Patent Publication Number: US-2022227604-A1

Title: Full-time anti-sway control method of bridge crane system based on inverter structure

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This patent application claims the benefit of U.S. Provisional Patent Application No. 63/138,640, filed Jan. 18, 2021, which is incorporated by reference herein. 
    
    
     BACKGROUND 
     Technical Field 
     The present disclosure relates to a full-time anti-sway control method of a bridge crane system, and more particularly to a full-time anti-sway control method of a bridge crane system based on an inverter structure. 
     Description of Related Art 
     Bridge (overhead) cranes have been widely used in industrial assembly and transportation applications. A typical bridge crane structure includes a crane bridge, a crane trolley, and a hoist that moves up and down in a Z direction so that the hanging objects move to the designated position by the operation of the crane bridge and the crane trolley. However, during the operation process, the hanging object will inevitably sway due to the speed change of the crane bridge and/or the crane trolley, which affects work efficiency and increases work safety problems. 
     The anti-sway function for crane is suitable for indoor bridge crane facilities, which is used in the inverter structure of the crane bridge (in an X direction) and the crane trolley (in a Y direction). When the hoist suspends heavy objects and moves in the X or Y direction, the anti-sway function is activated/enabled to eliminate unnecessary swaying during the moving process, reduce the occurrence of hazards, increase production capacity, and achieve better bridge crane control benefits. Under the same number of operations, the operation time is a Gaussian distribution. 
     Many references have proposed related anti-sway technologies. Based on cost considerations, most of the anti-sway technologies use a swing angle estimator to replace an image identifier or (swing) angle sensor. Since the anti-sway controller adopts the design of state feedback, the design of the estimator and the state controller requires a large number of system parameters to be set. In practical applications, therefore, the system parameters are difficult to be measured and difficult to be acquired so as to increase the trouble of use. 
     Since it is necessary to estimate the speed of the crane bridge and the crane trolley as well as to set system parameters in terms of angle estimation, the use of motor position sensor is necessary. However, for low-cost system configurations, the motor may not be equipped with an encoder or Hall sensor, and even additional installation of the encoder or Hall sensor will increase the cost of mechanism design and hardware configuration, and also increase the difficulty of implementation. 
     In order to solve the above technical difficulties, the present disclosure proposes the full-time anti-sway control method of the bridge crane system based on the inverter structure, which is simple, easy to implement, without requiring a motor position sensor, and having low-cost hardware configuration. 
     SUMMARY 
     An object of the present disclosure is to provide a full-time anti-sway control method of a bridge crane system based on an inverter structure to solve the problems of existing technology. 
     In order to achieve the object of the present disclosure, the bridge crane system includes an inverter for performing the control method and at least one motor controlled by the control method. The control method includes steps of: receiving a specified high frequency and a frequency change time, calculating a time setting range according to a plurality of system parameters and a rope length information of the bridge crane system, selecting a time setting value within the time setting range, dividing the frequency change time into a plurality of time intervals according to the time setting value, adjusting an operation frequency command to change between a low frequency and the specified high frequency within the plurality of time intervals to generate a frequency change curve, calculating a frequency correction amount according to the frequency change curve and the rope length information, and superimposing the frequency change curve and the frequency correction amount to generate an anti-sway frequency command to drive the at least one motor. 
