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1、起重机中英文对照外文翻译文献 中英文对照外文翻译 (文档含英文原文和中文翻译) Control of Tower Cranes With Double-Pendulum Payload Dynamics Abstract：The usefulness of cranes is limited because the payload is supported by an overhead suspension cable that allows oscilation to occur during crane motion. Under certain conditions, the paylo
2、ad dynamics may introduce an additional oscillatory mode that creates a double pendulum. This paper presents an analysis of this effect on tower cranes. This paper also reviews a command generation technique to suppress the oscillatory dynamics with robustness to frequency changes. Experimental resu
3、lts are presented to verify that the proposed method can improve the ability of crane operators to drive a double-pendulum tower crane. The performance improvements occurred during both local and teleoperated control. Key words：Crane , input shaping , tower crane oscillation , vibration I. INTRODUCT
4、ION The study of crane dynamics and advanced control methods has received significant attention. Cranes can roughly be divided into three categories based upon their primary dynamic properties and the coordinate system that most naturally describes the location of the suspension cable connection poi
5、nt. The first category, bridge cranes, operate in Cartesian space, as shown in Fig. 1(a). The trolley moves along a bridge, whose motion is perpendicular to that of the trolley. Bridge cranes that can travel on a mobile base are often called gantry cranes. Bridge cranes are common in factories, ware
6、houses, and shipyards. The second major category of cranes is boom cranes, such as the one sketched in Fig. 1(b). Boom cranes are best described in spherical coordinates, where a boom rotates about axes both perpendicular and parallel to the ground. In Fig. 1(b), y is the rotation about the vertical
7、, Z-axis, and q is the rotation about the horizontal, Y -axis. The payload is supported from a suspension cable at the end of the boom. Boom cranes are often placed on a mobile base that allows them to change their workspace. The third major category of cranes is tower cranes, like the one sketched
8、in Fig. 1(c). These are most naturally described by cylindrical coordinates. A horizontal jib arm rotates around a vertical tower. The payload is supported by a cable from the trolley, which moves radially along the jib arm. Tower cranes are commonly used in the construction of multistory buildings
9、and have the advantage of having a small footprint-to-workspace ratio. Primary disadvantages of tower and boom cranes, from a control design viewpoint, are the nonlinear dynamics due to the rotational nature of the cranes, in addition to the less intuitive natural coordinate systems. A common charac
10、teristic among all cranes is that the pay- load is supported via an overhead suspension cable. While this provides the hoisting functionality of the crane, it also presents several challenges, the primary of which is payload oscillation. Motion of the crane will often lead to large payload oscillati
11、ons. These payload oscillations have many detrimental effects including degrading payload positioning accuracy, increasing task completion time, and decreasing safety. A large research effort has been directed at reducing oscillations. An overview of these efforts in crane control, concentrating mai
12、nly on feedback methods, is provided in 1. Some researchers have proposed smooth commands to reduce excitation of system flexible modes 25. Crane control methods based on command shaping are reviewed in 6. Many researchers have focused on feedback methods, which necessitate the addition necessitate
13、the addition of sensors to the crane and can prove difficult to use in conjunction with human operators. For example, some quayside cranes have been equipped with sophisticated feedback control systems to dampen payload sway. However, the motions induced by the computer control annoyed some of the h
14、uman operators. As a result, the human operators disabled the feedback controllers. Given that the vast majority of cranes are driven by human operators and will never be equipped with computer-based feedback, feedback methods are not considered in this paper. Input shaping 7, 8 is one control metho
15、d that dramatically reduces payload oscillation by intelligently shaping the commands generated by human operators 9, 10. Using rough estimates of system natural frequencies and damping ratios, a series of impulses, called the input shaper, is designed. The convolution of the input shaper and the or
16、iginal command is then used to drive the system. This process is demonstrated with atwo-impulse input shaper and a step command in Fig. 2. Note that the rise time of the command is increased by the duration of the input shaper. This small increase in the rise time is normally on the order of 0.51 pe
