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起重机外文翻译
桥式起重机外文译文
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桥式起重机控制系统
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外文翻译-自适应耦合控制桥式起重机系统,起重机外文翻译,桥式起重机外文译文,桥式起重机外文翻译,桥式起重机控制系统
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Adaptive coupling control for overhead crane systems Yang Jung Hua *, Yang Kuang Shine Department of Vehicle Engineering, National Pingtung University of Science and Technology, Neipu, Pingtung, Taiwan Received 18 January 2006; accepted 4 August 2006 Abstract Due to the requirements of high positioning accuracy, small swing angle, short transportation time, and high safety, both motion and stabilization control for an overhead crane system becomes an interesting issue in the fi eld of control technology development. Since the overhead crane system is subject to underactuation with respect to the load sway dynamics, it is very hard to manipulate the crane system in a desired manner, namely, gantry position tracking and sway angle stabilization. Hence, in this paper, a nonlinear control scheme incorporating parameter adaptive mechanism is devised to ensure the overall closed-loop system stability. By applying the designed con- troller, the position error will be driven to zero while the sway angle is rapidly damped to achieve swing stabilization. Stability proof of the overall system is given in terms of Lyapunov concept. To demonstrate the eff ectiveness of the proposed controller, results for both computer simulation and experiments are also shown. ? 2006 Elsevier Ltd. All rights reserved. Keywords: Nonlinear adaptive control; Non-minimum phase; Lyapunov stability; Motion control 1. Introduction For low cost, easy assembly and less maintenance, over- head crane systems have been widely used for material transportation in many industrial applications. Due to the requirements of high positioning accuracy, small swing angle, short transportation time, and high safety, both motion and stabilization control for an overhead crane sys- tem becomes an interesting issue in the fi eld of control tech- nology development. Since the overhead crane system is underactuated with respect to the sway motion, it is very diffi cult to operate an overhead traveling crane automati- cally in a desired manner. In general, human drivers, often assistedbyautomaticanti-swaysystem,arealways involved in the operation of overhead crane systems, and the resulting performance, in terms of swiftness and safety, heavily depends on their experience and capability. For this reason, a growing interest is arising about the design of automatic control systems for overhead cranes. However, severely nonlinear dynamic properties as well as lack of actual control input for the sway motion might bring about undesired signifi cant sway oscillations, especially at take- off and arrival phases. In addition, these undesirable phenomena would also make the conventional control strategies fail to achieve the goal. Hence, the overhead crane systems belong to the category of incomplete control system, which only allow a limited number of inputs to control more outputs. In such case, the uncontrollable oscillations might cause severe stability and safety prob- lems, and would strongly constrain the operation effi ciency as well as the application domain. Furthermore, an over- head crane system may experience a range of parameter variations under diff erent loading condition. Therefore, a robust and delicate controller, which is able to diminish these unfavorable sway and uncertainties, needs to be developed not only to enhance both effi ciency and safety, but to make the system more applicable to other engineer- ing scopes. In 1 a nonlinear controller is proposed for the trolley crane systems using Lyapunov method and a modifi ed ver- sion of sliding-surface control is then utilized to achieve 0957-4158/$ - see front matter ? 