     In order to achieve the object of the present disclosure, the bridge crane system includes an inverter for performing the control method and at least one motor controlled by the control method. The control method includes steps of: receiving a specified high frequency and a frequency change time, calculating a time setting range according to a plurality of system parameters and a rope length information of the bridge crane system, selecting a time setting value within the time setting range, dividing the frequency change time into a plurality of time intervals according to the time setting value, adjusting an operation frequency command to change between a low frequency and the specified high frequency within the plurality of time intervals to generate a frequency change curve, acquiring a rotation angle of the at least one motor by the position sensor, estimating a swing angle and a swing speed of a bridge crane under a simple pendulum movement according to the rotation angle to calculate a frequency correction amount, and superimposing the frequency change curve and the frequency correction amount to generate an anti-sway frequency command to drive the at least one motor. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the present disclosure as claimed. Other advantages and features of the present disclosure will be apparent from the following description, drawings and claims. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The present disclosure can be more fully understood by reading the following detailed description of the embodiment, with reference made to the accompanying drawing as follows: 
         FIG. 1  is a structure diagram of a full-time anti-sway control of a bridge crane system according to a first embodiment of the present disclosure. 
         FIG. 2  is a flowchart of a full-time anti-sway control method of the bridge crane system based on an inverter according to a first embodiment of the present disclosure. 
         FIG. 3  is a structure diagram of an anti-sway controller in  FIG. 1 . 
         FIG. 4A  is a schematic block diagram of a swing angle estimation module of the full-time anti-sway control of the bridge crane system according to the first embodiment of the present disclosure. 
         FIG. 4B  is a schematic block diagram of a swing angle processing module of the full-time anti-sway control of the bridge crane system according to the first embodiment of the present disclosure. 
         FIG. 5A  is a schematic curve of an optimal frequency change of the full-time anti-sway control of the bridge crane system according to the first embodiment of the present disclosure. 
         FIG. 5B  is a schematic curve of an optimal anti-sway frequency command of the full-time anti-sway control of the bridge crane system according to the first embodiment of the present disclosure. 
         FIG. 6  is a schematic curve of the response of different damping coefficients to a swing angle and a motor speed according to the present disclosure. 
         FIG. 7  is a schematic curve of the response of different bandwidth ratios to the swing angle and the motor speed according to the present disclosure. 
         FIG. 8  is a structure diagram of the full-time anti-sway control of the bridge crane system according to a second embodiment of the present disclosure. 
         FIG. 9  is a flowchart of the full-time anti-sway control method of the bridge crane system based on the inverter according to a second embodiment of the present disclosure. 
         FIG. 10  is a structure diagram of the anti-sway controller in  FIG. 8 . 
         FIG. 11  is a structure diagram of the bridge crane system having a drive mode switch according to the present disclosure. 
         FIG. 12  is a structure diagram of an anti-sway frequency controller having the drive mode switch according to the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made to the drawing figures to describe the present disclosure in detail. It will be understood that the drawing figures and exemplified embodiments of present disclosure are not limited to the details thereof. The present disclosure provides a full-time anti-sway control method of a bridge crane system, and the function of the method is based on an inverter, and the method has the following characteristics and functions. 
     Regardless of whether there is a motor position sensor or not, the anti-sway function can be completed without a swing angle sensor, and the construction cost is low. That is, no motor position sensor and swing angle sensor/image recognizer are needed, and the construction cost is low. 
     Only the rope length information is required, and the dependence on the parameters of the crane and motor system is low, and it is easy to implement. That is, there is no need to highly rely on system parameters such as the weight of the crane bridge and the crane trolley, the weight of the suspended objects, the wheel diameter, and the reduction ratio, and it is easy to implement. 
     In the crane bridge structure, if the inverter is used to drive two motors, simple v/f (voltage/frequency) control can also be used to achieve anti-sway function. That is, the v/f motor control method is suitable for one-to-many structure (multiple motors driven by one inverter), and it has high versatility. 
     The anti-sway frequency generator is generated all-time, regardless of the general travel (normal acceleration and deceleration in one direction), repeated inching (repeated acceleration and deceleration in one direction), repeated forward and reverse rotation (repeated forward movement and reverse movement) can achieve the anti-sway effect before the crane stops. That is, the full-time anti-sway control is suitable for all working conditions of the crane operation, and it has high versatility. 