17、riods of the dominant vibration mode. Fig. 1. Sketches of (a) bridge crane, (b) boom crane, (c) and tower crane. Fig. 2. Input-shaping process. Input shaping has been successfully implemented on many vibratory systems including bridge 1113, tower 1416, and boom 17, 18 cranes, coordinate measurement
18、machines1921, robotic arms 8, 22, 23, demining robots 24, and micro-milling machines 25. Most input-shaping techniques are based upon linear system theory. However, some research efforts have examined the extension of input shaping to nonlinear systems 26, 14. Input shapers that are effective despit
19、e system nonlinearities have been developed. These include input shapers for nonlinear actuator dynamics, friction, and dynamic nonlinearities 14, 2731. One method of dealing with nonlinearities is the use of adaptive or learning input shapers 3234. Despite these efforts, the simplest and most commo
20、n way to address system nonlinearities is to utilize a robust input shaper 35. An input shaper that is more robust to changes in system parameters will generally be more robust to system nonlinearities that manifest themselves as changes in the linearized frequencies. In addition to designing robust
21、 shapers, input shapers can also be designed to suppress multiple modes of vibration 3638. In Section II, the mobile tower crane used during experimental tests for this paper is presented. In Section III, planar and 3-D models of a tower crane are examined to highlight important dynamic effects. Sec
22、tion IV presents a method to design multimode input shapers with specified levels of robustness. InSection V, these methods are implemented on a tower crane with double-pendulum payload dynamics. Finally, in Section VI, the effect of the robust shapers on human operator performance is presented for
23、both local and teleoperated control. II. MOBILE TOWER CRANE The mobile tower crane, shown in Fig. 3, has teleoperation capabilities that allow it to be operated in real-time from anywhere in the world via the Internet 15. The tower portion of the crane, shown in Fig. 3(a), is approximately 2 m tall
24、with a 1 m jib arm. It is actuated by Siemens synchronous, AC servomotors. The jib is capable of 340 rotation about the tower. The trolley moves radially along the jib via a lead screw, and a hoisting motor controls the suspension cable length. Motor encoders are used for PD feedback control of trol
25、ley motion in the slewing and radial directions. A Siemens digital camera is mounted to the trolley and records the swing deflection of the hook at a sampling rate of 50 Hz 15. The measurement resolution of the camera depends on the suspension cable length. For the cable lengths used in this researc
26、h, the resolution is approximately 0.08. This is equivalent to a 1.4 mm hook displacement at a cable length of 1 m. In this work, the camera is not used for feedback control of the payload oscillation. The experimental results presented in this paper utilize encoder data to describe jib and trolley
27、position and camera data to measure the deflection angles of the hook. Base mobility is provided by DC motors with omnidirectional wheels attached to each support leg, as shown in Fig. 3(b). The base is under PD control using two HiBot SH2-based microcontrollers, with feedback from motor-shaft-mount
28、ed encoders. The mobile base was kept stationary during all experiments presented in this paper. Therefore, the mobile tower crane operated as a standard tower crane. Table I summarizes the performance characteristics of the tower crane. It should be noted that most of these limits are enforced via
29、software and are not the physical limitations of the system. These limitations are enforced to more closely match the operational parameters of full-sized tower cranes. Fig. 3. Mobile, portable tower crane, (a) mobile tower crane, (b) mobile crane base. TABLE I MOBILE TOWER CRANE PERFORMANCE LIMITS
30、Fig. 4 Sketch of tower crane with a double-pendulum dynamics. III. TOWER CRANE MODEL Fig.4 shows a sketch of a tower crane with a double-pendulum payload configuration. The jib rotates by an angle q around the vertical axis Z parallel to the tower column. The trolley moves radially along the jib; it
31、s position along the jib is described by r. The suspension cable length from the trolley to the hook is represented by an inflexible, massless cable of variable length l1. The payload is connected to the hook via an inflexible, massless cable of length l2. Both the hook and the payload are represent
32、ed as point masses having masses mh and mp , respectively. The angles describing the position of the hook are shown in Fig. 5(a). The angle frepresents a deflection in the radial direction, along the jib. The angle c represents a tangential deflection, perpendicular to the jib. In Fig. 5(a), f is in
