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Overhead cranes fuzzy control design with deadzone.pdf
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ORIGINAL ARTICLEOverhead cranes fuzzy control design with deadzonecompensationCheng-Yuan Chang Tung-Chien ChiangReceived: 29 September 2007/Accepted: 24 March 2009/Published online: 9 April 2009? Springer-Verlag London Limited 2009AbstractThis article proposes a simple but effective wayto control 3D overhead crane. The proposed method usesPID control at the start for rapid transportation and fuzzycontrol with deadzone compensation when the crane isclose to the goal for precise positioning and moving theload smoothly. Only the remaining distance and projectionof swing angle are applied to design the fuzzy controller.No plant information of crane is necessary in this approach.Therefore, the proposed method greatly reduces the com-putational efforts. Several experiments illustrated theencouraging effectiveness of the proposed method througha scaled 3D crane model. The nonlinear disturbance, suchas abrupt collision, is also taken into account to check therobustness of the proposed method.KeywordsOverhead crane ? Projection ? Swing angle ?Fuzzy controller ? Deadzone compensation1 IntroductionThe 3D crane consists of a trolley, driving motors, and theflexible wire. It is often used in the factories and harborsfor moving heavy cargoes. The motors drive the trolley andthe flexible wire ties the load. Fast, smooth, and precisemoving to the goal is the main objective of crane control.Usually, the experienced crane operator moved the load tothe destination slowly, drove the trolley back and forth tomake the load stationary, and tried to stop the trolley at thedestination precisely and smoothly. However, due to thenonlinear load swing motion, smooth transportation andprecise load positioning by the crane operator are not easy.In addition, transporting the load rapidly but without swingis an even more difficult objective. Hence, only the visualfeedback of the crane operator is not enough to control thecrane well during transportation.Theobjective ofthecranecontrol istotransferthe loadtothe destination as fast as possible; meanwhile, to minimizethe swing during the transportation and to stop the trolleypreciselyatthedestination.However,the accelerationofthecranealwaysaccompanieswithnonlinearloadswing,whichmight cause the load damage and even accidents. Someinvestigations have developed the anti-swing methods forthe efficient control of the overhead crane. Some articles areinvestigating the existing problems of the crane controlsystem. Among these researches, Auernig and Troger 1used minimal time control to minimize the load swing.Corrigaet al.2appliedanimplicitgain-schedulingmethodtocontrolthecrane.Someresearchersalsousedthedynamicmodel of the crane to evaluate an optimal speed or pathreference that minimized the load swing 37. However,since the load swing depends on the movement and accel-eration of the trolley, minimizing the cycle time and loadswing are partially conflicting requirements. Some resear-ches also applied nonlinear control theory to analyze theproperties of the crane system 810. Besides, Karkoub andZribi 11 also developed the modeling and energy-basednonlinear control of the crane lifter. These methods are toocomplex to implement for the industry use; meanwhile, theytook much time to transfer the load smoothly and causedsevere swing at the beginning of transportation. In addition,Yoshida and Kawabe 12 proposed the real-time saturatingcontrol strategy for cranes. Matsuo et al. 13 used theC.-Y. Chang (&)Chung Yuan Christian University, Jhongli, Taiwane-mail: .twT.-C. ChiangChing Yun University, Jhongli, Taiwan123Neural Comput & Applic (2009) 18:749757DOI 10.1007/s00521-009-0264-0PID ? Q-based controller to anti-sway the crane. Takagiand Mishimura 14 developed a centralized control systemwith coupling between the up-and-down and rotation direc-tions to restrain the swing of a jib-type crane. These resear-ches focus the control on the suppression of load swing, butdidnotsolvetheproblemofpositionerrorattheendofcranemotion 15. Some fuzzy-based methods 1519 were alsoproposed to control the crane. Unfortunately, such fuzzycontrollers cannot provide the desired performance for thecranesystem,duetotheuncertaintyandlargedisturbancesofthe fuzzy system, reducing the working efficiency.In this article, we proposed a method to accommodate allthe objectives of 3D crane control, including fast moving ofcrane, anti-swing of the load, and concise designing pro-cedures of controller. One uses PID controller to drive thecrane in the fore part of the control for rapid transportationand to apply remaining distance and projection