     The control parameters can be automatically adjusted without repeated tests according to the intensity setting by the user. That is, it can perform full-time anti-sway and high control freedom. 
     Please refer to  FIG. 1 . The bridge crane system  1000  includes an operation apparatus  100 , an inverter  200 , at least one motor  300 , and a bridge crane  400 . In one embodiment, the bridge crane  400  includes a crane bridge and a crane trolley. The bridge crane system  1000  uses a plurality of motors to drive different cranes of the bridge crane  400 . In other embodiments, the bridge crane system  1000  uses only one motor to drive the bridge crane  400  having a single crane. Therefore, the number of the motors is not limited in the present disclosure. In addition, the bridge crane  400  is usually controlled to perform a simple pendulum movement. 
     The user may use the operation apparatus  100 , such as a remote controller, a calculator, a computer, or so on to provide an operation command f 0  to the inverter  200 . The operation command f 0  includes information such as movement command, movement direction, given frequency, and acceleration/deceleration time, but the present disclosure is not limited thereto. As shown in  FIG. 1 , the inverter  200  includes an anti-sway control unit  220 , a voltage/frequency (v/f) open-loop control unit  240 , and a drive unit  260 . The anti-sway control unit  220  outputs an anti-sway frequency command f 1  to the v/f open-loop control unit  240  according to the operation command f 0 . The v/f open-loop control unit  240  performs a voltage/frequency open-loop control (referred to as a v/f open-loop control) to the drive unit  260  according to the anti-sway frequency command f 1  so that the drive unit  260  generates a drive voltage signal v r  and a drive frequency signal f r  to drive (operate) the at least one motor  300 . In particular, the v/f open-loop control belongs to the technology well known to those of ordinary skill in the art, and therefore the detail description thereof is omitted here for conciseness. In general, the drive unit  260  may be a drive circuit with a plurality of switches, power converters, etc., but the present disclosure is not limited thereto. 
     Therefore, the focus of the present disclosure is how to generate the anti-sway frequency command f 1  to optimize the v/f open-loop control to reduce the sway phenomenon of the bridge crane. Please refer to  FIG. 1 ,  FIG. 2 ,  FIG. 3 ,  FIG. 4A ,  FIG. 4B ,  FIG. 5A , and  FIG. 5B  to explain the control method of the first embodiment of the present disclosure. 
     In the step (S 11 ) shown in  FIG. 2 , a time frequency processing module  220   a  (shown in  FIG. 3 ) of the anti-sway control unit  220  receives the operation command f 0  provided from the operation apparatus  100 . In particular, the operation command f 0  includes, for example, but not limited to, a specified high frequency fh and a time setting value (such as an acceleration time T 1  or a deceleration time T 3  shown in  FIG. 5A ), and a frequency change time T 0  is preset in the inverter  200 . In other embodiments, the operation command f 0  includes, for example, but not limited to, the specified high frequency fh, the time setting value (T 1  or T 3 ), and/or the frequency change time T 0 , but the present disclosure is not limited thereto. 
     In the step (S 12 ) shown in  FIG. 2 , the time frequency processing module  220   a  calculates a time setting range according to a plurality of system parameters and a rope length information L of the bridge crane system  1000 . In one embodiment, the plurality of the system parameters includes a system inertia of the bridge crane system  1000 , and a rated speed and a rated torque of the motor  300 . In particular, the plurality of system parameters and the rope length information L of the bridge crane system  1000  are program setting values preset in the inverter  200 . In one embodiment, the present disclosure provides users to set the acceleration and deceleration time of the bridge crane system  1000  by themselves so that the acceleration and deceleration time of the bridge crane system  1000  can be flexibly designed under the conditions of inverter overcurrent limit and anti-sway control allowable time. However, the acceleration and deceleration time of the bridge crane system  1000  needs to be designed within a reasonable time setting range. The following continues to describe how to acquire the time setting range in the step (S 12 ). 
     The time frequency processing module  220   a  calculates a lower limit value of the time setting range according to the system parameters of the bridge crane system  1000 . Please refer to the following equation (1). 
     
