Fuzzy Based Twin Controllers for Overhead Crane with Flexible Wire

Fuzzy Based Twin Controllers for Overhead Crane Cheng-Yuan Chang Department of Electronic Engineering Ching Yun University Jungli, Taoyuan 320, Taiwan, R.O.C.

Abstract This paper presents fuzzy based twin controllers for overhead crane. Instead of analyzing the complex nonlinear crane system, the proposed approach uses simple but effective way to control the crane. Twin fuzzy controller deals with the feedback information, the position of trolley crane and the swing angle of load, to suppress the sway and accelerate the speed when the crane transports the heavy load. This approach simplifies the designing procedure of crane controller; besides, the twin controller method reduces the rule number when fulfilling the fuzzy system. At last, experimental results through the crane model demonstrate the effectiveness of the scheme.

Keywords: fuzzy, overhead crane, feedback, swing angle, heavy load, twin controller

1. Introduction illustrate the effectiveness. This study presents a practical solution for the The overhead crane system is widely used in anti-swing and precise position control for the industry for moving heavy cargos. Thus anti-sway cranes. The position of trolley, swing angle of load and position control have become the requirements and their differentiations are applied to derive the as a core technology for automated crane system that proper control input of the trolley crane. Two fuzzy are capable of flexible spatial automatic conveyance. logic controllers (FLC) are used to deal separately The purpose of crane control is to reduce the with the feedback signals, swing angle and trolley swing of the load while moving the trolley to the position and their differentiations. The fuzzy rules desired position as fast as possible. However, the are designed according to the experience of crane overhead crane has serious problems; the crane workers. The main merit of this separated approach acceleration, required for motion, always induces is to greatly reduce the computational complexity of undesirable load swing. Such swing of load usually the crane control system. The total fuzzy rule number degrades work efficiency and sometimes causes load for fulfilling the control system is therefore less than damages and even safety accidents. Thus, the need the rule number of conventional fuzzy system. for faster cargo handling requires the precise control Besides, when designing the proposed fuzzy of crane motion so that its dynamic performance is controller, there is no mathematical model of the improved [4],[8],[11]. crane system needs to be taken into consideration in Various attempts have been made to solve the advance. Thus, the proposed algorithm is very easy problem of swing of load. Most of them focus the to be implemented. control on suppression of load swing without This paper is organized as follows. Section II considering the position error in crane motion [10]. reviews the proposed fuzzy twin controller structure Besides, several authors have considered for crane control system. In section III, several optimization techniques to control the cranes. They experimental results of crane control system are have used minimal time control technique to presented in comparison with the conventional crane minimize the load swing [2],[6],[14]. Since the swing control method to illustrate the merits of proposed of load depends on the moving and acceleration of fuzzy approach. This paper concludes with a the trolley, minimizing the cycle time and summary in section IV. minimizing the load swing are partially conflicting requirements. Besides, there are many papers investigate the stability problem of controller design 2. Fuzzy Logic Controllers for Crane [1],[5],[12], but those researches lack experiments to The physical apparatus of the overhead crane system is pictured in Fig. 1. The length of overhead  respective membership functions of e , , e , and crane model is five meters, and the height is two p e p  meters. The block diagram, which is represented in  , which obtained from the trolley position and Fig. 2, illustrates the proposed fuzzy logic crane e control system. In this diagram, two encoders with swing angle encoders. The ranges of input variables the resolution 2000 PPR (Pulses Per Round) are  e  ep and e p are [-d/8, d/8] and [-300, 300],  and installed on the trolley of crane to detect the motion e position and swing angle. The feedback signals from are [-45, 45] and [-50, 50], respectively, and the overhead crane act as the input variables of fuzzy ranges of the output variable up and u are [-5, 5]. controllers. The basic idea of fuzzy logic controller is The linguistic terms of output variables u and u shown in Fig. 3 [7],[15]. p  There are two similar fuzzy logic controllers, are defined as five fuzzy singletons, which are position controller and swing controller, deal represented in Fig. 4(e), controlling the servo driver separately with the motion position and swing angle of DC-motor to drive the trolley crane. information to drive the trolley crane. The twin fuzzy Step2: This step introduces the fuzzification controllers are like the conventional PD-type function for each input variable to express the associated measurement uncertainty. Generally controllers. In the design, the error ep and its  speaking, the purpose of the fuzzification function f derivative error e p are selected as the inputs is to interpret measurement of input variables, each linguistic variables of fuzzy position controller, expressed by a real number, as more realistic fuzzy where: approximations of the respective number. A likely definition of many researchers to fuzzify any real ep=Goal d-Trolley position (1)  number p is given in Fig. 5(a), where  is a (2) e p  ep (k  1)  ep (k) parameter that has to be determined of each The initial trolley position is set to be zero in particular application. However, the proposed paper this paper. The index k means the kth sample time. applies fuzzy singleton function, such as given in Besides, the input linguistic variables of fuzzy swing Fig. 5(b), in the fuzzification process. It means that the measurements for input variables are employed controller are selected as the swing angle e and its  in fuzzy inference engine directly.  