33、 the plane of the page, and c lies in a plane out of the page. The angles describing the payload position are shown in Fig. 5(b). Notice that these angles are defined relative to a line from the trolley to the hook. If there is no deflection of the hook, then the angle g describes radial deflections
34、, along the jib, and the angle a represents deflections perpendicular to the jib, in the tangential direction. The equations of motion for this model were derived using a commercial dynamics package, but they are too complex to show in their entirety here, as they are each over a page in length. To
35、give some insight into the double-pendulum model, the position of the hook and payload within the Newtonian frame XYZ are written as qhand qp, respectively Where I , Jand Kare unit vectors in the X , Y , and Z directions. The Lagrangian may then be written as -Fig. 5. (a) Angles describing hook moti
36、on. (b) Angles describing payload motion. Fig. 6. Experimental and simulated responses of radial motion. (a) Hook responses (f) for l1=0.48m，(b) Hook responses for l1=1.28m The motion of the trolley can be represented in terms of the system inputs. The position of the trolley qtr in the Newtonian fr
37、ame is described by This position, or its derivatives, can be used as the input to any number of models of a spherical double-pendulum. More detailed discussion of the dynamics of spherical double pendulums can be found in 3942. The addition of the second mass and resulting double-pendulum dramatica
38、lly increases the complexity of the equations of motion beyond the more commonly used single-pendulum tower model 1, 16, 4346. This fact can been seen in the Lagrangian. In (3), the terms in the square brackets represent those that remain for the single-pendulum model; no qp terms appear. This signi
39、ficantly reduces the complexity of the equations because qp is a function of the inputs and all four angles shown in Fig. 5. It should be reiterated that such a complex dynamic model is not used to design the input-shaping controllers presented in later sections. The model was developed as a vehicle
40、 to evaluate the proposed control method over a variety of operating conditions and demonstrate its effectiveness. The controller is designed using a much simpler, planar model. A. Experimental Verification of the Model The full, nonlinear equations of motion were experimentally verified using sever
41、al test cases. Fig.6 shows two cases involving only radial motion. The trolley was driven at maximum velocity for a distance of 0.30 m, with l2=0.45m .The payload mass mp for both cases was 0.15 kg and the hook mass mhwas approximately 0.105 kg. The two cases shown in Fig. 6 present extremes of susp
42、ension cable lengths l1 . In Fig. 6(a), l1 is 0.48 m , close to the minimum length that can be measured by the overhead camera. At this length, the double-pendulum effect is immediately noticeable. One can see that the experimental and simulated responses closely match. In Fig. 6(b), l1 is 1.28 m, t
43、he maximum length possible while keeping the payload from hitting the ground. At this length, the second mode of oscillation has much less effect on the response. The model closely matches the experimental response for this case as well. The responses for a linearized, planar model, which will be de
44、veloped in Section III-B, are also shown in Fig. 6. The responses from this planar model closely match both the experimental results and the responses of the full, nonlinear model for both suspension cable lengths. Fig. 7. Hook responses to 20jib rotation: (a) f (radial) response;(b) c (tangential)
45、response. Fig. 8. Hook responses to 90jib rotation: (a) f (radial) response;(b) c (tangential) response. If the trolley position is held constant and the jib is rotated, then the rotational and centripetal accelerations cause oscillation in both the radial and tangential directions. This can be seen
46、 in the simulation responses from the full nonlinear model in Figs. 7 and 8. In Fig. 7, the trolley is held at a fixed position of r = 0.75 m, while the jib is rotated 20. This relatively small rotation only slightly excites oscillation in the radial direction, as shown in Fig. 7(a). The vibratory d
47、ynamics are dominated by oscillations in the tangential direction, c , as shown in Fig. 7(b). If, however, a large angular displacement of the jib occurs, then significant oscillation will occur in both the radial and tangential directions, as shown in Fig. 8. In this case, the trolley was fixed at
48、r = 0.75 m and the jib was rotated 90. Figs. 7 and 8 show that the experimental responses closely match those predicted by the model for these rotational motions. Part of the deviation in Fig. 8(b) can be attributed to the unevenness of the floor on which the crane sits. After the 90jib rotation the hook and payload oscillate about a slightly different equilibrium point, as measured by the overhead camera. Fig.9.Planardouble-pendulummodel. B. Dynamic
