A cascade control method and system for a four-degree-of-freedom overhead crane space spherical swing system

Abstract

The present invention provides a cascade control method and system for a 4-DOF overhead crane space spherical swing system, which relates to the field of overhead crane control technology. The method comprises: determining a first input error according to target position information and current position information; determining a first control function; determining a first control output according to the first control function and the first input error; determining a second input error according to the first control output and the spatial swing angle; determining a second control function according to a preset performance function, load mass, bridge mass, trolley mass and cable length; obtaining a second control output according to the second control function and the second input error; obtaining a control law of position information and a control law of spatial swing angle according to the second control output. According to the present invention, the adjustment of a dual feedback loop can be realized, the position and swing angle of the load can be controlled, and the robustness and control quality of the control system can be improved based on the dual feedback loop, and the anti-interference ability can be enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of overhead crane control, and in particular to a cascade control method and system for a four-degree-of-freedom overhead crane spatial spherical swing system. Background Art

[0002] In the related art, CN112429640B discloses a method for controlling the anti-sway of the crane, wherein the crane swing angle data is measured by an inclinometer, and the anti-sway controller calculates the optimal speed model for controlling the crane to stop according to the swing angle of the crane on the XY axis measured by the inclinometer. The crane PLC no longer needs to calculate the crane speed separately, but directly transmits the optimal speed value given by the anti-sway controller to the frequency converter, and controls the speed of the crane trolley and the trolley through the frequency converter, thereby realizing automatic control of the crane. The present invention has the characteristics of high control accuracy and strong real-time performance.

[0003] CN112079256A discloses a method and system for real-time control of the swing angle of a crane hoisting a load, comprising: identifying the swing length of the crane after hoisting the load; l . Real-time identification of the relative displacement d between the crane and the cargo along the direction of the crane's movement. Real-time identification of the crane's acceleration a along the direction of the crane's movement. In the first stage, the crane is started to drive the cargo forward. In the second stage, the crane's speed is adjusted to control the boom's angle. In the third stage, the crane drives the cargo to move in a uniform straight line. In the fourth stage, the crane's speed is adjusted to control the boom's angle and prepare for deceleration. In the fifth stage, the crane is braked to stop the cargo. Among them, the absolute value of the acceleration in each stage is less than or equal to the maximum acceleration limit a max This solution can eliminate the swing of the overhead crane and the cargo at the fastest speed during the starting and braking stages, thereby improving the stability of cargo transportation, improving transportation efficiency, and reducing the occurrence of safety accidents.

[0004] The overhead crane system is a typical under-actuated nonlinear system. At present, the operation methods for the overhead crane mainly include manual direct operation or remote teleoperation. The operation method with direct human participation requires the operator to be trained in advance, and the operator can only operate after being proficient in the operation process. There are shortcomings such as low operation efficiency, long time-consuming training of skilled operators, and large load swing amplitude. However, there are still some shortcomings in the automatic control method for the overhead crane. Most of the control methods currently designed are designed for plane swing systems. For example, the relevant technology only calculates and simulates the swing in one direction. However, in practical applications, in order to efficiently complete complex lifting tasks, the traverse trolley and the bridge frame are usually required to run synchronously during operation. When the traverse trolley and the bridge frame run synchronously, the load swing is no longer a plane swing, but presents a more complex spatial spherical swing. Therefore, the control method designed based on the plane swing system model cannot be applied to the spatial spherical swing system. In addition, the overhead crane will inevitably encounter some external interference, such as crosswind, collision, etc. The existing control method has a complex structure, poor control quality and anti-interference ability, and only one feedback loop. When the feedback fails, the entire system is paralyzed, making system maintenance more difficult.

[0005] The information disclosed in the background technology section of this application is only intended to deepen the understanding of the general background technology of this application, and should not be regarded as an admission or any form of implication that the information constitutes the prior art already known to those skilled in the art. Summary of the invention

[0006] The present invention provides a cascade control method and system for a four-degree-of-freedom overhead crane spatial spherical swing system, which can solve the technical problems that related technologies are difficult to analyze complex spatial spherical swings and the control system has poor control quality and anti-interference performance.

[0007] According to a first aspect of the present invention, there is provided a cascade control method for a spherical swing system of a four-degree-of-freedom overhead crane, comprising: determining a first input error of an outer loop main controller according to target position information of a connection between a cable and a transverse trolley and a bridge, and current position information of a connection between a cable and a transverse bridge; determining a first control function of the outer loop main controller according to a proportional control gain and an integral control gain, wherein the direction of the overhead crane track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley and the bridge through a cable; determining a first control output of the outer loop main controller according to the first control function and the first input error; determining a first control function of the outer loop main controller according to the first control function and the first input error; determining a first control function of the outer loop main controller according to the first control gain and the first integral control gain. A control output and a spatial swing angle of the load are used to determine a second input error of the inner loop sub-controller; a preset performance function is set; a second control function of the inner loop sub-controller is determined according to the preset performance function, the load mass, the bridge mass of the bridge moving in the Y-axis direction, the trolley mass of the transverse trolley moving in the X-axis direction, and the cable length; a control output of the second control function is obtained according to the second control function and the second input error; a control law of the position information of the connection between the cable and the transverse trolley and the bridge, as well as a control law of the spatial swing angle of the load are obtained according to the second control output, the load mass, the bridge mass, the trolley mass and the cable length.