derivative e , where: Step3: In order to fulfill the fuzzy logic control  system, each the position and swing controller e  swing angle of load (3) consists twenty-five IF-THEN rules with the  following form: e e (k 1) e (k) (4)        (6) If e  A and e*  B then u  C The load swing left is defined as positive swing * * and swing right is negative swing. After the where A, B and C are fuzzy numbers chosen from the procedures of fuzzy fuzzification, inference process set of fuzzy numbers that represent the linguistic and defuzzification, one denotes the output linguistic states NL, NS, AZ, PS and PL, the notation “*” in variables of the respective fuzzy position and swing Eq.(6) means p or  . The IF part of the fuzzy rules ' ' are formed by the error and its derivative, and the controllers as u and u . The actual power to drive p  consequents are decided according to the crane the trolley is defined as u. workers' experience and judgment. Since that each ' ' u  u p  u (5) input variable has five linguistic variables, the total number of possible nonconflicting fuzzy rules for The designing procedures for both the fuzzy both position and swing controllers is 2*52=50. The based position and swing angle controllers, are rule bases are shown in Table 1 and Table 2. These described in the following steps [13]. fuzzy rules can be understood very easily. Step1: This step fuzzifies the input signals into Step4: The designer has to select suitable fuzzy variables. The input and output space are inference and defuzzification methods for designing partitioned into five fuzzy regions overlapping each fuzzy controller. The inference and defuzzification other. In general, each fuzzy region is labeled by a procedures convert the conclusions obtained from linguistic term. These linguistic terms for the input fuzzy rules to a single real number. The resulting real variables of the twin controllers are given as NL, NS, number, in some sense, summarizes the elastic AZ, PS, and PL. One uses the triangular and constraint imposed on possible values of the output trapezoidal membership functions to fuzzify the variable by the fuzzy set. input linguistic variables. Figs. 4(a)-(d) show the For each input singleton pair ( e and  ), one defuzzification, each fuzzy controller gets a control * e* value. The authors use the summation of the control ' ' calculates the degree of their compatibility  j ( e , * values, u p and u , to drive the trolley. The fuzzy  ) with the antecedent of each inference rule j. controllers will control the trolley until the existing e* distance to goal is less than 0.01*d, meanwhile, the When  ( e ,  )>0, the jth rule is fired. At least one j * e* swing angle of load is less than 10 units. The rule fires for all possible input pair in the fuzzy notation d is the initial distance to the goal. For using controller design. The min-min-max inference 2000 PPR encoders, a unit of swing equals to method is used to conclude all the fired rules in this 360/2000 degrees. paper. Fig. 6 depicts the fuzzy inference procedures Several experiments illustrate the enhancement with two rules fired. of fuzzy scheme. One uses the conventional method In order to obtain the defuzzified real value, to control the crane to be a contrast. When operating one utilizes the most frequently used centroid the crane according to the speed reference curve such method to defuzzify the inference results. The as shown in Fig. 7, the friction and limitation of outputs of the fuzzy position and swing controllers mechanism will make the trolley precisely stop at the fixed position become impossible, hence additional u' ' are p and u , respectively. backing the trolley to the goal is necessary. One The proposed twin controller structure provides applies the flexible wire with 50cm long in the first an easy but effective way to control the fuzzy system experiment. The load for transportation is 0.5kg. The well. The twin controllers in this paper separate the distance to goal is 40000 normalized units, i.e. d input antecedents of fuzzy rules into two parts, =40000. Suppose that position of trolley is 0 position and swing angle parts. Hence, both position normalized unit at the start, Fig. 9(a) shows the and swing controllers have only M/2 fuzzy position of trolley and swing angle of load when antecedents, each containing N linguistic terms, then transporting the heavy load by conventional control the necessary rule number to fulfill the system is method. One can easily find that the swing is too 2*NM/2. The rule number is greatly reduced. For severe to damage the load. Fig. 9(b) shows the result example, both the position and swing fuzzy of fuzzy based approach. It is obvious that the trolley controllers have two input linguistic variables. The