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2006.08.004 * Corresponding author. Tel.: +886 8 7703202; fax: +886 8 7740398. E-mail address: jhyang.tw (J.H. Yang). Mechatronics 17 (2007) 143152 cart position control. However, the sway angle dynamics has not been considered for stability analysis. In 2, a sim- ple proportional derivative (PD) controller is designed to asymptotically regulate the overhead crane system to the desired position with natural damping of sway oscillation. A fuzzy logic control system with sliding mode Control concept is developed for an overhead crane system 3. Fang et al. 4 develop a nonlinear coupling control law to stabilize a 3-DOF overhead crane system by using LaS- alle invariance theorem. However, the system parameters must be known in advance. In 5, Burg et al. regulate the crane system by using the variable transformation method. The authors in 6 use an adaptive feedback linearization method to stabilize a class of mechanical systems. In 7, the passivity property of mechanical system is utilized to regulate the overhead crane system. Ishide et al. 8 train a fuzzy neural network control architecture for an over- head traveling crane by using back-propagation method. However, the trolley speed is still large even when the des- tination is arrived, which would result in signifi cant resid- ual swing motion, low safety, and poor positioning accuracy. In the paper 9, a nonlinear tracking controller for the load position and velocity is designed with two loops: an outer loop for position tracking, and an inner loop for stabilizing the internally oscillatory dynamics using a singular perturbation design. But the result is avail- able only when the sway angle dynamics is much faster than the cart motion dynamics. The authors in 10 propose an output feedback PD controller that stabilizes a nonlin- ear crane system. Liu et al. 11 propose an adaptive sliding mode control method with fuzzy tuning of slope of sliding surface for a 2-dimension overhead crane. The paper 12 discusses the comparison of a fuzzy logic control system with respect in to the Linear Quadratic Gaussian control (LQG) for an overhead crane. In this paper 13 a new fuzzy controller for anti-swing and position control of an overhead traveling crane is proposed based on the Single Input Rule Modules (SIRMs) dynamically connected fuzzy inference model. Computer simulation results show that by using the fuzzy controller, the crane can be smoothly dri- ven to the destination in short time with swing angle and almost no overshoot. In the paper 14 a simple control scheme, based on second-order sliding modes, which guar- antees a fi rst precise load transfer and swing suppression during the load movement is propose, despite of model uncertainties and unmodeled dynamic actuators. The paper 15 in the controller design, in which combines a feedback linearization approach and a time delay control scheme. The time delay control is applied to complete the feedback linearization for a nonlinear system under the infl uence of uncertainly. This paper is organized as follows: Section 2 describes the nonlinear mathematical model of an overhead crane. Then an adaptive control scheme is presented which guar- antees both tracking and stabilization of the crane system. In Section 3, the proposed controllers are applied and com- pared with respect to conventional sliding mode technique by simulation studies so that the validity of the proposed control strategies could be confi rmed. Experiments are also performed to verify the eff ectiveness of the designed con- troller in Section 4. Finally, some conclusions are given in Section 5. 