[0008] According to a second aspect of the present invention, there is provided a cascade control system for a four-degree-of-freedom overhead crane space spherical swing system, comprising: a first input error module, for determining a first input error of an outer loop main controller according to target position information of a connection between a cable and a transverse trolley and a bridge, and current position information of a connection between a cable and a transverse bridge; a first control function module, for determining a first control function of the outer loop main controller according to a proportional control gain and an integral control gain, wherein the direction of the overhead crane track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley through a cable; a first control output module, for determining a first control output of the outer loop main controller according to the first control function and the first input error; a second input error module, for determining a first control function of the outer loop main controller according to the first The control output and the spatial swing angle of the load are used to determine the second input error of the inner loop sub-controller; a preset performance function module is used to set the preset performance function; a second control function module is used to determine the second control function of the inner loop sub-controller according to the preset performance function, the load mass, the bridge mass of the bridge moving in the Y-axis direction, the trolley mass of the transverse trolley moving in the X-axis direction, and the cable length; a second control output module is used to obtain the second control output of the second control function according to the second control function and the second input error; a control law module is used to obtain the control law of the position information of the connection between the cable and the transverse trolley and the bridge according to the second control output, the load mass, the bridge mass, the trolley mass and the cable length, as well as the control law of the spatial swing angle of the load.

[0009] Technical effect: According to the present invention, the outer loop main controller and the inner loop sub-controller can be determined according to the swinging condition of the load in space, and the two state parameters of the position of the connection between the cable and the traverse trolley and the bridge frame and the spatial swing angle of the load can be used as the feedback parameters of the outer loop main controller and the inner loop sub-controller respectively, so as to realize the adjustment of the dual feedback loop, which can not only control the position and swing angle of the load in space, but also improve the robustness of the control system based on the dual feedback loop, improve the control quality, and enhance the anti-interference ability. When determining the second control function, the error conversion function can be set based on the preset performance function, so that the first layer sliding surface function and the second layer sliding surface function can be solved based on the error conversion function by means of sliding mode control, and then the sliding mode control law function can be obtained, so that the swing of the load follows the dynamic model of the four-degree-of-freedom spherical swing system, and the driving motor of the traverse trolley and the bridge frame is controlled by the sliding mode control law function to constrain the swing of the load, so that the swing of the load is limited to a certain range, the danger of the overhead crane when moving is reduced, and the control accuracy and robustness are improved. When verifying the stability of the system, the Yapunov candidate function can be set, and the value range of its first-order derivative can be used to determine whether its first-order derivative is semi-negative definite, thereby determining the global stability of the system and obtaining the convergence time, improving the accuracy of the system's stability judgment, and improving the robustness of the system. It has been verified that the control system has strong robustness, is insensitive to external disturbances and parameter changes, and has high control accuracy.

[0010] It should be understood that the above general description and the following detailed description are exemplary and explanatory only and do not limit the present invention. Other features and aspects of the present invention will become more apparent from the following detailed description of exemplary embodiments with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other embodiments can be obtained based on these drawings without creative work.

[0012] Figure 1 A flow chart of a cascade control method for a spherical swing system of a four-degree-of-freedom overhead crane according to an embodiment of the present invention is exemplarily shown;

[0013] Figure 2 A schematic diagram exemplarily shows a control system of a dual feedback loop according to an embodiment of the present invention;

[0014] Figure 3 A schematic diagram exemplarily showing a first group of simulations according to an embodiment of the present invention;

[0015] Figure 4 A schematic diagram exemplarily showing a second group of simulations according to an embodiment of the present invention;

[0016] Figure 5 A schematic diagram exemplarily showing a third group of simulations according to an embodiment of the present invention;

[0017] Figure 6 A schematic diagram of a cascade control system of a four-degree-of-freedom overhead crane spatial spherical swing system according to an embodiment of the present invention is exemplarily shown. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] The technical solution of the present invention is described in detail with specific embodiments below. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0020] Figure 1 A flow chart of a cascade control method for a spherical swing system of a four-degree-of-freedom overhead crane according to an embodiment of the present invention is exemplarily shown, the method comprising:

[0021] Step S101, determining a first input error of the outer loop main controller according to target position information of the connection between the cable and the traverse trolley and the bridge, and current position information of the connection between the cable and the traverse bridge;

[0022] Step S102, determining a first control function of the outer loop main controller according to a proportional control gain and an integral control gain, wherein the direction of the overhead travelling vehicle track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley through a cable;

[0023] Step S103, determining a first control output of an outer loop main controller according to the first control function and the first input error;

[0024] Step S104, determining a second input error of the inner loop sub-controller according to the first control output of the outer loop main controller and the spatial swing angle of the load;

[0025] Step S105, constructing a preset performance function;

[0026] Step S106, determining a second control function of the inner loop sub-controller according to the preset performance function, the load mass, the mass of the bridge moving in the Y-axis direction, the mass of the trolley moving in the X-axis direction, and the cable length;

[0027] Step S107, obtaining a second control output of a second control function according to the second control function and the second input error;

[0028] Step S108, obtaining the control law of the position information of the connection between the cable and the transverse trolley and the bridge, and the control law of the spatial swing angle of the load according to the second control output, the load mass, the bridge mass, the trolley mass and the cable length.

