7 Development of Feedforward Anti-Sway Control for Highly efficient and Safety Crane Operation Noriaki Miyata* Tetsuji Ukita* Masaki Nishioka* Tadaaki Monzen* Takashi Toyohara* Container handling at harbor is conducted using container cranes and rail-mounted gantry cranes (RMGCs). To attain high handling efficiency, an automatic crane operation system needs to adopt a load anti-sway control. On the other hand, safe handling operation not colliding a load with stacked containers in the yard is required. To this point, we applied a method to preliminarily calculate the crane motions that avoid collision with stacked containers and that can prevent load swaying, in the form of a feedforward pattern. We developed a control method combining the feedforward control with a feedback control using an optimum regulator, and combined the control method with the automatic operation system. The automatic operation system was tested on a crane, and the effectiveness was proved.. Introduction Physical distribution using containers has recently been increasing, and the container-handling at harbor is becoming more important than ever. Along with this trend, the requests for automatization of handling machines have been increasing. We have conducted the development work for the control system of handling machines such as container cranes and rail-mounted gantry cranes (RMGCs). In particular, RMGCs which conduct the work of stacking containers in a yard is requested to perform precision positioning of containers for assuring automatic operation of the system. To do this, it is necessary to accurately move the crane to the target position, and to establish control to promptly diminish the sway of the load induced by the crane movement (anti-sway control). The conventional positioning control and anti-sway control of the crane are performed by a state feedback control using an optimizing regulator. When, however, the crane becomes large and the rope length increases, the conventional method induces a problem of extending the time for positioning the crane and of reducing the handling efficiency. As a solution to this problem, we have developed a method of preliminarily determining a speed pattern that can shorten the crane travel time, thus controlling the crane by using the determined speed pattern as a feedforward pattern. As for RMGC, the avoidance of collision with stacked containers in the yard is an important function from the safety point of view. Since the developed method is able to preliminarily calculate the trajectory of the load, the function of setting the load trajectory to avoid collision is readily performed. This paper describes the developed control method for anti-swaying and positioning a load, and also the function for setting the load trajectory.. Brief description of the automated crane First, the crane automatic operation system targeting RMGC is described. An RMGC which is used at a container yard has the appearance given in Fig.. For example, the receiving operation of that type of crane is conducted by a combination of lifting motions and trolley travel, including hoisting of the load on the chassis lane, travel of the trolley from the chassis lane to the target position, and lowering the load to the target position followed by landing the load. For carrying out these movements by the automatic operation system, the following-described functions are required. () The trolley must be moved accurately to a target position in the yard. At that moment, the sway of the Stacked container height detector Girder Trolley 6.7 m Load displacement meter Spreader Container 7. m Fig. General view of RMGC Chassis lane Machine room Gantry travel unit Chassis * Hiroshima Machinery Works * Hiroshima Research & Development Center, Technical Headquarters Technical Review Vol.8 No. (Jun. )
74 load induced from the trolley movement must be promptly reduced to assure accurate landing of the load. () During the transfer of the load, the load must not collide with stacked containers in the yard. To attain function (), we applied a state feedback control using an optimizing regulator to configure the control system which performs the positioning of the trolley and the anti-swaying of the load at the same time (). Positioning of a container in the yard is requested to have an accuracy of better than ±5 mm. We confirmed that the control system gives satisfactory positioning accuracy through a commercial crane operation. When the rope length is large, however, the handling efficiency is not always satisfactory owing to the prolonged time for positioning of the crane. In this regard, we have developed a method which preliminarily determines a crane speed pattern that can set the transfer time of the crane, and which controls the crane using the thus determined crane speed pattern as a feedforward pattern. A simple means to attain function () is to firstly hoist the load sufficiently high above the stacked containers to complete the hoisting, and to conduct trolley travel to complete the travel, then to lower the load. Although that type of operation is safe in view of collision prevention, the operation time becomes long so that the operation is not satisfactory from the point of handling efficiency. Consequently, it is necessary to conduct the lifting operation of the load and the travel of the trolley simultaneously with full safety assurance. If a method to preliminarily feedforward the crane operation pattern to controller were used, the trajectory of the load could be calculated in advance. Therefore, we developed a method for setting the load trajectory using the preliminarily calculated load trajectory and the information about the height of stacked containers separately observed, to increase the handling efficiency within