       
         
           
             
               
                 
                   
                     t 
                     
                       acc 
                       / 
                       dec 
                     
                   
                   ≥ 
                   
                     
                       
                         J 
                         sys 
                       
                       × 
                       
                         ω 
                         rate 
                       
                     
                     
                       2 
                       ⁢ 
                       
                         T 
                         rate 
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (1), t acc/dec  is the time setting range; ω rate  is the rated speed; T rate  is the rated torque; J sys  is the system inertia. Afterward, the time frequency processing module  220   a  calculates the natural swing period of a simple pendulum according to the rope length information L of the bridge crane  400 . Please refer to the following equation (2). 
     
       
         
           
             
               
                 
                   
                     T 
                     
                       s 
                       ⁢ 
                       w 
                       ⁢ 
                       i 
                       ⁢ 
                       n 
                       ⁢ 
                       g 
                     
                   
                   = 
                   
                     2 
                     ⁢ 
                     π 
                     ⁢ 
                     
                       
                         L 
                         g 
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (2), T swing  is the natural swing period; g is the acceleration of gravity; L is the rope length information. Afterward, the time frequency processing module  220   a  calculates an upper limit value of the time setting range according to the natural swing period. Please refer to the following equation (3). 
     
       
         
           
             
               
                 
                   
                     t 
                     
                       acc 
                       / 
                       dec 
                     
                   
                   ≤ 
                   
                     
                       0.9 
                       ⁢ 
                       
                         T 
                         swing 
                       
                     
                     2 
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (3), t acc/dec  is the time setting range; T swing  is the natural swing period. Therefore, the time setting range can be reasonably inferred by the combination of equations (1), (2), and (3). 
     In the step (S 13 ) shown in  FIG. 2 , the user may select the appropriate time setting values within the time setting range through the time frequency processing module  220   a , and the selected time setting values are used as the acceleration and deceleration time of the bridge crane system  1000 . Please refer to  FIG. 5A , the selected time setting values are used as the acceleration time T 1  and the deceleration time T 3 . In one preferred embodiment, the acceleration time T 1  and the deceleration time T 3  are the same, but the present disclosure is not limited thereto. 
     In the step (S 14 ) shown in  FIG. 2 , the time frequency processing module  220   a  divides the frequency change time T 0  into multiple time intervals (as shown in  FIG. 5A ) according to the time setting values selected in the step (S 12 ). The multiple time intervals include the acceleration time T 1 , the maintain time T 2 , and the deceleration time T 3 . In one embodiment, as shown in  FIG. 5A , the selected time setting values may be used as the acceleration time T 1  and the deceleration time T 3 , and the acceleration time T 1  and the deceleration time T 3  are the same. Therefore, the maintain time T 2  can be inferred based on the frequency change time T 0 , the acceleration time T 1 , and the deceleration time T 3 . In other words, multiple maintain times T 2  within the multiple time intervals can be acquired according to the frequency change time T 0  and the time setting values. The multiple maintain times T 2  are between the acceleration time T 1  and the deceleration time T 3 . In particular, in the present disclosure, the user selects the time setting values within the time setting range to set the acceleration time T 1  and the deceleration time T 3 . However, the user cannot operate the time of starting or stopping the bridge crane system  1000 . 
     In the step (S 15 ) shown in  FIG. 2 , the time frequency processing module  220   a  adjusts an operation frequency command to change between a low frequency (such as 0 Hz) and the specified high frequency f h  within multiple time intervals T 1 -T 3  so as to generate a frequency change curve f line  (as shown in  FIG. 5A ). In particular, the operation frequency command is a signal generated in the time frequency processing module  220   a  in advance, or a signal preset in the time frequency processing module  220   a.    
     In one embodiment, as shown in  FIG. 5A , in the acceleration time T 1 , the frequency change curve f line  linearly increases from the low frequency to the specified high frequency f h . In the maintain time T 2 , the frequency change curve f line  maintains at the specified high frequency f h . In fact, frequency change curve f line  oscillates within an error range of the specified high frequency f h . In the deceleration time T 3 , the frequency change curve f line  linearly decreases from the specified high frequency f h  to the low frequency, but the present disclosure is not limited thereto. In other words, the frequency change curve f line  linearly increases from the low frequency (such as 0 Hz) to the specified high frequency f h , maintains at the specified high frequency f h , and linearly decreases from the specified high frequency f h  to the low frequency. 
     As shown in  FIG. 3 , the anti-sway control unit  220  includes a swing angle estimation module  220   b  and a swing angle processing module  220   c . Please refer to  FIG. 2  and  FIG. 3 , in the step (S 16 ), the swing angle estimation module  220   b  and the swing angle processing module  220   c  calculate a frequency correction amount f cmp  according to the frequency change curve f line  and the preset rope length information L. The calculation method of the frequency correction amount f cmp  will be detailed below. 
     Please refer to  FIG. 2  (S 16 ),  FIG. 3 , and  FIG. 4A , the swing angle estimation module  220   b  firstly receives the frequency change curve f line  outputted from the time frequency processing module  220   a . The swing angle estimation module  220   b  calculates a frequency change amount of the operation frequency command within the frequency change time T 0  according to the frequency change curve f line . Please refer to  FIG. 5A , the frequency on the vertical axis represents the speed, and the acceleration (that is, the frequency change amount) may be acquired by differentiating the speed once (i.e., the frequency change amount). However, the calculation method of the frequency change amount of the present disclosure is not limited to the above-mentioned method. 
     Afterward, the swing angle estimation module  220   b  calculates a swing angle θ s  of the bridge crane  400  under the simple pendulum movement according to the rope length information L and the frequency change amount. Please refer to the following equation (4). 
     