[0029] According to the cascade control method of the spatial spherical swing system of a four-degree-of-freedom overhead crane according to an embodiment of the present invention, an outer-loop main controller and an inner-loop sub-controller can be determined according to the swing condition of the load in space, and two state parameters, namely the position of the connection between the cable and the transverse trolley and the bridge frame and the spatial swing angle of the load, can be used as feedback parameters of the outer-loop main controller and the inner-loop sub-controller respectively, thereby realizing the adjustment of the dual feedback loop, which can not only control the position and swing angle of the load in space, but also improve the robustness of the control system based on the dual feedback loop, improve the control quality, and enhance the anti-interference ability.

[0030] According to one embodiment of the present invention, the main structure of the overhead crane includes a bridge and a transverse trolley. The bridge can be erected on two parallel overhead crane tracks, and the bridge can move along the direction of the overhead crane tracks. The direction of the overhead crane tracks is the Y-axis direction, so the bridge can move along the Y-axis direction. A transverse trolley can be arranged on the bridge, and the direction of the bridge is perpendicular to the direction of the overhead crane tracks. The transverse trolley can move on the bridge, so the transverse trolley can move along the X-axis direction. The cable of the overhead crane can be connected to the transverse trolley, so when the bridge and the transverse trolley move at the same time, the cable, the transverse trolley and the bridge are connected at the same time and move along the X-axis direction and the Y-axis direction, so that the load suspended on the cable swings in space.

[0031] According to one embodiment of the present invention, in order to control the overhead travelling crane and accurately describe the load that performs complex swinging in space, a control system with dual feedback loops can be set to improve the robustness of the control. The outer loop main controller is used to control the horizontal displacement of the bridge and the traverse trolley, and the inner loop sub-controller is used to suppress the swing angle of the load to constrain the swing angle of the load within a certain range.

[0032] Figure 2 A schematic diagram of a control system of a dual feedback loop according to an embodiment of the present invention is exemplarily shown.

[0033] According to one embodiment of the present invention, Figure 2 As shown, the input and output of the main controller and the sub-controller in the dual feedback loop can be gradually analyzed to construct a feedback loop. In step S101, the first input error of the main controller of the outer loop can be determined based on the target position information of the connection between the cable and the traverse trolley and the bridge, and the current position information of the connection between the cable and the traverse trolley and the bridge.

[0034] According to one embodiment of the present invention, according to the target position information of the connection between the cable, the traverse trolley and the bridge, and the current position information of the connection between the cable, the traverse trolley and the bridge, the first input error of the outer loop main controller is determined, including: according to formula (1), the first input error of the outer loop main controller is determined , (1),

[0035] in, is the state vector of the connection between the cable, the traverse trolley and the bridge, , is the X-axis coordinate of the current position information of the connection between the cable, the traverse trolley and the bridge, is the Y-axis coordinate of the current position information of the connection between the cable and the transverse bridge, It is the target position information of the connection between the cable, the transverse trolley and the bridge.

[0036] According to one embodiment of the present invention, the state vector of the connection between the cable, the traverse trolley and the bridge can represent the current position information of the connection between the cable, the traverse trolley and the bridge. The target position information of the connection between the cable, the traverse trolley and the bridge is the parameter input into the control system. The target position of the connection between the cable, the traverse trolley and the bridge has an error with the current position of the connection between the cable, the traverse trolley and the bridge. Therefore, the connection between the cable, the traverse trolley and the bridge can be controlled to move to the target position. The above error can be used as the first input error of the main controller of the outer loop. In addition, after the overhead crane starts to move, the position of the connection between the cable, the traverse trolley and the bridge changes after being controlled. For example, after a series of control actions, the output position information of the connection between the cable, the traverse trolley and the bridge is , that is, the position information represented by the control law of the position information of the connection between the cable and the transverse trolley and the bridge. Then, in the process of continuing the control action, the error between the target position information and the position information represented by the control law of the position information can be used as an input item in the subsequent control process, that is, the first input error of the outer loop main controller, and continue the subsequent calculation and the subsequent control process until there is no error between the position information represented by the control law of the position information of the connection between the cable and the transverse trolley and the bridge and the target position information, in other words, until the connection between the cable and the transverse trolley and the bridge reaches the target position.

[0037] According to one embodiment of the present invention, in step S102, the outer loop main controller is a proportional-integral controller, and the proportional control gain and the integral control gain can be set to obtain the first control function of the outer loop main controller, and in step S103, the first input error is used as an input parameter of the first control function, so as to obtain the first control output of the outer loop main controller through calculation of the first control function.

[0038] According to one embodiment of the present invention, determining the first control output of the outer loop main controller according to the first control function and the first input error includes: determining the first control output of the outer loop main controller according to formula (2): , (2),

[0039] Among them, t is the time variable, For the current moment, is the proportional control gain, is the integral control gain.

[0040] According to an embodiment of the present invention, when the input information of the first control function is the first input error, the first control output corresponding to the first control function can be calculated by the first control function, wherein: is the output term of the proportional control gain, is the output term of the integral control gain, and the sum of the two is the output term of the proportional integral controller, that is, the first control output. The control accuracy and robustness of the horizontal displacement of the bridge and the transverse trolley can be improved by the proportional integral controller.

