the maximum acceleration 'a' is determined based on the duration of each stage. u It should meet the following requirements:

[0089]

[0090] a u The value of is derived from the discrete domain ( By transforming n∈{1,2,…} into any value within a continuous domain, the system performance of the vehicle drive can be fully utilized, allowing for more flexible planning of acceleration magnitude and duration. Based on the model parameters p in this example... dl =0.5m, l0=2.5m, v d =1 m / s², the maximum acceleration a can be calculated. u Scope: a u ≤0.87m / s 2 In this example, we take a. u =0.4m / s 2 .

[0091] Based on the trajectory planning process described above, the trajectory parameters can be obtained as follows: T1 = T7 = 1.59s, T3 = T5 = 0.71s, T4 = 4.59s, T2 = T6 = 1.35s.

[0092] 4) Obtain the seven-segment trajectory planning curve for the variable rope length trolley, such as... Figure 4 As shown.

[0093] 5) Based on the specific parameters given in this example, the effect of the seven-segment trajectory planning and control with variable rope length is as follows: Figure 6 As shown. By Figure 6 It can be seen that when the load is raised or lowered during the acceleration and deceleration phase of the trolley, the trolley can still reach the target position quickly and accurately, and the load remains undisturbed during the constant speed phase and after stopping. This also verifies the invariance of the swing angle of the above method during the process of changing rope length.

[0094] 6) The hardware device of the control system for the variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning mainly includes: a PLC controller, a frequency converter, an AC asynchronous motor, an angle measuring instrument, a Gray bus distance measuring cable, and a host computer, such as... Figure 5As shown, a variable rope length anti-sway control method based on seven-segment trajectory planning is implemented through the configuration software of the DCS system's host computer. The output of the host computer is connected to the input of the PLC controller, and the seven-segment trajectory planning program is written into the PLC controller as the system's reference input. The output of the PLC controller is connected to the input of the frequency converter, and the output of the frequency converter is connected to the input of the AC asynchronous motor. The PLC controller controls the frequency converter, which in turn controls the speed of the AC asynchronous motor, realizing the movement of the crane and the change of the suspension rope. The output of the angle measuring instrument and the Gray bus distance measuring cable are connected to the PLC signal input, providing real-time feedback of the crane's angle and position information and transmitting it to the host computer's database.

[0095] The PLC controller and host computer are the control modules of the NT6000 DCS system independently developed by Nanjing Keyuan Company. The Gray bus ranging cable is the GC2000 ranging system of Nanjing Keyuan Company, and the angle measuring instrument is a product of Saike Company.

[0096] It should be noted that the above embodiments are not intended to limit the scope of protection of the present invention. Equivalent transformations or substitutions made based on the above technical solutions all fall within the scope of protection of the claims of the present invention.

Claims

1. A variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning, characterized in that, The method specifically consists of the following steps: Step 1) Establish a dynamic model of the variable rope length trolley system based on the Euler-Lagrange method to obtain the phase plane trajectory of angle and angular velocity; Step 2) According to the idea of switching according to the trajectory of the driving load swing angle, the maximum acceleration allowed by the driving device is set Under the control of the acceleration , after half a single pendulum period , the acceleration becomes , the length of the rope is changed from to , and the acceleration is switched to , and the acceleration curve, the driving speed curve and the length of the rope are planned in each acceleration stage; Step 3) The deceleration phase is symmetrical to the acceleration phase in Step 2), and the acceleration curve, vehicle speed curve, and rope length curve for each deceleration phase are planned. Step 4) Calculate the maximum acceleration allowed by the drive based on the setpoint speed v d and the rope length The range of accelerations is arbitrary; it could be continuous or discrete. Among them, step 4) maximum acceleration To obtain any value within a continuous domain, the specific steps are as follows: According to the duration of the phases and the target speed v d , the maximum acceleration should be satisfied, where g is the acceleration of gravity, is the initial rope length, is the target rope length, v d is the target speed, the value of the discrete domain (D) to an arbitrary value in the continuous domain (C), and the ability to ) to an arbitrary value in the continuous domain (C), and the ability to Fully utilize the system performance of the vehicle's drive system to more flexibly plan the magnitude and duration of acceleration; Step 5) Based on the input system model parameters and the maximum acceleration obtained in Step 4), calculate the magnitude and duration of acceleration in each stage of acceleration and deceleration; Step 6) Output the seven-segment trajectory planning curve; Step 7) Use the PLC to control the frequency converter to drive the horizontal conveyor motor and the rope motor; Step 8) Measure the driving angle and position information in real time and feed the data back to the host computer; Step 9) Determine if the vehicle's stopping position is the target position. If yes, end the process; otherwise, proceed to step 7.

2. The variable rope length industrial trolley anti-sway control method based on seven-segment trajectory planning according to claim 1, characterized in that: Steps 2) and 3) plan the acceleration curves, vehicle speed curves, and rope length curves for each acceleration and deceleration stage. The specific steps are as follows: Based on the vehicle load swing angle phase trajectory, during acceleration... Under the control of the pendulum, the pendulum angle state moves clockwise from the origin O along the elliptic curve Γ1 for half a pendulum period. At time t1, after the first stage of acceleration ends, the intersection of the elliptic curve Γ1 and the x-axis is reached. That is, the swing angle state At this point, the acceleration is doubled. Substituting this into the mathematical model of the driving system, we can see that the swing angle will remain stable at point A during this period of time, and the rise and fall of the rope length will have no effect on the swing angle of the load. At time t2, the rope length reaches the target length. At this point, switch the acceleration back to After the pendulum angle state moves clockwise from point A along the ellipse Γ1 for half a pendulum cycle, it reaches the origin O at time t3. At this time, if the acceleration is zero, the load pendulum angle will remain at the origin, and the vehicle will move at a constant speed. The phase trajectory movement process of the deceleration phase is symmetrical with that of the acceleration phase. Let the duration of each segment of the acceleration three-stage be: , the duration of the uniform speed stage T4, the duration of each segment of the deceleration three-stage ; according to the length of the rope of each stage and the symmetry, determine where g is the acceleration of gravity, is the initial rope length, is the target rope length, and then according to the target speed v d The variable rope length phase duration T2, T6 is obtained as The duration T4 of the uniform velocity phase is then expressed as: where p dx is the target position, v d is the target velocity.

3. The variable rope length industrial trolley anti-sway control method based on seven-segment trajectory planning according to claim 1, characterized in that: Steps 7) and 8) describe the control system for the variable rope length industrial crane anti-sway control method based on seven-segment trajectory planning. The system mainly includes: a PLC controller, a frequency converter, an AC asynchronous motor, an angle measuring instrument, a Gray busbar distance measuring cable, and a host computer. The variable rope length anti-sway control method based on seven-segment trajectory planning is implemented through the configuration software of the host computer in the DCS system. The output of the host computer is connected to the input of the PLC controller, and the program is written into the PLC controller. The output of the PLC controller is connected to the input of the frequency converter, and the output of the frequency converter is connected to the input of the AC asynchronous motor. The PLC controller controls the frequency converter, thereby controlling the speed of the AC asynchronous motor, realizing the movement of the crane and the change of the suspension rope. The output of the angle measuring instrument and the Gray busbar distance measuring cable are connected to the PLC signal input, providing real-time feedback of the crane's angle and position information, which is then transmitted to the database of the host computer.

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