       
         
           
             
               
                 
                   
                     θ 
                     s 
                   
                   = 
                   
                     
                       1 
                       
                         
                           s 
                           2 
                         
                         + 
                         
                           G 
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           L 
                         
                       
                     
                     × 
                     
                       
                         Δ 
                         ⁢ 
                         f 
                       
                       L 
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (4), θ s  is the swing angle; s is a Laplace operator; G is a gravitational acceleration constant; L is the rope length information; Δf is the frequency change amount. Afterward, the swing angle estimation module  220   b  calculates a swing speed ω s  of the bridge crane  400  under the simple pendulum movement according to the swing angle θ s . In some embodiments, the swing angle estimation module  220   b  differentiates the swing angle θ s  to acquire the swing speed ω s  of the bridge crane  400  under the simple pendulum movement. The swing angle estimation module  220   b  provides the swing angle θ s  and the swing speed ω s  to the swing angle processing module  220   c.    
     Please refer to  FIG. 2  (S 15 ),  FIG. 3 , and  FIG. 4B , the swing angle processing module  220   c  includes a first control parameter C and a second control parameter γ. The swing angle processing module  220   c  firstly calculates a control variable X 1  according to the swing angle θ s , the swing speed ω s , and the first control parameter C. Please refer to the following equation (5). 
     
       
         
           
             
               
                 
                   
                     X 
                     ⁢ 
                     1 
                   
                   = 
                   
                     
                       C 
                       ⁢ 
                       
                         θ 
                         s 
                       
                     
                     + 
                     
                       ω 
                       s 
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     Afterward, the swing angle processing module  220   c  multiplies the control variable X 1  with the second control parameter γ to calculate a rotation speed correction amount ω cmp . Please refer to the following equation (6). 
     
       
         
           
             
               
                 
                   
                     ω 
                     cmp 
                   
                   = 
                   
                     γ 
                     × 
                     X 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     After the swing angle processing module  220   c  calculates the rotation speed correction amount ω cmp , the frequency correction amount f cmp  can be calculated according to the following equation (7). 
     
       
         
           
             
               
                 
                   
                     f 
                     cmp 
                   
                   = 
                   
                     
                       
                         ω 
                         
                           cmp 
                           × 
                         
                       
                       ⁢ 
                       P 
                     
                     
                       1 
                       ⁢ 
                       2 
                       ⁢ 
                       0 
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     The following will continue to introduce an embodiment of the present disclosure for designing the first control parameter C and the second control parameter γ. In general, the bridge crane system  1000  may be simplified into a second-order control system, as the following equation (8). 
     