[0041] According to one embodiment of the present invention, in step S104, the first control output and the spatial swing angle of the load can be used to determine the second input error of the inner loop sub-controller, so that the second control output is output after the second control function of the inner loop sub-controller is calculated.

[0042] According to one embodiment of the present invention, the second input error of the inner loop sub-controller is determined according to the first control output of the outer loop main controller and the spatial swing angle of the load, including: determining the second input error of the inner loop sub-controller according to formula (3): , (3),

[0043] in, is the load's spatial swing angle state vector, , is the swing angle of the load along the X-axis, is the swing angle of the load along the Y-axis.

[0044] According to one embodiment of the present invention, in formula (3), the difference between the first control output and the load's spatial swing angle state vector can be used as the second input error of the inner loop sub-controller, wherein the two components of the load's spatial swing angle state vector are the load's swing angle along the X-axis direction and the load's swing angle along the Y-axis direction, respectively. When the overhead crane starts to move and the control system starts to work, the two components of the load's spatial swing angle state vector are the load's initial swing angle along the X-axis direction (for example, 0°) and the load's initial swing angle along the Y-axis direction (for example, 0°). As the overhead crane starts to move and the load starts to swing, the two components of the load's spatial swing angle state vector change. For example, after a series of control actions, the output load's spatial swing angle state vector is: , that is, the swing angle described by the control law of the spatial swing angle of the load. Therefore, in the subsequent control process, the error between the first control output and the swing angle described by the control law of the spatial swing angle of the load can be used as an input item in the subsequent control process, that is, the second input error of the inner loop sub-controller, and continue the subsequent calculations and the subsequent control process until the connection between the cable, the transverse trolley and the bridge reaches the target position, the overhead crane stops moving, the control process can be stopped immediately, and wait for the swing to stop.

[0045] According to one embodiment of the present invention, in step S105, the control system performs control for the purpose of controlling the swing angle of the load so that the swing angle is within a certain range while moving the connection between the cable and the transverse trolley and the bridge to the target position, so as to avoid danger caused by excessive swing angle. Based on this purpose, a preset performance function can be set, and the second control function of the sub-controller can be determined based on the preset performance function, so that the output calculated by the second control function (i.e., the second control output) can reasonably control the drive motors of the transverse trolley and the bridge, so that the swing angle of the load is controlled within a certain range.

[0046] According to an embodiment of the present invention, setting a preset performance function includes: setting a preset performance function according to formula (4) and formula (5): ,

[0047] (4),

[0048] (5),

[0049] in, is the preset initial value, is the preset final value, and is a preset constant.

[0050] According to one embodiment of the present invention, the preset performance function makes the second input error range, that is, the second input error at each moment is within the convergence interval, so that the difference between the first control output and the spatial swing angle state vector of the load converges, so that the spatial swing angle state vector of the load is controllable, in other words, the swing angle of the load is within a certain range.

[0051] According to an embodiment of the present invention, in step S106, the second control function may be determined based on the preset performance function set above, so that the second control output output by the second control function can make the swing angle of the load within a certain range.

[0052] According to one embodiment of the present invention, the second control function of the inner loop sub-controller is determined according to the preset performance function, the load mass, the mass of the bridge moving in the Y-axis direction, the mass of the trolley moving in the X-axis direction, and the cable length, including: obtaining the error conversion function E according to formula (6),

[0053] (6),

[0054] Where t is the time variable, and the parameters in formula (6) are shown in the following formulas (7), (8) and (9):

[0055] (7),

[0056] (8),

[0057] (9),

[0058] Obtain the first derivative (10) and second derivative (11) of the error transfer function E,

[0059] (10),

[0060] (11),

[0061] in, for The first derivative of for The second-order derivative of for The first derivative of for The second-order derivative of , where the parameters in the first-order derivative (10) and the second-order derivative (11) are as shown in the following formulas (12), (13), (14), (15), (16), (17), (18), (19) and (20),

[0062] (12),

[0063] (13),

[0064] (14),

[0065] (15),

[0066] (16),

[0067] (17),

[0068] (18),

[0069] (19),

[0070] (20),

[0071] in, for The first derivative of for The first derivative of for The second-order derivative of for The first derivative of for The first derivative of ;

[0072] According to formula (21) and formula (22), the first layer sliding surface function is obtained and the second sliding surface function ,

[0073] (twenty one),

[0074] (twenty two),

[0075] in, , , and is the preset control gain, and , is the symbolic function, Used to indicate is a positive or negative number; the second layer sliding surface function Set to 0 and obtain the sliding mode control law function (23), (twenty three),

[0076] in, for The first derivative of for The second-order derivative of the sliding mode control law function (23) is as shown in the following formulas (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39) and (40).

[0077] (twenty four),

[0078] (25),

[0079] (26),

[0080] (27),

[0081] (28),

[0082] (29),

[0083] (30),

[0084] (31),

[0085] (32),

[0086] (33),

[0087] (34),

[0088] (35),

[0089] (36),

[0090] (37),

[0091] (38),

[0092] (39),

[0093] (40),

[0094] Where m is the load mass, is the mass of the trolley for the transverse movement, is the sum of the masses of the traverse trolley and the bridge, is the cable length, for The first derivative of for The first derivative of is the gravitational acceleration; according to formula (41), the reaching law function is obtained ,

[0095] (41),

[0096] in, and is the preset coefficient, express is a positive or negative number; the second control function of the inner loop sub-controller is determined according to formula (42): (42).