2. Problem formulation and nonlinear controller design In this section, a nonlinear control scheme incorporating adaptive law is presented for the crane system with all parameters being unknown. For convenience, we fi rst assume that the dynamic model have the following characteristics: (A1) The payload and the gantry are connected by a mass- less, rigid cable. (A2) The angular position and velocity of the payload and the rectilinear position and velocity of the gantry are measurable. (A3) The hinged joint that connects the payload link to the gantry is frictionless. 2.1. Problem formulation Based on Lagrangian formulation, the dynamic equa- tions of an overhead crane system, as shown in Fig. 1, can be expressed by Mq q Cq; _ q_ q Kq Q1 where qT xh? Mq mc mlmllcosh mllcoshmll2 ? M11M12 M21M22 ? Cq; _ q 0?mllsinh_h 00 “# C11C12 C21C22 ? Nomenclature xposition displacement of the crane hswing angle of the payload mcthe mass of the cart mlthe mass of the payload lthe cable length gthe gravity term uthe driving force for the cart k1, k2, k3, k4the controller gain ka, kbthe adaptive gain 144J.H. Yang, K.S. Yang / Mechatronics 17 (2007) 143152 Kq 0 mlglsinh ? Q u 0 ? The above model corresponds to the model used for the in- verted pendulum on the cart, by replacing h ! h + p. As well known to the researchers, the inertia matrix M(q) is always symmetric and positive-defi nite. Besides, another well-known property is that _ Mq ? 2Cq; _ q 0mllsinh_h ?mllsinh_h0 “# 2 which is skew-symmetric. To proceed with the controller design, we fi rst defi ne the following error surfaces: s _ e x k1ex _ eh k2eh ? sx sh ? 3 where k1, k2are some designated positive constants. e ex eh ? x?xd h?hd ? 4 Remark 1. The desired trajectories xdand hdshould be carefully chosen so as to satisfy the internal dynamics as shown in the lower part of Eq. (1). Without loss of generality, we always choose an asymptotically convergent trajectory with fi nal constant value for xd, and zero for hd. Based on the above defi nitions, the dynamics of the newly defi ned signals sx, shcan be derived as M11M12 M21M22 ? _ sx _ sh ? C11C12 C21C22 ? sx sh ? k30 0k4 ? sx sh ? sm u k3sx sa k4sh ? 5 where sm M11? xd k1_ ex M12k2_ eh C11?_ xd k1ex C12k2eh6 sa M21? xd k1_ ex M22k2_ eh C21?_ xd k1ex C22k2eh7 2.2. Nonlinear adaptive control law In this subsection, an adaptive nonlinear control scheme is presented to account for the parameter uncertainty. The controller structure is depicted in Fig. 2. The dynamic equations of an overhead crane system can be verifi ed to possess the well-known linear-in-parameter property. Firstly,thefollowingso-calledlinear-in-parameter property is defi ned: x1/1 M11? xd k1_ ex M12k2_ eh C11?_ xd k1ex C12k2eh8 x2/2 M21? xd k1_ ex M22k2_ eh C21?_ xd k1ex C22k2eh9 where x1, x2are regressor vectors, and /1, /2are the vec- tors of unknown constant parameters which will be esti- mated in the controller design. It can be easily verifi ed that x1, x2and /1, /2satisfy the following equalities: x1? xd k1ex ?k2 _ e hcosh k2ehsinh_h ? x2 ? xd k1_ excoshk2_ eh? /T 1 mc mlmll? /T 2 mllmll2 ? 10 Fig. 1. Two degree of freedom overhead crane system. Plant u d x - + . . . . . , x x Adaptive controller , xx, xx, Fig. 2. A self-tuning controller block diagram. J.H. Yang, K.S. Yang / Mechatronics 17 (2007) 143152145 To facilitate the controller design, let us defi ne the follow- ing signal: _ Zxt 2 ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Zxt p axt bxt ?; Zxt 0 2bxt;Zxt 0;bxt 0 dx;Zxt 0;bxt 6 0 8 : 11 where dxis some small positive constant and axt s2 x s2 x e shx2/2 k4s2 h 12 bxt ?e s2 x e shx2/2 k4s2 h 13 where /1and /2are respectively the estimates for /1and /2, and e is a very small positive constant. It can be shown that, by defi ning k ffi ffi ffi ffi ffi Zx p , the following equation holds: _ k 1 k ks2 x e s2 x e ? ?shx2/2? k4s2 h; k 6 014 Remark 2. Note that (11) is simply to defi ne a diff erential equation of which its variable Zx(t) remains positive always. k(t) in (14) is defi ned to be its positive root. In the subsequent stability analysis, we will assume that there exists a measure zero set of time sequences tif g1 i1such that Zx(ti) = 0 or k(ti) = 0, i = 1,2,3,.,1. Now, let the adaptive control scheme be designed as u ?x1/1? sf? k3sx15 sf k ? 