       
         
           
             
               
                 
                   
                     
                       θ 
                       s 
                     
                     
                       f 
                       * 
                     
                   
                   = 
                   
                     
                       s 
                       
                         
                           L 
                           ⁡ 
                           
                             ( 
                             
                               γ 
                               + 
                               1 
                             
                             ) 
                           
                         
                         
                           
                             s 
                             2 
                           
                           + 
                           
                             
                               
                                 L 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 C 
                               
                               
                                 L 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     γ 
                                     + 
                                     1 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             s 
                           
                           + 
                           
                             g 
                             
                               L 
                               ⁡ 
                               
                                 ( 
                                 
                                   γ 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           ω 
                           n 
                         
                         2 
                       
                       
                         
                           s 
                           2 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             ζω 
                             n 
                           
                           ⁢ 
                           s 
                         
                         + 
                         
                           
                             ω 
                             2 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (8), L is the rope length information; θ s  is the swing angle; f* is a frequency command; ζ is a damping coefficient; ω n  is a bandwidth. In particular, the frequency command (f*) is the equation (8) is the frequency change curve f line  in  FIG. 5A . Afterward, the equation (8) is transformed into a standard second-order equation to derive the equation (9) and the equation (10) as follows. 
     
       
         
           
             
               
                 
                   
                     2 
                     ⁢ 
                     
                       ζω 
                       n 
                     
                   
                   = 
                   
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       C 
                     
                     
                       L 
                       ⁡ 
                       
                         ( 
                         
                           γ 
                           + 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       ω 
                       n 
                     
                     2 
                   
                   = 
                   
                     G 
                     
                       L 
                       ⁡ 
                       
                         ( 
                         
                           γ 
                           + 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
           
         
       
     
     After adjusting the equation (9) and the equation (10), the first control parameter C and the second control parameter γ can be inferred, as shown in the following equation (11) and equation (12). 
     
       
         
           
             
               
                 
                   γ 
                   = 
                   
                     
                       
                         G 
                         
                           L 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               ω 
                               n 
                             
                             2 
                           
                         
                       
                       - 
                       1 
                     
                     &gt; 
                     0 
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     11 
                     ) 
                   
                 
               
             
             
               
                 
                   C 
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         ζ 
                         ⁢ 
                         
                           ω 
                           n 
                         
                         ⁢ 
                         G 
                       
                       
                         G 
                         - 
                         
                           
                             
                               ω 
                               n 
                             
                             2 
                           
                           ⁢ 
                           L 
                         
                       
                     
                     &gt; 
                     0 
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     12 
                     ) 
                   
                 
               
             
           
         
       
     
     According to the equation (11) and the equation (12), the first control parameter C and the second control parameter γ can be acquired by designing different damping coefficients ζ and bandwidths ω n . In one preferred embodiment, a range of the damping coefficient ζ is between 0.1 and 1 (ζ∈(0.1,1)), and the bandwidth ω n  is shown in the following equation (13). 
     
       
         
           
             
               
                 
                   
                     ω 
                     n 
                   
                   = 
                   
                     
                       n 
                       × 
                       
                         ω 
                         
                           s 
                           ⁢ 
                           w 
                           ⁢ 
                           i 
                           ⁢ 
                           n 
                           ⁢ 
                           g 
                         
                       
                     
                     = 
                     
                       n 
                       × 
                       
                         
                           G 
                           ⁢ 
                           
                             / 
                           
                           ⁢ 
                           L 
                         
                       
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     13 
                     ) 
                   
                 
               
             
           
         
       