a range assuring safety.. Anti-sway function and load trajectory setting function For the anti-sway control for automatic operation of the crane, a control method using an optimum regulator is described first, and the calculation method for the trolley speed pattern as a feedforward pattern is given next. Then, the method for setting the load trajectory to avoid collision with obstacles is described.. Anti-sway control using an optimization regu- lator A crane is simulated by the model given in Fig.. To configure the control system, the equations of motion relating to the trolley and the load are solved. From the Lagrange equations of motion based on the kinetic en- ergy and the potential energy of the system, equations () and () are derived. For the thus derived equations of motion of the load system and the trolley system, the relative displacement of the load from the trolley is expressed by d = l, and the state equation is expressed by, then the speed control of the trolley driving system using u as the speed reference is considered to derive the state equation (). When the trolley position X is defined as a relative displacement to the target position, the trolley travel to the target position and the stop of swaying the load can be attained by transferring the state variable to zero using the state feedback control using an optimum regulator. To do this, a cost function J [equation (4)] using weighting matrix of Q and R is introduced. On the basis of the LQ control theory, the optimum control rule to minimize the cost function J is determined by equation (5) applying P as a solution of the Riccati equation. By applying the control rule, it is possible for all final state values to be brought to zero, that is the trolley is stopped at the target position without swaying.. Method to calculate the anti-swaying speed pat- tern There is a known pattern of trolley travel speed, in a particular trapezoidal speed pattern that gives zero load sway after completing the acceleration and deceleration, under the condition of fixed trolley acceleration and of making the acceleration time and the deceleration time the same as the sway period (). In this case, the load sway is assumed to be zero. f M l X M: Trolley weight m : Load weight l : Rope length X : Trolley displacement m d : Load displacement : Sway angle d f : Driving force Fig. Dynamics of single pendulum Technical Review Vol.8 No. (Jun. )
75 Although that type of operation is effective, an increase in the rope length increases the time necessary for acceleration/deceleration of the trolley. To this point, we investigated on a speed patterns which conduct the acceleration/deceleration of trolley within a specified time and which can stop load sway. Since the rope length l is a variable in the equation of motion () of the rope system, equation (6) is combined with equation () to derive equation (7). A base rope length l is introduced, and a trapezoidal speed pattern that accelerates the trolley at a fixed acceleration is assumed. In that case, since the base rope length l is a fixed value, equation (7) can be rewritten as equation (8). Equation (8) is rewritten by the equation (9) to determine. where, The equations indicate that, by setting the base rope length l to a fixed value and by setting the acceleration time of the trolley to a single cycle of sway of the base rope length l, the sway after completion of the trolley acceleration returns to zero. Regarding the actual rope length l, the control of the trolley acceleration is designed to make the sway equal to equation (8). In that case, since the right side of equation (7) is equal to the right side of equation (8), equation () is derived, further equation () is derived. When operating the crane, the height of stacked containers is detected by a sensor. Consequently, the lift necessary to avoid collisions with obstacles can be predicted. As a result, variations in the rope length l with time are known in advance. When an adequate base rope length l and an acceleration are given, and when the sway angle determined by equation (9) is substituted into equation (), the trolley acceleration during the single sway period of the base rope length l can be determined. When trolley acceleration is integrated on the basis of an initial value zero, the acceleration portion in the trolley speed pattern is obtained. After completing the acceleration, the trolley is traveled at a fixed speed as in the case of the trapezoidal speed pat- tern. Also for the case of deceleration of the trolley, the speed pattern of the deceleration portion is determined by the method described above. If the trolley is traveled conforming to the thus obtained speed patterns, it is possible to accelerate/ decelerate the trolley within a sway period of the base rope length l and also to stop all swaying of the load even with a relatively long rope length. In the calculation of the trolley speed pattern, when equation (9) and the rope length l are applied, the sway displacement pattern of the load during the trolley travel can also be calculated in advance. Disturbances such as an initial sway can be suppressed by applying the state feedback control described in the preceding section using the detected value of sway displacement on a sway detection sensor and using the deviation from the sway displacement pattern which was calculated in advance.. Method for setting the load trajectory The displacement of the trolley is determined by integrating the trolley speed which was determined by the method described in the preceding section. The load displacement in the travel direction is determined from the sum of the trolley displacement and the load displacement. The load displacement in the lifting direction is determined from the rope length