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Using Singular Perturbation Method for Controlling a Crane System with a Flexible Cable and Large Swing Angle

Published on Jun 1, 2015in Journal of Low Frequency Noise Vibration and Active Control
路 DOI :10.1260/0263-0923.34.3.361
Mohammad H. Fatehi3
Estimated H-index: 3
(IAU: Islamic Azad University),
Mohammad Eghtesad17
Estimated H-index: 17
(Shiraz University),
Roya Amjadifard4
Estimated H-index: 4
(Kharazmi University)
Abstract
This paper aims to develop an advanced control system for an overhead crane with transverse vibrations of flexible cable while considering large angle of the cable swing. The control objective is to move the payload to a desired position and at the same time, to reduce the payload swing and to suppress the cable transverse vibrations only by applying a directional (horizontal) driving force to the trolley. The crane system with cable vibrations and large swing angle is categorized as a multi-degree under-actuated system whose characteristics impose serious challenges when applying control methods. One reasonable way to overcome the challenges is to separate the degrees of under actuation. To do so, singular perturbation approach is used to divide the dynamical system into a fast subsystem for cable vibrations (with flexible un-actuated coordinates) and a slow subsystem for trolley motion and cable swing (with one degree of under actuation). Based on two-time scale control method, a composite control syste...
  • References (55)
  • Citations (4)
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References55
Newest
#1Mohammad H. Fatehi (IAU: Islamic Azad University)H-Index: 3
#2Mohammad Eghtesad (Shiraz University)H-Index: 17
Last. Roya Amjadifard (Kharazmi University)H-Index: 4
view all 3 authors...
This paper deals with modelling and control of an overhead crane with a flexible cable. The developed dynamical model includes both transverse vibrations of the flexible cable and large swing angles of cable while the trolley is moving horizontally. To carry out the modelling, Rayleigh-Ritz discretization method is used to achieve an ordinary differential equation (ODE) model for transverse deflection of the cable with finite generalized degrees of freedom. Using the Euler鈥揕agrange formulation, ...
3 CitationsSource
#1Ning Sun (NKU: Nankai University)H-Index: 22
#2Yongchun Fang (NKU: Nankai University)H-Index: 33
SUMMARY In this paper, a trajectory planning approach is proposed for underactuated overhead cranes. Different from existing trajectory planning methods, the presented approach generates trajectory commands online without the necessity of iterative optimization, which is convenient for practical implementation. We demonstrate the performance of the proposed method, including swing elimination and precise trolley positioning, with rigorous Lyapunov-based mathematical analysis. Both numerical simu...
45 CitationsSource
#1Yang Liu (Aberd.: University of Aberdeen)H-Index: 15
#2Hongnian Yu (BU: Bournemouth University)H-Index: 24
An underactuated mechanical system (UMS) is a system which has fewer independent control actuators than degrees of freedom to be controlled. Control of UMS is considered as one of the most active fields of research because of its diverse engineering applications. This survey reviews UMS from its history to the state-of-the-art research on modelling, classification, control, and to some extent, provides some unique insights for bottleneck issues and future research directions.
103 CitationsSource
#1Wai Man Ng (UW: University of Waterloo)H-Index: 1
#2Dong Eui Chang (UW: University of Waterloo)H-Index: 16
Last. George Labahn (UW: University of Waterloo)H-Index: 28
view all 3 authors...
We study the stabilizability, via the method of energy shaping, of a given Lagrangian system with two degrees of underactuation and with n\geq4degrees of freedom. By making use of the formal theory of PDEs, we derive an involutive system of PDEs which governs energy shapability, and thus deduce, for the first time, easily verifiable conditions under which energy shaping is guaranteed. We illustrate our results with an example of a three-cart-one-inverted pendulum system.
9 CitationsSource
SUMMARY A Lyapunov direct method is presented for a class of second-order systems that includes mechanical systems. This method shall be called a pseudo-energy shaping method because it reduces to the energy shaping method when a given second-order system is a mechanical system. The pseudo-energy shaping method comprehends both the Lyapunov direct method for mechanical systems proposed by Aguilar-Ibanez and the controlled Lagrangian method that has been successfully applied to stabilize mechanic...
5 CitationsSource
#1Ning Sun (NKU: Nankai University)H-Index: 22
#2Yongchun Fang (NKU: Nankai University)H-Index: 33
In this paper, we present a novel end-effector (payload) motion-based control development approach for the regulation of underactuated overhead cranes, which is efficient even in the presence of external disturbance and system parameter variations/uncertainties. The control system is elegantly constructed so that the problem of simultaneously regulating the trolley motion and suppressing the payload swing is successfully addressed by stabilizing a newly defined payload motion signal. Specificall...