1sx s2 x e ?shx2/2? k4s2 h 16 where x1/1 b M11k1_ ex b M12k2_ ehbC11k1exbC12k2eh17 x2/2 b M21k1_ ex b M22k2_ ehbC21k1exbC22k2eh18 Then the error dynamics can be obtained as M11M12 M21M22 ? _ sx _ sh ? C11C12 C21C22 ? sx sh ? k30 0k4 ? sx sh ? ?x1/1? sf x2/2 k4sh “# 19 or more compactly as Mq_ s Cq; _ qs Kvs ?x1/1? sf x2/2 k4sh “# 20 with the parameter error being defi ned as /1 /2 “# /1? /1 /2? /2 “# 21 In addition, we choose the adaptation laws as follows: _ /1 ?kax1sx _ /2 ?kbx2sh 22 where kaand kb are some positive-defi nite gain matrices. In the following we will show that the error dynamics (20) along with the adaptive algorithms (22) is asymptotically stable as shown in the following theorem. Theorem. Consider the overhead crane dynamic model described by (1). If the control law proposed in (15) and (16) and the adaptive laws (22) are applied, then the objec- tives of tracking and stabilization for the dynamic system can be achieved, i.e., all signals in the closed-loop system (20) are bounded and, further, e ! 0 asymptotically as t ! 1 in the sense of Lyapunov. Proof. Let the Lyapunov function candidate be defi ned as V t 1 2 sTMx;hs 1 2 /T 1k ?1 a /1 1 2 /T 2k ?1 b /2 1 2 Zx 1 2 sTMx;hs 1 2 /T 1k ?1 a /1 1 2 /T 2k ?1 b /2 1 2 k223 By taking the time derivative of V and substituting (15) and (16) into (1), we can get _ V t sTMx;h_ s 1 2 sT_Mx;hs _ /T 1k ?1 a /1 _ /T 2k ?1 b /2k_k sT?Cx; _ x;h;_hs?Kvs ?x1/?sf x2/2k4sh “# ! 1 2s T_ Mx;hssxx1/1shx2/2 ks2 xe s2 xe ?shx2/2?k4s2 h ?sTKvs? k ?1s2 x s2 xe ?shx2/2?k4s2 h ? shx2/2shx2/2k4s2 h ks2 xe s2 xe ?shx2/2?k4s2 h ?sTKvs;when k 6 024 in which (14) and (22) are applied and the skew-symmetric property of _ M ? 2C is used. It is clear from (24) that _ V t 1 2kf where kmin(Kv) denotes the minimum eigen- value of Kv.h 5. Conclusion In this paper, an adaptive nonlinear coupling control law has been presented for the motion control of overhead crane. By utilizing a Lyapunov-based stability analysis, we can achieve asymptotic tracking of the crane position and stabilization of payload sway angle of an overhead crane system which is subject to both underactuation and para- metric uncertainties. Computer simulations are performed to validate the proposed control algorithm. To practically facilitate the proposed adaptive schemes, an overhead crane system is built up and experiments are also con- ducted. Both simulations and experiments show better per- formance in comparison with the conventional PD control and sliding controller, which, in turn, verifi es the eff ective- ness of our propose schemes. References 1 Barmeshwar Vikramaditya, Rajesh Rajamani. Nonlinear control of a trolley crane system. In: Proceedings of the American control conference, Chicago, IL. 2000. p. 10326. 2 Fang Y, Zergeroglu E, Dixon WE, Dawson DM. Nonlinear coupling control laws for an overhead crane system. In: Proceedings of the IEEE international conference on control applications, Mexico. 2001. p. 63944. 3 Liu D, Yi J, Zhoa D. Fuzzy tuning sliding mode control of transporting for an overhead crane. In: Proceedings of the 2nd international conference on machine learning and cybernetics, Xian, China. 2003. p. 25416. 4 Fang Y, Dixon WE, Dawson DM, Zergeroglu E. Nonlinear coupling control laws for a 3-DOF overhead crane system. In: Proceedings of the IEEE international conference on decision and control, Orlando, FL, USA. 2001. 5 Burg T, Dawson D, Rahn C, Rhodes W. Nonlinear control for an overhead crane via the saturating control approach of teel. In: Proceedings of the IEEE international conference on robotics and automation, Minnesota, USA. 1996. 6 dAndrea-Novel B, Boustany F. Adaptive control for a class of mechanical systems using linearization and Lyapunov methods. A comparative study on the overhead crane exampl
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