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 payload 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 results 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. INTRODUCTION
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 point. 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, warehouses, 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), ? is the rotation about the vertical, Z-axis, and ? 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 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 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 characteristic 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 oscillations. 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 mainly on feedback methods, is provided in [1]. Some researchers have proposed smooth commands to reduce excitation of system flexible modes [2]–[5]. Crane control methods based on command shaping are reviewed in [6].
Many researchers have focused on feedback methods, which necessitate the addition necessitate 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 human 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 method 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 original 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 0.5–1 periods 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 [11]–[13], tower [14]–[16], and boom [17], [18] cranes, coordinate measurement machines[19]–[21], 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 despite system nonlinearities have been developed. These include input shapers for nonlinear actuator dynamics, friction, and dynamic nonlinearities [14], [27]–[31]. One method of dealing with nonlinearities is the use of adaptive or learning input shapers [32]–[34].
Despite these efforts, the simplest and most common 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 shapers, input shapers can also be designed to suppress multiple modes of vibration [36]–[38].
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. Section 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 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 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 trolley 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 research, 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 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-mounted 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 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
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 ? around the vertical axis Z parallel
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