l. The thus obtained coordinates of the load are drawn using the travel direction in the horizontal axis and the lifting direction in the vertical axis to obtain the load trajectory, which is shown in Fig.. We have investigated a method to set the load trajectory to one that satisfies both the set safety and handling efficiency standards using the information of the height of stacked containers, whose height is observed separately using height sensor. From the point of handling efficiency, the lifting and trolley travel are preferably conducted simultaneously. Fig. 4 shows an example of the handling operation. The handling period is shortened by beginning travel immediately after starting the hoisting operation. When the load trajectory preliminarily calculated is compared with the information of the height of stacked containers, the expectation of collision and the shortage in hoisting Target position Load travel trajectory Fig. Trajectory of load Original position Technical Review Vol.8 No. (Jun. )
76 Lifting speed, trolley speed (m/s) Lifting speed, trolley speed (m/s) Lifting position - - 5 5 5 5 4 - - Shortage of lifting Fig. 4 Trajectory setting of load (a) Conventional method Travel trajectory after correction Starting point of trolley travel after correction Starting point of trolley travel before correction Travel trajectory before correction : Lifting speed : Trolley speed : Sway : Lifting speed : Trolley speed : Sway 5 5 5 5 4 (b) Proposed method Fig. 5 Test result of anti-sway control height, if a collision is expected, can be determined. In actual handling operation, a collision-free trajectory is selected by delaying the time for beginning the trolley travel. The safe trajectory is assured by shifting the height for beginning trolley travel by calculated the amount of the shortage in lifting. During actual operation of a crane, an emergency stop may occur due to some facility failure. Upon an emergency stop, the load may sway greatly. It is important to avoid collisions with stacked containers even in such an emergency. In this regard, the calculation of the load trajectory is carried out to assure high safety, taking into account the sway of the load under an emergency stop operation. - - - - Sway (m) Sway (m) 4. System configuration The crane automatic operation system is comprised of: () A driving system including a drive panel and a PLC, (trolley travel, gantry travel, lift); () A sensor system; and () A control unit provided with control software, (micro-computer). The driving system conducts the operations of lifting, trolley traveling, and gantry traveling. The PLC in the driving system is provided with software which conducts mainly manual operations by the operator. The sensor system includes a sensor to detect the information of a height of stacked containers, and a sway sensor to detect the sway of the load. The control micro-computer has the control software necessary for automatic operation including a control to stop the swaying of the load, which is described above, the computation of the anti-sway speed pattern, and operation to avoid a collision with stacked containers. 5. Test results The control method described in the paper was applied to a test crane, and the effectiveness of the proposed method was proved. First, the results of application of the anti-sway control is shown in Fig. 5. 5 Fig. 5(a) is the result of anti-sway tests using only the conventional optimizing regulator. On the other hand, Fig. 5(b) is the result of anti-sway tests using the developed feedforward pattern. The difference between the two methods appears significantly during the trolley deceleration, showing a shortening of the operation period in the developed method compared with the conventional method. Next, the test results on the load trajectory setting function is given in Fig. 6. 6 This figure indicates the trajectory of the central position of the bottom of a container which moves from right to left. The figure shows that the load moves along a safe trajectory avoiding collision with stacked containers. These results proved that the load trajectory setting function by the application of the feedforward pattern functions effectively and that the method is effective at shortening the handling period. 6. Conclusion This paper introduces the crane automatic operation system focusing on the anti-sway and positioning control technology and the function for setting load trajectory. The applied method is the one that calculates the trolley travel pattern to stop load swaying, in advance, and that the calculated pattern is com- Technical Review Vol.8 No. (Jun. )
77 Displacement (m) 8 7 6 5 Stacked container Load travel trajectory 4 Lifting speed Load displacement - Trolley - speed 5 5 5 5 5 5 Trolley travel position (m) (a) Load travel trajectory (b) Operating pattern Fig. 6 Load travel trajectory (test result) Lifting speed, trolley speed (m/s).5.75.5 -.5 -.75 -.5 -.75 Load displacement (m) bined with the feedback control. Furthermore, the paper describes the method for setting trajectories for avoiding collisions between the load and the stacked containers. The proposed method assures safe and efficient operation owing to the detection of the information of the height of obstacles existing in the range of the crane travel. Thus the method should be applicable also to overhead traveling cranes and bucket type unloaders. References () Murata, I. et al., Anti-Sway Control of the Container Crane, Transactions of the Robotics and Mechatronics Conference 9 of the Japan Society of Mechanical Engineering p. () Mita, T., Optimal Control of the Crane System Using the Maximum Speed of the Trolley, Journal of The Society of Instrument and Control Engineers Vol.5 No.6 (979) pp.8-88 Technical Review Vol.8 No. (Jun. )