of swingangle to design the fuzzy controller. The proposed articlealso provides the compensating algorithm to overcome thecontrol deadzone problem, enhancing the performance. Ascaled crane mode, with 2-m long, 2-m wide, and 2-m high,is used to illustrate the effectiveness of proposed approach.This method does not use complex plant model of crane todesign the crane controller, but both the positioning andsway problems can be solved. So, the proposed fuzzycontrol method greatly helps to control the complex system.This article is organized as follows. Section 2 shows theproposed projection method and Sect. 3 reveals the com-pensating algorithm for overhead crane control system.In Sect. 4, several experimental results are presented toillustrate the merits of the proposed approach. This articleconcludes with a summary in Sect. 5.2 Crane controller designThe physical apparatus of the 3D crane system is composedof a trolley and a flexiblewire ties the load, such as shown inFig. 1.TwoDC motors drive the trolleyalong X- and Y-axesand four 12-bit encoders (two for sensing X-, Y-positions oftrolley and the other two for measuring swing angle of loadin 3D space) are applied to measure the related parameters.The swing diagram of the load in 3D is shown in Fig. 2.Generally, the motion of the trolley will accompany withswing of load. When the trolley is driven forward, thebackward swing angle can be expected, and vice versa. Thatis, the direction of corresponding swing is contrary to thetrolley motion; meanwhile, the acceleration of trolley willalso cause the additional swing of load. Hence, transferringthe load fastly and smoothly in the meantime is not easy.Since one of the objectives of the crane control isto transfer the load as fast as possible; therefore, we utilizethe PID control in the previous 95% distance for rapidtransportation and then switch to the fuzzy projectionmethod to restrain the load swing. The block diagramof the fuzzy crane control system is shown in Fig. 3.The present position of the trolley on the XY-plane isP,px;py? 2 R2and the destination is D,dx;dy? 2 R2.The PID control is Up upx;upy?, whereUpKPKIs KD? s?E1The vector of the remaining distance E isE D ? P dx? px;dy? py?,ex; ey? 2 R22where exand eyare the components of the vector E in thedirections of X-axis and Y-axis, respectively. The constantsFig. 1 The physical apparatus of the 3D crane control systemFig. 2 The swing diagram of 3D crane750Neural Comput & Applic (2009) 18:749757123KP kpx;kpy?, KI kix;kiy? and KD kdx;kdy? in the PIDcontroller are designed to transfer the load rapidly underthe assumed safety constraints:jhxzj15?andjhyzj15?3where hxz; hyzrepresents the swing angle of load along theXZ-plane and YZ-plane, depicted in Fig. 2. The PID controlhelps to transfer the load rapidly under the assumed safetyconstraints.After the trolley has arrived at the 95% distance, the PIDcontrol is switched to fuzzy projection control. The pro-posed method utilizes the projection of the 3D swing angleto be another input variable of the fuzzy controller, shownin Fig. 4. The factor of swing angle is taken into consid-eration in this stage. One denotes the swing angle of theload in 3D space to beW hxz; hyz?4We use the projection of 3D swing angle on a 2D planeto present the level of load swing. The severer swing willlead to longer projection, and vice versa. Hence, the pro-jection of swing angle can be represented by u 2 R2:u /x;/y?;5where /xand /yare the projections of swing with respectto the X-axis and Y-axis. Since the projection and theremaining distance are all in length, it is more reasonable toapply both the factors to design the fuzzy output at thesame time. The length of projections can be represented by/x L ? sinhxz6/y L ? sinhyz7L is the fixed length of the flexible wire hanging the load.These projection vectors are depicted in Fig. 4.In order to achieve the addressed control objective, fasttraveling during the journey, stopping precisely andswinging smoothly at the end, the trolley should be drivenwith the following criteria. First of all, the trolley should bedriven along the direction of E to reach the destination asfast as possible. Second, the trolley should be driven alongthe direction of u to eliminate the swing angle. However,the directions of E and u may not be the same, and drivingthe trolley along the directions of E and u in the meantimemight be impossible. Therefore, the author applies thefuzzy method to control the trolley along the directions ofE and u.Two motors for X- and Y-axes are used to drive thecrane. One uses exand /xto be the antecedents of fuzzycontroller to derive the fuzzy control for X-axis motor, andthe other applies eyand /yto derive the control for Y-axismotor. Suppose that the output of the fuzzy controller isUF, where the output acts as the fuzzy function of inputvariables,UF ufx;ufy fxex;/x; fyey;/y;8where ex, ey, /x, and /yare the input variables, fxand fyrepresent for the functions of fuzzy controller, and ufxandufyare the fuzzy output power to drive the X- and Y-axesmotors. In this case, we use five linguistic states for eachinput variable e*and /*to fuzzify the input variables anduse 11 states for output variables uf?. The notation *means x or y, and the linguistic states are shown inFig. 