[0097] According to one embodiment of the present invention, in order to constrain the swing angle of the load by the second control function, an error conversion function may be set based on a preset performance function, and the specific form of the error conversion function may be determined based on formula (6), formula (7), formula (8) and formula (9). Furthermore, in order to make the swing angle of the load converge, the second control function may be determined by a sliding mode control method, so that the swing angle state vector of the load is controllable, that is, the swing angle is converged within a certain range.

[0098] According to one embodiment of the present invention, in order to set a sliding mode controller, the first-order derivative and the second-order derivative of the error conversion function E with respect to the time variable t can be solved, the first-order derivative of the error conversion function E with respect to the time variable t can be determined according to formula (10), the second-order derivative of the error conversion function E with respect to the time variable t can be determined according to formula (11), and the various parameters in formula (10) and formula (11) can be determined based on formula (12), formula (13), formula (14), formula (15), formula (16), formula (17), formula (18), formula (19) and formula (20).

[0099] According to one embodiment of the present invention, after determining the error conversion function E and its first-order derivative and second-order derivative, the first-layer sliding surface function can be determined according to formula (21), and then the second-layer sliding surface function can be determined based on the first-layer sliding surface function, as shown in formula (22).

[0100] According to one embodiment of the present invention, the second layer sliding surface function is set to 0, and the position where the cable is connected to the traverse trolley and the motion law followed by the spatial swing angle of the load are solved in detail, and the sliding mode control law function (23) can be obtained. Among them, the position where the cable is connected to the traverse trolley and the bridge, and the motion law followed by the spatial swing angle of the load can be determined based on the Lagrange equation. Based on the Lagrange equation, the dynamic model of the four-degree-of-freedom spherical swing system can be determined, which is the position where the cable is connected to the traverse trolley and the bridge, and the motion law followed by the spatial swing angle of the load.

[0101] According to one embodiment of the present invention, the dynamic model of the four-degree-of-freedom spherical swing system can be expressed by the following formula (42), formula (43), formula (44) and formula (45), (42),

[0102] (43),

[0103] (44),

[0104] (45),

[0105] in, for The second-order derivative of for The second-order derivative of for The second-order derivative of for The second-order derivative of is the motor driving force of the traverse trolley, is the motor driving force of the bridge. Further, formula (42), formula (43), formula (44) and formula (45) can be rearranged to obtain formula (46) and formula (47),

[0106] (46),

[0107] (47),

[0108] in, for The second-order derivative of for The second-order derivative of , , and The specific expressions of are shown in formula (24), formula (25), formula (26), formula (27), formula (28), formula (29), formula (30), formula (31), formula (32), formula (33), formula (34), formula (35), formula (36), formula (37), formula (38), formula (39) and formula (40). .

[0109] According to one embodiment of the present invention, based on the above analysis, the second-layer sliding surface function includes the term of the vector of the motor driving force of the transverse trolley and the bridge. When the second-layer sliding surface function is set to 0, the vector of the motor driving force of the transverse trolley and the bridge is the sliding mode control law function, as shown in formula (23), which can be used to represent the vector of the motor driving force of the transverse trolley and the bridge when the swing of the load is constrained and controlled based on the above-mentioned four-degree-of-freedom spherical swing system dynamics model.

[0110] According to one embodiment of the present invention, a reaching law function (41) can be designed, which can be used to represent the vector of the motor driving force of the traverse trolley and the bridge frame when the swing of the load approaches convergence based on the above-mentioned four-degree-of-freedom spherical swing system dynamics model. Further, by summing the reaching law function and the sliding mode control law function, a second control function can be obtained, which can be used to represent the vector of the motor driving force of the traverse trolley and the bridge frame when the swing of the load is restricted within a certain range based on the above-mentioned four-degree-of-freedom spherical swing system dynamics model.

[0111] In this way, an error conversion function can be set based on a preset performance function, and then the first-layer sliding surface function and the second-layer sliding surface function can be solved based on the error conversion function by means of sliding control, and then the sliding mode control law function can be obtained, so that the swing of the load follows the dynamic model of the four-degree-of-freedom spherical swing system, and the driving motors of the transverse trolley and the bridge are controlled by the sliding mode control law function to constrain the swing of the load, and a reaching law function is set, so that the swing of the load follows the dynamic model of the four-degree-of-freedom spherical swing system, and the driving motors of the transverse trolley and the bridge are controlled by the reaching law function to converge the swing of the load, thereby limiting the swing of the load within a certain range, reducing the danger of the overhead crane when moving, and improving the control accuracy and robustness.

[0112] According to one embodiment of the present invention, in step S107, the second input error is used as input information of the second control function to obtain the second control output of the second control function, that is, the vector of the motor driving force of the transverse trolley and the bridge.

[0113] According to one embodiment of the present invention, in step S108, under the control of the second control output, the control law of the position information of the connection between the cable and the traverse trolley and the bridge and the control law of the spatial swing angle of the load can be obtained, and the position information described by the control law of the position information of the connection between the cable and the traverse trolley and the bridge replaces the state vector of the connection between the cable and the traverse trolley and the bridge in formula (1). , so that the outer loop is closed and subsequent control actions are performed, and the load's spatial swing angle state vector in formula (3) is replaced by the swing angle described by the control law of the load's spatial swing angle , so that the inner loop is closed and subsequent control actions are performed.