stops at the correct position and the swing is four input linguistic variables are partitioned into negligible, and meanwhile the transporting time of five parts each; hence the necessary rule number to load is shortened. The steady state error is caused by control the crane is reduced to 50. When compared some airstreams. with traditional fuzzy schemes, the separated twin The load in the first experiment is very light. It controllers method helps to make fuzzy control is one of the reasons why the swing of conventional easier than usual. Besides, the proposed twin method in Fig. 9(a) is very severe. Hence, one controllers structure is suitable for any use of fuzzy transports 3kg load in the second experiment. The control applications. length of flexible wire to tie the load is still 50cm. The Figs. 10(a) and 10(b) show the results. The load 3. Experimental Results swing of conventional method is about 8 degrees. There are several experimental results illustrate However, the swing angle of load with fuzzy control the enhancements of fuzzy based crane control is almost zero. Besides, the fuzzy based approach system. Traditionally, the crane operator drives the provides better performance to stop the trolley at the trolley with the steps of accelerated motion, uniform goal. motion, decelerated motion, creeped motion and The third experiment uses 100cm long flexible breaking. The Fig. 7 shows the distance-speed wire to tie the 3kg load. Figs. 11(a) and 11(b) show reference curve of conventional operation of the results of conventional and fuzzy based methods overhead crane [3],[9]. The experienced crane respectively. When transporting the load with longer workers drive the trolley carefully to keep the load flexible wire, it is more difficult to restrain the sway from severe swing. However, the conservative especially by conventional approach. However, Fig. control method is ineffective in modern industry. 11(b) shows that the load sway by fuzzy approach is This study proposed the fuzzy twin controllers to still very smooth. control the trolley crane. The last experiment applies 150cm flexible The control strategy is shown in Fig. 8. wire to tie the 3kg load. For the length of wire is very Encoders' data make us know the real position of long, the sway of load by conventional method trolley and swing angle of load at any time. After the becomes severe. Fig. 12(a) illustrates this condition. procedures of fuzzification, fuzzy inference and The sway is about 15 degrees. When transporting the load by fuzzy controllers, the result is shown in Fig. [7] G. J. Klir and B. Yuan, \QTR{it}{Fuzzy sets and 12(b). The performances for fixing the crane on fixed fuzzy logic, theroy and applications}, Prentice position and restraining the sway of load are better Hall, New Jersey, 1995. than conventional scheme. [8] F. L. Lewis, W. K. Tim, L. Z. Wang, and Z. X. Li, Through the illustrations of these experiments, ''Deadzone compensation in motion control it is easily to find that the fuzzy based approach systems using adaptive fuzzy logic control,'' IEEE provides rapid and smooth transportation of load. Trans. Contr. Syst. Technol., vol. 7, no. 6, pp. When the length of flexible wire is increased, the 731-742, Nov. 1999. proposed control algorithm still provides an excellent [9] C. Li and C. Y. Lee, ''Fuzzy motion control of an performance to control the overhead crane well. auto-warehousing crane system,'' IEEE Trans. Ind. Electron., vol. 48, no. 5, pp. 983-994, Oct. 2001. 4. Conclusions [10]Y. C. Liang and K. K. 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Virkkunen, ''Optimal path planning for a trolley crane: fast and smooth transfer of load,'' IEE Proc.-Contr. Theory Appl., vol. 142, no. 1, Jan. 1995. [4] Y. Izuno, T. Izumi, H. Yasutsune, E. Hiraki and M. Nakaoka, ''Speed tracking servo control system incorporating traveling-wave-type Fig. 1: The physical apparatus of the overhead crane ultrasonic motor and feasible evaluations,'' IEEE system Trans. Ind. Applicat., vol. 34, no. 1, pp. 126-132, Jan./Feb. 1998. [5] P. Ji and H. Wu, ''Algebraic solution to forward kinematics of a 3-DOF spherical parallel manipulator,'' J. Robotic Systems, vol. 18, no. 5, pp. 251-257, Jan. 2001. [6] M. A. Karkoub and M. Zribi, ''Modelling and energy based nonlinear control of crane lifters,'' IEE Proc.-Contr. Theory Appl., vol. 149, no. 3, May 2002. Fig. 2: The block diagram of fuzzy logic crane control system

(c) Fig. 3: Basic idea of fuzzy logic controller

(d) (a)

(e)  Fig. 4: (Continued) (c) e (d) (e)u p and u  e 

 Fig. 4: Membership functions, (a) e (b) p e p

(a) Fig. 5: Fuzzification of number p, (a) general case Fig. 8: Flowchart of fuzzy crane control system

Fig. 5: (Continued) (b)fuzzy singleton

Fig. 6: Example of fuzzy min-min-max inference method

Fig. 7: Distance-speed reference curve for Fig. 9: Transporting the 0.5kg load with 50cm conventional operation of overhead crane flexible wire by:(a) conventional method, (b) fuzzy based twin controllers method

Fig. 10: Transporting the 3kg load with 50cm flexible wire by: (a) conventional method, (b) (a) Fig. 10: (Continued), (b) fuzzy based twin controllers method

(b) Fig. 12: Transporting the 3kg load with 150cm flexible wire by: (a) conventional method, (b) fuzzy based twin controllers method (a)

Table. 1: The rule map of fuzzy position controller

Fig. 11: Transporting the 3kg load with 100cm flexible wire by: (a) conventional method, (b) fuzzy based twin controllers method Table. 2: The rule map of fuzzy swing controller