5ac. The dynamic ranges are -0.1 m 0.1 m,-0.05 m 0.05 m, and -1 1 for e*, /*and uf?. Onenames the five linguistic states of input variables e*and /*as Negative Big (NB), Negative Small (NS), Zero (ZO),Positive Small (PS), and Positive Big (PB). Besides, theauthor uses 11 linguistic variables to describe the outputvariables uf?including Negative Big_Big (NBB), NegativeBig (NB), Negative Middle (NM), Negative Small (NS),Fig. 3 The block diagram offuzzy crane control systemEyeyxLoadTrolleyxeDestinationFig. 4 The concept of the projective methodNeural Comput & Applic (2009) 18:749757751123NegativeSmall_Small(NSS),Zero(ZO),PositiveSmall_Small (PSS), Positive Small (PS), Positive Middle(PM), Positive Big (PB), and Positive Big_Big (PBB). Theoutput of the fuzzy controller UFis obtained by combiningthe rules defined in Table 1 using minimum inference andcentroid defuzzification 20. The author uses the outputsignals to control the X- and Y-axes motors.Since the factors to reach the destination and to elimi-nate the swing are both taken into consideration to designthe fuzzy-based crane controller, the projection methodguarantees that the swing is suppressed meanwhile thecrane is driven along the direction to reach the destination.It works better than the usual fuzzy-based method to drivethe crane back and forth to restrain the swing.By the way, to achieve fast and smooth transfer of theload, driving the trolley along the directions E and u mustbe obeyed. The remaining distance E and swing level ualso present the objective of control. Thus, the purpose ofcrane control is to minimize E and u. However, there is aflexible wire between the trolley and load. The control toeliminate E and u is not on the same surface, and power isnot necessary to transfer completely from the trolley to theload. Therefore, some nonlinear properties will exhibit.Besides, the control through the flexible wire also increasesthe nonlinearity and complexity. Hence, nonlinear con-troller would be the more proper choice to design the cranecontroller. This is the main reason why the author chosefuzzy-based controller in this paper.3 Deadzone compensation methodThe trolley crane is a heavy mechanical system driven bythe DC motors. If the control input voltage is very small,the DC motor is not able to drive the trolley crane due tothe nonlinear friction, causing the control deadzone andreducing the performance. Figure 6 shows the deadzone ofthe practically scaled crane control system in this article.One can find that both the X- and Y-axes motors exhibit thedeadzone effect. When the absolute value of driving forceis less than about 0.24 for X-axis motor and 0.1 for Y-axismotor, the trolley could stop due to the deadzone, reducingthe performance. In order to avoid these conditions, theFig. 5 The linguistic state of fuzzy variables a e*, b /*, c u*Table 1 Rule table of the main fuzzy controller/*e*NBNSZOPSPBNBNBBNBBNMNSPSSNSNBBNSNSSNSSPSZONBNSSZOPSSPBPSNSPSSPSSPSPBBPBNSSPSPMPBBPBBFig. 6 The control deadzone diagram, dashed: X-axis motor, solid:Y-axis motor752Neural Comput & Applic (2009) 18:749757123proposed system uses the compensating algorithm tocompensate for the driving forces of motors.When the distance to the goal is far enough, the fuzzycontroller addressed in Sect. 2 will generate the sufficientpower to drive the trolley. However, the power will grad-ually decrease when the trolley is close to the destination.When the derived fuzzy power is too small, the trolleycould stop before the destination due to the controldeadzone. In this situation, the fuzzy-based compensatingalgorithm will activate to accumulate the control power todrive the crane departing from the deadzone. The blockdiagram along with the compensating algorithm is shownin Fig. 7. The designing procedures are depicted asfollows.Step 1 In the compensating fuzzy controller, the absolutevalue of DE is used to be the antecedent, and the extrapower to drive the crane Uc ucx;ucy? is used to be theconsequent part, wherejDEj jEt ? Et ? 1j jDexj;jDeyj?9andDex ext ? ext ? 1andDey eyt ? eyt ? 