[0114] According to one embodiment of the present invention, according to the second control output, the load mass, the bridge mass, the trolley mass and the cable length, a control law for the position information of the connection between the cable and the transverse trolley and the bridge, and a control law for the spatial swing angle of the load are obtained, including: according to formula (48), obtaining the second-order derivative of the control law of the spatial swing angle of the load ,

[0115] (48),

[0116] According to the second-order derivative of the control law of the load's spatial swing angle, the control law of the load's spatial swing angle is obtained; according to formula (49), the second-order derivative of the control law of the position information of the connection between the cable and the transverse trolley and the bridge is obtained: ,

[0117] (49),

[0118] According to the second-order derivative of the control law of the position information of the connection between the cable, the traverse trolley and the bridge, the control law of the position information of the connection between the cable, the traverse trolley and the bridge is obtained.

[0119] According to one embodiment of the present invention, the second control output can be used as the vector of the motor driving force of the traverse trolley and the bridge in the dynamic model described by formula (47), thereby obtaining the second-order derivative of the control law of the spatial swing angle of the load, which can be integrated to obtain the first-order derivative of the control law of the spatial swing angle of the load, and after integration again, the control law of the spatial swing angle of the load can be obtained. Similarly, the second control output can be used as the vector of the motor driving force of the traverse trolley and the bridge in the dynamic model described by formula (46), thereby obtaining the second-order derivative of the control law of the position information of the connection between the cable and the traverse trolley and the bridge, which can be integrated to obtain the first-order derivative of the control law of the position information of the connection between the cable and the traverse trolley and the bridge, and after integration again, the control law of the position information of the connection between the cable and the traverse trolley and the bridge can be obtained, thereby completing the control closed loop.

[0120] According to one embodiment of the present invention, after completing the control closed loop, the following is obtained: Figure 2 After the control system shown is established, the stability of the control system can be verified. The method further includes: obtaining a Lyapunov candidate function V according to formula (50);

[0121] (50),

[0122] Get the first derivative of the Lyapunov candidate function V (51),

[0123] (51),

[0124] According to formula (52), determine is negative semidefinite, and determines that the Lyapunov candidate function is globally stable,

[0125] (52),

[0126] According to formula (53), the convergence time is obtained ,

[0127] (53),

[0128] in, is the initial value of the Lyapunov candidate function.

[0129] According to one embodiment of the present invention, according to the Lyapunov stability theorem, a Lyapunov candidate function can be set. If the derivative function of the Lyapunov candidate function is semi-negative definite, the Lyapunov candidate function is globally stable. Therefore, the Lyapunov candidate function can be set based on formula (50), and the first-order derivative of the Lyapunov candidate function can be solved based on formula (51). According to formula (52), ,and Therefore, it can be determined that the first-order derivative of the Lyapunov candidate function is semi-negative definite, and thus the Lyapunov candidate function is globally stable. Then, the convergence time can be calculated according to formula (53), that is, the time for the load swing angle to converge within a certain range.

[0130] In this way, the Yapunov candidate function can be set, and the value interval of its first-order derivative can be used to determine whether its first-order derivative is semi-negative definite, so as to determine the global stability of the system, and obtain the convergence time, improve the accuracy of the system's stability judgment, and improve the robustness of the system.

[0131] According to an embodiment of the present invention, the feasibility of the above control system can be verified by data. , , , , , in the initial state, , , , , , , , , , , , , , .

[0132] Figure 3 A schematic diagram exemplarily illustrating a first set of simulations according to an embodiment of the present invention is shown.

[0133] According to one embodiment of the present invention, three groups of simulations are performed using the above data. In the first group of simulations, the traverse trolley and the bridge can quickly reach the set target position, the maximum load swing angle does not exceed 2°, and after the trolley stops running, the load swing angle quickly tends to be stable, and the residual swing is small; it can be seen from the motor driving force of the two circuits that the motor driving force of the outer circuit (i.e., the first control output) is small, the required power consumption of the drive motor is low, the energy consumption of the drive motor is saved, and the service life of the drive motor is extended. The virtual driving force of the inner circuit (i.e., the second control output) is also small, the hardware configuration requirements for the drive circuit are low, the cost is low, and the resource allocation is optimized.

[0134] Figure 4 A schematic diagram exemplarily illustrating a second set of simulations according to an embodiment of the present invention is shown.

[0135] According to one embodiment of the present invention, in the second group of simulations, pulse interference signals and sinusoidal interference signals are applied between 11s-12s and between 15s-16s, respectively, with a signal amplitude of 0.5°. The interference signals are used to simulate the load being subjected to external disturbances during the load lifting process, thereby verifying the anti-interference performance of the control system. It can be seen from the simulation results that the interference signal will not destroy the stability of the system. When the load is subjected to external interference, the controller takes effect and effectively resists the external interference.

[0136] Figure 5 A schematic diagram exemplarily illustrating a third set of simulations according to an embodiment of the present invention is shown.

[0137] According to one embodiment of the present invention, in the third group of simulations, the cable length and the load mass are increased by 50% respectively, that is, , From the simulation results, it can be seen that when the cable length increases by 50%, the displacement curve of the connection between the cable and the traverse trolley and the bridge is almost the same as when it is not increased, and the swing angle curve has a slight deviation. This is because the increase in cable length aggravates the load swing amplitude and residual swing delay, but the deviation is also within the allowable range. The simulation results show that the control system has excellent robustness and is insensitive to changes in system parameters.