     
     In the equation (13), ω swing  is a swing frequency of the bridge crane  400 ; n is a bandwidth ratio. In particular, the swing frequency ω swing  of the bridge crane  400  is derived by the natural swing period T swing  (such as the equation (2)) of the bridge crane  400 . 
     In the present disclosure, the damping coefficient ζ and the bandwidth ratio n are designed by users to adjust to meet the requirements of controlling the system. In particular, by designing different damping coefficients ζ, the anti-sway system rigidity can be adjusted, and by designing different bandwidth ratios n, the response speed (strength) can be adjusted. 
     As shown in  FIG. 6 , which shows a schematic curve of the response of different damping coefficients to a swing angle and a motor speed according to the present disclosure. In  FIG. 8 , when the damping coefficient ζ is smaller, the degree of suppression of the swing angle is smaller, and the maximum overshoot of the motor speed is larger. On the contrary, when the damping coefficient ζ is larger, the degree of suppression of the swing angle is larger, and the maximum overshoot of the motor speed is smaller. Therefore, when the motor decelerates, the larger the damping coefficient ζ, the less likely it is to reverse rotation. In general, the damping coefficient ζ may be set at a relatively intermediate value at the factory (ζ=0.707). However, the design of the damping coefficient ζ may be adjusted according to the user&#39;s operating habits and preferences. Since the effect of the damping coefficient ζ may be compared to the shock-absorbing effect of a vehicle, if the damping coefficient ζ is small, the amount of shaking will be more obvious. 
     As shown in  FIG. 7 , which shows a schematic curve of the response of different bandwidth ratios to the swing angle and the motor speed according to the present disclosure. In  FIG. 9 , when the bandwidth ratio n is larger, an anti-sway time (that is, the time from the start of deceleration to the speed reaching a steady state) is relatively small. On the contrary, when the bandwidth ratio n is smaller, the anti-sway time is relatively large. Under the principle of reasonable swing angle, the larger the bandwidth ratio n, the faster the speed of compensating the swing angle (zero), i.e., returning to the steady state faster), and the swing will be more severe. 
     By the combination of equations (2), (11), (12), and (13), the design method of the first control parameter C and the second control parameter γ has the following steps. According to the natural swing period T swing , the response frequency (referred to as the bandwidth ω n ) is calculated. According to the response frequency (i.e., the bandwidth ω n ), the damping coefficient ζ, and the rope length information L, the first control parameter C is calculated. According to the response frequency (i.e., the bandwidth ω n ) and the rope length information L, the second control parameter γ is calculated. In particular, the first control parameter C and the second control parameter γ may be preset in the swing angle processing module  220   c  after calculation by the user, but the present disclosure is not limited thereto. 
     Please refer to  FIG. 1 ,  FIG. 2  (S 17 ),  FIG. 3 , and  FIG. 5B , the inverter  200  superimposes the frequency change curve fine and the frequency correction amount f cmp  generated by the swing angle processing module  220   c  to generate an anti-sway frequency command f 1  to drive the at least one motor  300 . As shown in  FIG. 5B , since the frequency change curve fine and the frequency correction amount f cmp  are superimposed to generate the anti-sway frequency command f 1 , the anti-sway frequency command f 1  nonlinearly increases from a low frequency (for example, but not limited to 0 Hz) to a specified high frequency f h . After the anti-sway frequency command f 1  maintains at the specified high frequency f h  for a period of time, the anti-sway frequency command f 1  nonlinearly decreases from the specified high frequency f h  to the low frequency. 
     Please refer to  FIG. 8 , the bridge crane system  2000  includes an operation apparatus  100 , an inverter  200 A, at least one motor  300 , a bridge crane  400 , and a position sensor  500 . The inverter  200 A includes an anti-sway control unit  230 , a voltage/frequency (v/f) open-loop control unit  240 , and a drive unit  260 . Please refer to  FIG. 10 , the anti-sway control unit  230  includes a time frequency processing module  220   a , a frequency estimation module  231 , a swing angle estimation module  220   b , and a swing angle processing module  220   c . In the second embodiment, the position sensor  500  is used to detect/sense the motor  300 , and outputs a motor position signal Pm to the anti-sway control unit  230 . The anti-sway control unit  230  generates an anti-sway frequency command f 1  to the v/f open-loop control unit  240  according to the motor position signal Pm. Please refer to  FIG. 8 ,  FIG. 9 , and  FIG. 10  to explain the control method of the second embodiment of the present disclosure. 