1:10The dynamic range of |DE| is partitioned into three lin-guistic terms: Zero (Z), Small (S), and Big (B). Afterfuzzification, inference, and defuzzification procedures, theoutput power Ucis obtained. Figure 8a and b shows thecorresponding membership functions, and the fuzzy rulesare shown in Table 2.Step 2 While the distance to the goal is still far enough,the fuzzy controller will generate the sufficient power todrive the trolley crane. However, the power will reducewhen the trolley is close to the destination. The speed ofthe trolley is hence slowed down. If the variation of thetrolley position |DE| is less than a, then the trolley cranecould gradually stop for the deadzone. The compensatingmethod activates in this moment to provide the additionalpower, U0c u0cx;u0cy?, to increase the control. This helps toavoid the crane stop in front of the destination. The com-pensating principles are shown in the following equations.ifjDEj?au0c?t 1 uc?t u0c?t11otherwise;u0c?t 1 0;? 2 fx;yg12The constant a is 5 9 10-4m and u0c?0 is set to 0 in thebeginning.Step 3 In order to reduce the computation effort, thecompensating fuzzy controller uses |DE| instead of DE asFig. 7 The block diagramalong with the compensatingalgorithmFig. 8 The membership functions of a |DE|, b UcTable 2 Rule table of the compensating fuzzy controller|DE|ZSBUcBSZNeural Comput & Applic (2009) 18:749757753123the antecedent part of compensating fuzzy rules. Hence, theoutput of the compensating power needs to be modifiedaccording to the actual situation. The actual compensatingpower will be U00c u00cx;u00cy?:ifuf?0;u00c? u0c?13otherwise;u00c? ?u0c? 2 fx;yg14Hence, the additional voltage, U00c, is activated to increasethe driving power of the trolley when the variation is lessthan 5 9 10-4m. The actual power U to control the cranewill be modified:U UF U00c15A flexible wire is tied to the load. Therefore, thenonlinearity of the crane system is hence increased toexamine the ability of the compensating control algorithm.The author sets the stop criterion of the crane controlsystem with the following qualifications: the distance to thegoal is less than 0.001 m; meanwhile, the swing angle ofload is less than 0.5?. While the crane could stop due to thecontrol deadzone, the compensating algorithm will activateto provide the extra power until the stop criterion issatisfied.4 Experimental resultsA scaled crane model was built in the laboratory to illus-trate the effectiveness of the proposed method. Two DCmotors for X- and Y-axes are applied to drive the overheadcrane system. Four 12-bit encoders send the information ofthe present position (including the coordinates of X- and Y-axes) of the trolley and the swing angles of the load, hxzandhyz, to the controller. The weight of the load is 0.7 Kg andthe length of the hanging flexible wire is 1 m. Suppose thatthe destination of the load is set to be (1.5 m, 1.5 m), whilethe initial position of the load is at the location of (0 m,0 m). The corresponding constants in the experiments areKP= 10, 9.85, KI= 0, 0.002, and KD= 9.6, 8.65.Figure 9 shows the experimental results with only PIDcontroller. Figure 9a shows the remaining distance to thegoal and Fig. 9b shows the swing angles hxzand hyz. Onecan find that the trolley is driven fast but with severe swing.The final position of the trolley is (1.47156 m, 1.50002 m)and the remaining swing amplitude is about 12? for hxzand8? for hyz. It took only about 8 s to reach the goal, but theswing was unable to restrain well.Figure 10ab shows the experimental results with theproposed method. One can find that the trolley took about5 s to the destination; in the meanwhile, the swing anglesof the projective method performed very well. Theremaining swing amplitude is about 0.09? for hxzand 0.02?for hyz. However, it is difficult for the trolley to stop pre-cisely at the goal; the final position of the trolley is(1.48274 m, 1.49956 m). Hence, the steady-state error ofthe trolley was 28.44 and 0.02 mm for the X- and Y-axes,respectively. This problem is caused by the friction of theX- and Y-axes track of trolley. Therefore, if the trolley isvery close to the destination, the fuzzy controller willprovide small power to reach the goal. When the power isnot enough to overcome the control deadzone, the trolleywould stop on the wrong place, making the performanceworse. Besides, the positioning error of X-axis is worsethan that of Y-axis. This result matches the controldeadzone problem of X-motor is severer than Y-motor,shown in Fig. 6.Fig. 9 The experimental results with only PID controller a remainingdistance, dashed: X-axis, solid: Y-axis, b swing angle, dashed hxz,solid hyz754Neural Comput & Applic (2009) 18:749757123In Fig. 11ab, the proposed compensating method isapplied to the projection control. The main differencebetween Figs. 10 and 11 is at the position error of thetrolley. One