125 CitationsSource
#1Ning Sun (NKU: Nankai University)H-Index: 22
#2Yongchun Fang (NKU: Nankai University)H-Index: 33
Last. Bojun MaH-Index: 6
view all 4 authors...
Motivated by the desire to achieve smooth trolley transportation and small payload swing, a kinematic coupling-based off-line trajectory planning method is proposed for 2-D overhead cranes. Specifically, to damp out unexpected payload swing, an antiswing mechanism is first introduced into an S-shape reference trajectory based on rigorous analysis for the coupling behavior between the payload and the trolley. After that, the combined trajectory is further tuned through a novel iterative learning ...
122 CitationsSource
#1Yongchun Fang (NKU: Nankai University)H-Index: 33
#2Bojun Ma (NKU: Nankai University)H-Index: 6
Last. Xuebo Zhang (NKU: Nankai University)H-Index: 18
view all 4 authors...
This brief proposes a motion planning-based adaptive control strategy for an underactuated overhead crane system. To improve the transportation efficiency and enhance the safety of the crane system, the trolley is required to reach the desired position fast enough, while the swing of the payload needs to be within an acceptable domain. To achieve these objectives, a novel two-step design strategy consisting of a motion planning stage and an adaptive tracking control design stage, is proposed to ...
140 CitationsSource
#1A. Yesildirek (AUS: American University of Sharjah)H-Index: 12
For a class of underactuated systems, a switching Lyapunov functions based nonlinear controller is given. Underactuated configuration space is split in to two subsets. Two simplified controllers with local guaranteed performances are derived. A direct controller is designed on actuated configuration space while another feedback controller is utilized indirectly to act on the unactuated configuration space. A switching algorithm between those controllers is based on maximum projection strategy. D...
2 CitationsSource
May 1, 2011 in ICRA (International Conference on Robotics and Automation)
#1Ning Sun (NKU: Nankai University)H-Index: 4
#2Yongchun Fang (NKU: Nankai University)H-Index: 33
Last. Yinghai Yuan (NKU: Nankai University)H-Index: 2
view all 4 authors...
Inspired by the desire to achieve fast payload transportation as well as sufficient swing suppression, a novel phase plane based motion planning method is proposed for underactuated overhead cranes. Specifically, the variation law of the underactuated system states in the phase plane is firstly derived via mathematical analysis for the phase portraits. Based on this, an analytical three-segment acceleration trajectory (namely, a trapezoid velocity trajectory) with the coupling behavior being tak...
26 CitationsSource
Cited By4
Newest
#1Huasen Liu (THU: Tsinghua University)
#2Wenming Cheng (Southwest Jiaotong University)H-Index: 1
Last. Yinqi Li (Southwest Jiaotong University)
view all 3 authors...
An overhead crane with a flexible cable is an underactuated system; the vibration of the crane鈥檚 beam and the residual swinging of the payloads cause fatigue in the crane and affect the precise positioning of the payloads. In this paper, the coupling system of an overhead crane was simplified to that of a moving mass with pendulum swing passing beam model. The differential equation motion of a coupled overhead crane system was derived based on the Lagrange equation. Mathematical solution was car...
Source
#1Mohammad H. Fatehi (IAU: Islamic Azad University)H-Index: 3
#2Mohammad Eghtesad (Shiraz University)H-Index: 17
Last. Ali A. Fatehi (IAU: Islamic Azad University)H-Index: 1
view all 4 authors...
A flexible-cable overhead crane system having large swing is studied as a multi-degree underactuated system. To resolve the system dynamics complexities, a second order singular perturbation (SP) f...
2 CitationsSource
#1Canchang Liu (SDUT: Shandong University of Technology)H-Index: 4
#2Chicheng Ma (SDUT: Shandong University of Technology)H-Index: 1
Last. Changcheng Zhou (SDUT: Shandong University of Technology)H-Index: 1
view all 4 authors...
Source
This paper considers the problem of position control and active vibration damping of a planar, array (or grid) of masses and springs, by a single actuator, attached to one corner of the array, which is required to translate and rotate the entire system from rest to rest, through target linear and angular displacements, simultaneously. An obvious challenge is that the system has many degrees of freedom, with many undamped vibration modes, and is clearly highly under-actuated. The control techniqu...
Source