Proceedings of the American Control Conference Chicago, Illinois June 2000
An Anti-Swing Control of a 3-Dimensional Overhead Crane Sung-Kun Cho' and Ho-Hoon Lee2 Continuous Casting Project Team RISTl P.O.BOX 135 Pohang(Korea) Tel: +82 0562 279 6512 Fax: +82 0562 279 6488 Email:
[email protected] Department of Mechanical Engineering, Univ. of Suwon2 Abstract In this paper, new anti-swing control law is proposed for a 3-dimensional(3-D) overhead crane. The overall controller consists of position servo controller and fuzzy logic controller. The position servo controller is designed via the loop shaping method based on the experimental crane velocity servo system. The fuzzy logic controller is used to suppress the load swing and the effects of the varying dynamics of the load swing as a function of the rope length. This control method guarantees not only fast damping of the load swing but also zero steady state position error for the 3-D motion of the crane. The proposed control law is evaluated by the 3-D overhead crane. Finally, the effectiveness of the proposed control method is shown by experimental results.
1. Introduction Overhead cranes are essential facilities in steel, harbor industry etc. But as heavy loads are transported by using wire rope, load swing could happen. Such a load swing degrades work efficiency and also, in the worst case, causes damage of the load and safety accidents. Many people have studied to solve aforementioned problems [I,2, 3, 4, 51. The control methods of overhead cranes are classified as open loop control [l]and closed loop control [2, 3 , 4 , 51. The former is the method which use the optimal velocity profile calculated using the dynamics of load swing. So this method does not measure the load swing. But if there are uncertainties in the dynamics of load swing, disturbance, initial load swing, and/or collision, this control method does not guarantee good control performance. On the contrary, the latter method computes controller input using the angle of load swing, crane velocity, and crane position. So if control logic is designed appropriately, the fast damping of the angle of load swing and accurate position control of a crane could be obtained. In general, even if there are many 3-D cranes in industry which have simultaneous motion of girder(X-axis), trolley(Y-axis), and vertical motion of load(2-axis), researches for control of cranes have been studied almost for 1 or 2-D cranes [l,2, 3, 4,51. In this paper, we presented controller design procedure for a 3-D overhead crane and also showed the ex-
0-7803-5519-9/00 $10.00 0 2000 AACC
cellence of control performance through experiments of a prototype overhead crane. As the 1st step, the position servo control systems for X-axis, Y-axis, and Zaxis motion are designed using a new dynamic model of the crane which is derived in [ 5 ] . For this purpose, we derived the velocity servo systems for X-axis, Y-axis, and Z-axis motion by an experimental method. And then, position servo control systems are implemented by PI(Proportiona1-Integral) controller using the loop shaping method [6]based on the above velocity servo systems. Also fuzzy logic controller is used t o suppress the angle of load swing. In case of 3-axis simultaneous motion of 3-D crane, when the rope length changes, the dynamics of load swing also changes. It means that as the rope length varies, the location of roots of the overall closed loop transfer function also varies. Therefore, if swing angle controller is designed by conventional methods(P1D etc), the gain of swing angle controller must be appropriately recalculated as a function of the rope length to maintain the optimal damping of the angle of load swing. If swing angle controller is designed as the fuzzy logic controller proposed in this paper, above gain computation problem disappears. The detailed paper structure is as follows. In Section 2, a new 2-degree of freedom(D0F) angle of load swing is defined. And then a 3-D nonlinear dynamic model of the crane is derived. In Section 3, an overall feedback controller which is comprised of position servo controller and fuzzy logic controller is designed. In Section 4, the effectiveness of the proposed control law is shown by experiments. Finally, Section 5 draws conclusions
2. Modeling of a 3-D overhead crane 2.1. Definition of 2-DOF angle of load swing In Fig. 1, X, Y, 2 is a fixed coordinate system and X M ,Y M 2~ , is a trolley coordinate. The trolley is moving on the XY-plane and (x, y, 0) in the fixed coordinate corresponds t o the origin of the trolley coordinate. 0 is a 2-D angle of load swing and could be divided by 0, and OY. So the load position in the fixed coordinate system is given by as below.
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xm = x+lsin0,cos0,
+ lsine,
ym
= y
z,
= -lsin6,cosi9,
(1)
where 1 is the rope length. As the position of trolley and load is function of ( E , y , 1, e,, e,), this generalized coordinate is used to describe the motion of the 3-D overhead crane.
Y directions, respectively; g and m represent the gravitational acceleration and the mass of load. And D, and D, denote the viscous damping coefficients of the crane in the X and Y directions, respectively; f, and fy are the external forces to the crane in the each direction. Also D1 is the damping coefficient for the time rate of change of rope length, and f i is the force from the vertical motion motor to load in the downward direction. The derived dynamic equations of the crane are highly nonlinear and severely coupled. Therefore, appropriate linearization and decoupling are necessary for controller design. Actually, while cranes are operated, the angle of load swing is possibly depressed for load protection and safety. So almost all cranes used in industry are designed to satisfy the following inequality [5].
1x1