can find that the swing was also restrainedwithin 7 or 8 s; meanwhile, the trolley stopped preciselyat the goal after the compensating algorithm was acti-vated. The final position of the trolley is (1.49967 m,1.49991 m). The positioning error is only 0.33 mm forX-axis and 0.09 mm for Y-axis. Besides, the remain-ing swing amplitude is about 0.04? for hxzand 0.02?for hyz.One sets two indexes to compare the experimentalresults, where the position index isposT 12exT eyT16and swing index is:swingT 12amplitude of hxzT amplitude of hyzT17where T is the final time to control. Comparisons betweenthe presented methods are depicted in Fig. 12a and b. Onecan find that the deadzone compensation greatly improvesthe control performance of the 3D overhead crane system.However, the overhead crane system is often used in theoutdoors. The disturbance such as the abrupt collision ofthe load might affect the control performance. In the lastFig. 10 Theexperimentalresultswiththeprojectivemethoda remaining distance, dashed: X-axis, solid: Y-axis, b swing angle,dashed: hxz, solid: hyzFig. 11 The experimental results with compensating algorithma remaining distance, dashed: X-axis, solid: Y-axis, b swing angle,dashed: hxz, solid: hyzNeural Comput & Applic (2009) 18:749757755123experiment, the author uses the additional driving force,-0.5, to act as abrupt collision of load. This collisioncontinues for half a second after the trolley was driven20 s. Figure 13ab shows the experimental results. Onecan easily find that the swing becomes very severe whenthe collision of load happened. However, the proposedmethod still can do it well. The trolley can be driven torestrain the swing angle soon.Compared with another practical 3D crane control sys-tem shown in other researches, the proposed method savesthe traveling time and provides the simple technique torestrain the load swing and position errors very well.Besides, the proposed fuzzy-based controller does not needto drive the trolley back and forth to control the swing,which also reduces the chance of load damage. No plantinformation applied to design the controller also helps tosimplify the controller design.Remark There are some parameters to be decided in theproposed design. Most constants in this article, such as thePID parameters, are obtained by Matlab simulations underthe same stop criterion and safety constraint with themathematical model of the crane in 10. The switchingcondition and stop criterion are decided to speed thetransportation. Both parameters can be set arbitrarily tomeet different control requirements. Basically, the mem-bership functions of FLC can be chosen to be equallydistributed in the dynamic range. However, we focus on thecrane control near the destination. It is the reason why themembership functions are closer near zero.5 ConclusionsA simple but effective method is proposed to control the3D crane system. This method is based on the positionerror and projection of the swing angle to design the cranecontroller. There are no complex dynamic equations of thecrane that have to be taken into consideration in the con-troller design. The author also designs a compensatingalgorithm for deadzone compensation, enhancing the per-formance. Experimental results show that the proposed2 28 8. .4 46 61 18 8. .7 70 0. .4 42 2051015202530position error(a)2 20 00 0. .1 11 10 0. .0 06 605101520PID Fuzzy Projectionwith deadzonecompensationswing amplitude(b)PID Fuzzy Projectionwith deadzonecompensationFig. 12 The performance indexes a position error, b swing amplitudeFig. 13 The experimental results with abrupt collision a remainingdistance, dashed: X-axis, solid: Y-axis, b swing angle, dashed: hxz,solid: hyz756Neural Comput & Applic (2009) 18:749757123method can greatly restrain the swing without exposing theperformance to fast traveling; meanwhile, stop the trolleyat the destination perfectly.AcknowledgmentThis work was supported by the National Sci-ence Council of the Republic of China under Grant NSC-94-2213-E-231-020.References1. Agostini MJ, Parker GG, Schaub H, Groom K, Robinett RD(2003) Generating swing-suppressed maneuvers for crane sys-tems with rate saturation. IEEE Trans Control Syst Technol11:471481. doi:10.1109/TCST.2003.8134022. Corriga G, Giua A, Usai G (1998) An implicit gain-schedulingcontroller for cranes. IEEE Trans Control Syst Technol 6:1520.doi:10.1109/87.6548733. Omara HM, Nayfeh AH (2005) Gantry cranes gain schedulingfeedback control with friction compensation. J Sound Vib 281:120. doi:10.1016/j.jsv.2004.01.0374. Hamalainen JJ, Marttinen A, Baharova L, Virkkunen J (1995)Optimal path planning for a trolley crane: fast and smoothtransfer of load. IEE Proc Con
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