     In the second embodiment, the time frequency processing module  220   a  performs the steps (S 21 ) to (S 25 ) to generate the frequency change curve fine (as shown in  FIG. 5A ). In particular, the operation method of steps (S 21 ) to (S 25 ) in  FIG. 9  is the same as that of steps (S 11 ) to (S 15 ) in  FIG. 2 , and the detail description is omitted here for conciseness. 
     Please refer to  FIG. 9  (S 26 ) and  FIG. 10 , the anti-sway control unit  230  acquires a rotation angle of the motor  300  according to the motor position signal Pm outputted from the position sensor  500 . 
     Please refer to  FIG. 9  (S 27 ) and  FIG. 10 , the anti-sway control unit  230  estimates the swing angle θ s  and the swing speed ω s  of the bridge crane  400  under the simple pendulum movement according to the rotation angle of the motor  300  so as to calculate the frequency correction amount f cmp . In this embodiment, the frequency estimation module  231  differentiates the rotation angle of the motor  300  to acquire the rotation speed of the motor  300 , and uses the rotation speed of the motor  300  as an electrical frequency command fdb. The frequency estimation module  231  outputs the electrical frequency command fdb to the swing angle estimation module  220   b.    
     Afterward, the swing angle estimation module  220   b  differentiates the electrical frequency command fdb once to acquire the frequency change amount (i.e., the acceleration) so as to estimate the swing angle θ s  and the swing speed ω s . The method of estimating the swing angle θ s  has been described in the previous paragraph, please refer to equation (4). The swing angle estimation module  220   b  differentiates the swing angle θ s  to acquire the swing speed ω s . Afterward, the swing angle estimation module  220   b  outputs the swing angle θ s  and the swing speed ω s  to the swing angle processing module  220   c . The swing angle processing module  220   c  calculates the frequency correction amount f cmp  according to the above-mentioned equations (5) to (13). 
     Please refer to  FIG. 9  (S 28 ) and  FIG. 10 , the inverter  200 A superimposes the frequency change curve fine and the frequency correction amount f cmp  generated by the swing angle processing module  220   c  to generate an anti-sway frequency command f 1  to drive the at least one motor  300 . In particular, the waveform of the anti-sway frequency command f 1  is shown in  FIG. 5B . 
     The anti-sway control structure of the present disclosure may also use a drive mode switch  235  to select the power unit applied to the motor with/without the position sensor to configure to the bridge crane structure, and to switch the drive mode according to the actual hardware configuration to provide the flexibility in use, as shown in  FIG. 11 . 
     In summary, the anti-sway control structure proposed in the present disclosure may be used for the bridge crane system having the motor without position sensor, such as an incremental encoder, an absolute encoder, or a Hall sensor, and swing angle sensor, such as an angle sensor, a gyroscope, an inclinometer, and an image recognizer. In addition, the anti-sway control structure proposed in the present invention does not require too many other bridge crane system parameters (for example, the equivalent radius of the rotation to line, and the number of motor rotors). The present disclosure only needs low-cost power unit configuration and v/f drive control mode to linearly move the anti-sway control structure, and can perform full-time anti-sway during operation, even if the inching movement command is executed, it also has the effect of the anti-sway control. Whether using the v/f control or the vector control (FOC) requiring rotor information, the full-time anti-sway performance can be achieved through the control method of the present disclosure. The present disclosure uses the motor input frequency as the input source of the swing angle estimation module  220   b  (or referred to as a swing angle estimator) under the v/f control so that the anti-sway control unit has the characteristics of stability and no additional filter design is required. 
     The swing angle estimation module  220   b  of the present disclosure can estimate the swing angle of the hanging object or the hook without relying on the weight of the long travel, the trolley, and the hanging object, and without the gear ratio of the reduction box and the wheel diameters of the long travel and the trolley. 
     Although the present disclosure has been described with reference to the preferred embodiment thereof, it will be understood that the present disclosure is not limited to the details thereof. Various substitutions and modifications have been suggested in the foregoing description, and others will occur to those of ordinary skill in the art. Therefore, all such substitutions and modifications are intended to be embraced within the scope of the present disclosure as defined in the appended claims.