[0138] According to the cascade control method of the spatial spherical swing system of a four-degree-of-freedom overhead crane according to an embodiment of the present invention, an outer-loop main controller and an inner-loop sub-controller can be determined according to the swing condition of the load in space, and two state parameters, namely the position of the connection between the cable and the transverse trolley and the bridge frame and the spatial swing angle of the load, can be used as feedback parameters of the outer-loop main controller and the inner-loop sub-controller respectively, thereby realizing the adjustment of the dual feedback loop, which can not only control the position and swing angle of the load in space, but also improve the robustness of the control system based on the dual feedback loop, improve the control quality, and enhance the anti-interference ability. When determining the second control function, the error conversion function can be set based on the preset performance function, so that the first layer sliding surface function and the second layer sliding surface function can be solved based on the error conversion function by means of sliding mode control, and then the sliding mode control law function can be obtained, so that the swing of the load follows the dynamic model of the four-degree-of-freedom spherical swing system, and the motor driving force of the traverse trolley and the bridge frame is controlled by the sliding mode control law function to constrain the swing of the load, and the approaching law function is set, so that the swing of the load follows the dynamic model of the four-degree-of-freedom spherical swing system, and the driving motor of the traverse trolley and the bridge frame is controlled by the approaching law function to make the swing of the load converge, so that the swing of the load is limited within a certain range, reducing the danger of the overhead crane when moving, and improving the control accuracy and robustness. When verifying the stability of the system, the Yapunov candidate function can be set, and the value range of its first-order derivative can be used to determine whether its first-order derivative is semi-negative definite, so as to determine the global stability of the system, and the convergence time can be obtained, so as to improve the accuracy of the stability judgment of the system and improve the robustness of the system. It has been verified that the control system has strong robustness, strong anti-interference ability, is insensitive to external disturbances and parameter changes, and has high control accuracy.

[0139] Figure 6 A schematic diagram showing a cascade control system of a 4-DOF overhead crane space spherical swing system according to an embodiment of the present invention is shown, the system comprising:

[0140] A first input error module is used to determine a first input error of the outer loop main controller according to target position information of the connection between the cable and the traverse trolley and the bridge, and current position information of the connection between the cable and the traverse bridge;

[0141] The first control function module is used to determine the first control function of the outer loop main controller according to the proportional control gain and the integral control gain, wherein the direction of the overhead travelling vehicle track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley through a cable;

[0142] A first control output module, used for determining a first control output of an outer loop main controller according to the first control function and the first input error;

[0143] A second input error module is used to determine a second input error of the inner loop sub-controller according to the first control output of the outer loop main controller and the spatial swing angle of the load;

[0144] A preset performance function module is used to set a preset performance function;

[0145] A second control function module is used to determine the second control function of the inner loop sub-controller according to the preset performance function, the load mass, the mass of the bridge moving in the Y-axis direction, the mass of the trolley moving in the X-axis direction, and the cable length;

[0146] A second control output module, used for obtaining a second control output of a second control function according to the second control function and the second input error;

[0147] A control law module is used to obtain the control law of the position information of the connection between the cable and the transverse trolley and the bridge frame, as well as the control law of the spatial swing angle of the load based on the second control output, the load mass, the bridge frame mass, the trolley mass and the cable length.

[0148] It should be understood by those skilled in the art that the embodiments of the present invention described above and shown in the accompanying drawings are only examples and do not limit the present invention. The purpose of the present invention has been fully and effectively achieved. The functional and structural principles of the present invention have been demonstrated and explained in the embodiments, and the embodiments of the present invention may be deformed or modified in any way without departing from the principles.

Claims

1. A cascade control method for a 4-DOF overhead crane space spherical swing system, characterized in that: include: Determine the first input error of the outer loop main controller according to the target position information of the connection between the cable and the transverse trolley and the bridge, and the current position information of the connection between the cable and the transverse trolley and the bridge; determine the first control function of the outer loop main controller according to the proportional control gain and the integral control gain, wherein the direction of the overhead crane track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley through the cable; determine the first control output of the outer loop main controller according to the first control function and the first input error; determine the second input error of the inner loop sub-controller according to the first control output of the outer loop main controller and the spatial swing angle of the load; set a preset performance function; determine the second control function of the inner loop sub-controller according to the preset performance function, the load mass, the bridge mass of the bridge moving in the Y-axis direction, the trolley mass of the transverse trolley moving in the X-axis direction, and the cable length; obtain the second control output of the second control function according to the second control function and the second input error; Based on the second control output, the load mass, the bridge mass, the trolley mass and the cable length, the control law of the position information of the connection between the cable and the transverse trolley and the bridge, as well as the control law of the spatial swing angle of the load are obtained.

2. The cascade control method for the spherical swing system of a four-degree-of-freedom overhead crane according to claim 1 is characterized in that: According to the target position information of the connection between the cable, the traverse trolley and the bridge, and the current position information of the connection between the cable, the traverse trolley and the bridge, the first input error of the main controller of the outer loop is determined, including: according to the formula , determine the first input error of the outer loop main controller ,in, is the state vector of the connection between the cable, the traverse trolley and the bridge, , is the X-axis coordinate of the current position information of the connection between the cable, the traverse trolley and the bridge, is the Y-axis coordinate of the current position information of the connection between the cable and the transverse bridge, It is the target position information of the connection between the cable, the transverse trolley and the bridge.

3. The cascade control method for the spherical swing system of a four-degree-of-freedom overhead crane according to claim 2 is characterized in that: Determining a first control output of an outer loop main controller according to the first control function and the first input error includes: determining a first control output of an outer loop main controller according to the formula , determine the first control output of the outer loop main controller , where t is the time variable, For the current moment, is the proportional control gain, is the integral control gain.

4. The cascade control method for the spherical swing system of a four-degree-of-freedom overhead crane according to claim 3 is characterized in that: According to the first control output of the outer loop main controller and the spatial swing angle of the load, the second input error of the inner loop sub-controller is determined, including: according to the formula , determine the second input error of the inner loop sub-controller ,in, is the load's spatial swing angle state vector, , is the swing angle of the load along the X-axis, is the swing angle of the load along the Y-axis.

5. The cascade control method for the spherical swing system of a four-degree-of-freedom overhead crane according to claim 4 is characterized in that: Set preset performance functions, including: , , set the preset performance function ,in, is the preset initial value, is the preset final value, and is a preset constant.

6. The cascade control method for a 4-DOF overhead crane space spherical swing system according to claim 5, characterized in that: According to the preset performance function, the load mass, the mass of the bridge frame moving in the Y-axis direction, the mass of the trolley moving in the X-axis direction and the cable length, the second control function of the inner loop sub-controller is determined, including: according to the formula , obtain the error conversion function E, where t is the time variable, , , ; Get the first-order derivative of the error transfer function E , and the second-order derivative ,in, for The first derivative of for The second-order derivative of for The first derivative of for The second-order derivative of , for The first derivative of , , , , for The first derivative of for The second-order derivative of for The first derivative of , for The first derivative of , , According to the formula , , get the first layer sliding surface function and the second sliding surface function ,in, , , and is the control gain, and , is the symbolic function, Used to indicate is a positive or negative number; the second layer sliding surface function Set to 0 to obtain the sliding mode control law function ,in, for The first derivative of for The second-order derivative of , , , , , , , , , , , , , , , , , where m is the load mass, is the mass of the trolley for the transverse movement, is the sum of the masses of the traverse trolley and the bridge, is the cable length, for The first derivative of for The first derivative of is the acceleration due to gravity; according to the formula , and obtain the reaching law function ,in, and is the preset coefficient, express is a positive or negative number; according to the formula , determine the second control function of the inner loop sub-controller.

7. The cascade control method for a 4-DOF overhead crane space spherical swing system according to claim 6, characterized in that: According to the second control output, the load mass, the bridge mass, the trolley mass and the cable length, the control law of the position information of the connection between the cable and the transverse trolley and the bridge, and the control law of the spatial swing angle of the load are obtained, including: according to the formula , obtain the second-order derivative of the control law of the load's spatial swing angle ;According to the second-order derivative of the control law of the load's spatial swing angle, the control law of the load's spatial swing angle is obtained; According to the formula , the second-order derivative of the control law for obtaining the position information of the connection between the cable, the traverse trolley and the bridge ; According to the second-order derivative of the control law of the position information of the connection between the cable, the transverse trolley and the bridge, the control law of the position information of the connection between the cable, the transverse trolley and the bridge is obtained.

8. The cascade control method for a 4-DOF overhead crane space spherical swing system according to claim 7, characterized in that: The method further comprises: according to the formula , obtain the Lyapunov candidate function V; obtain the first-order derivative of the Lyapunov candidate function V According to the formula ,Sure is semi-negative definite, and determines that the Lyapunov candidate function is globally stable; according to the formula , get the convergence time ,in, is the initial value of the Lyapunov candidate function.

9. A cascade control system for a 4-DOF overhead crane space spherical swing system, characterized in that: include: The first input error module is used to determine the first input error of the outer loop main controller according to the target position information of the connection between the cable and the transverse trolley and the bridge frame, and the current position information of the connection between the cable and the transverse trolley and the bridge frame; the first control function module is used to determine the first control function of the outer loop main controller according to the proportional control gain and the integral control gain, wherein the direction of the overhead crane track is the Y-axis direction, the direction perpendicular to the Y-axis direction is the X-axis direction, and the load is connected to the transverse trolley through the cable; the first control output module is used to determine the first control output of the outer loop main controller according to the first control function and the first input error; the second input error module is used to determine the first control output of the inner loop main controller according to the first control output of the outer loop main controller and the spatial swing angle of the load. A second input error of the loop sub-controller; a preset performance function module, used to set a preset performance function; a second control function module, used to determine the second control function of the inner loop sub-controller according to the preset performance function, the load mass, the bridge mass of the bridge moving in the Y-axis direction, the trolley mass of the transverse trolley moving in the X-axis direction, and the cable length; a second control output module, used to obtain the second control output of the second control function according to the second control function and the second input error; a control law module, used to obtain the control law of the position information of the connection between the cable and the transverse trolley and the bridge, and the control law of the spatial swing angle of the load according to the second control output, the load mass, the bridge mass, the trolley mass and the cable length.

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