In this paper, a simple and efficient technique to control overhead crane based on fuzzy logic inferrence system is proposed. A second order fuzzy logic controller (DLFLC) is proposed to track the desire position, aliminate the payload swing and resist unknown dirturbance exerted on the system.
Electronics and Automation ANTI-SWING TRACKING CONTROL FOR 2D OVERHEAD CRANE USING DOUBLE LAYER FUZZY LOGIC CONTROLLERS Vu ThiThuy Nga1, Le Xuan Hai1,*, Le Viet Anh1, Ta Van Truong1, Hoang Nghia Hiep1, Ha Thi Kim Duyen2, Phan Xuan Minh1 Abstract: In this paper, a simple and efficient technique to control overhead crane based on fuzzy logic inferrence system is proposed A second order fuzzy logic controller (DLFLC) is proposed to track the desire position, aliminate the payload swing and resist unknown dirturbance exerted on the system The simulation and experiment results show that the improvement of proposed control scheme for example smaller swing, improved accuratly position Keywords: Tracking Control, Payload Anti-swing, Fuzzy Logic Controller (FLC), Overhead Crane, Double Layer Fuzzy Logic Controller (DLFLC) INTRODUCTION Overhead cranes are essential load and unload equipment, widely used in many areas such as at construction sites , factories and harbors Modelling of crane belong to a class of underactuated mechanical systems, with one control input (a trolley driving force) and two system variables to be controlled (a trolley position and a load swing angle) That leads to the unexpected swing of payload in operation process Therefore, the control principle of the crane is to move trolley on the desire path and make the payload oscillation smaller as possible Researching on increasing the control quality of crane system is always considered and developed by many researchers Various attempts for control of overhead crane have been proposed For many years, the anti-swing trajectory tracking control methods for cranes mainly included non-linear, adaptive, sliding mode control technique For example, the papers [1] and [2] presented non-linear control laws based on feedback linearization method and Lyapunov stability theory, or in the papers [3] and [4], sliding mode control was used Nevertheless, this control structure is relatively complex, so applied it to microcontroller is not really simple That is the main reason for improving the control design with fuzzy logic system due to its applicability on digital controller In [5], Benhjdjeb et al constructed a fuzzy logic controller, and it is a effective method in comparison to other traditional methods presented before That scheme have been developed in some works [6], [7], [8] Nearly, Wang et al [9] proposed a new control structure, with double fuzzy controller in order to seperate tracking control task and antiswing control task However, the experimental results are not presented in [9] In [10], [11], adaptive fuzzy controllers are used for overhead crane, output scaling factor of that fuzzy controller is updated according to the process trend by a fuzzy gain modifier The controllers guarantee the good performances for overhead crane despite of system uncertainties However, the swing of the angle still high Some other methods combined fuzzy logic system in some different structures, to enhence the quality of system [12],[13],[14],[15] In this paper, a double layer fuzzy logic controller (DLFLC) is proposed to solve effectively the problem for overhead crane system This control structure contains three fuzzy logic controllers in two layers, which have a serial connection Two fuzzy controllers belong to the first layer, to solve two separate problems, achieve the expected location of crane and confine the swing of crane as small as possible The second layer has one controller, is designed combining the effectiveness of first layers’s controllers The 68 V.T.T.Nga, L.X.Hai,…,“Anti-swing tracking control for 2D overhead crane…” Research fuzzy logic system is used with inference rules are chosen by experience expert to make a ideal control method This paper is divided into six parts: Introduction, Overhead Crane Dynamic model, Construction of Double Layer Fuzzy Logic Controller, Simulation Results, Experiment Results and Conclusion OVERHEAD CRANE DYNAMIC MODEL Figure shows the schema of a 2D overhead crane, that includes trolley and load The following notation are defined as: mc , ml , l , u are the weight of trolley, the weight of load, the length of cable and impact force, respectively Trolley and load are considered like moving on Oxy plane Figure Overhead crane model The dynamic equations are constructed based on Lagrange type II: d T dt qi T Qi* qi qi ( q1 x; q2 ) (1) * Where: Qi is generalized force, T is kinetic energy, is potential energy, qi is generalized coordinate The kinetic energy and potential energy of the crane system are described by: 1 T (mc ml ).x ml l 2 ml lx cos 2 (2) ml gl cos (3) T (mc ml ) x ml l cos x d T x ml lcos ml l2 sin (mc ml ) dt x T 0; 0; Qx* u x x (mc ml ) x ml lcos ml l2 sin u Journal of Military Science and Technology, No 48A, - 2017 (4) 69 Electronics and Automation T ml l 2 ml lx cos d T ml l ml lxcos ml lx sin dt T ml gl sin ; ml lx sin ; Q* x cos g sin l (5) From equations (4) and (5), dynamic model of overhead crane is obtained as followed: (mc ml ) x ml lcos ml l2 sin u x cos g sin l (6) From (6), it is noticed that the parameters of model are difficult to determine accurately Moreover, a number of parameters such as the payload, tension of cable wire also very susceptible to change during operation In such conditions, the fuzzy logic controller has advantage because this control law is constr constructed ucted based on experience and not depend on precise knowledge about model DOUBLE LAYER FUZZY LOGIC CONTROLLER In this paper, three fuzzy controllers in two layers are used, in order to achieve two separate task, track the desired path of trolley and ddecrease ecrease the swing of payload Control laws are designed by Takagi Takagi-Sugeno Sugeno fuzzy model [16] The first layer contains two controllers and each solves one problem Ouputs of two controllers in the first layer are the inputs of the second layer This layer hass only one controller, which combines interaction between two control tasks to provide the appropriate control signal u for the system The diagram of DLFLC is shown in Figure Figure The diagram of DLFLC DLFLC 3.1 Design FLCs for the first layer These two fuzzy controllers (FLC1 and FLC2) have same structure, including two input variables and one output variable FLC1 with input variables ex and ex , output variabl variablee u1is designed to achieve the expected location of trolley trolley FLC2 with input variables e and angle In order to simplify the e , output variable u2, decreases the payload’s swing angle design, each input variable contains three fuzzy sets with triangular membership functions 70 V.T.T.Nga, L.X.Hai,… L.X.Hai,…,,“Anti nti swing swing tracking control for 22D D overhead crane crane…” ” Research (Ak1=NS, Ak2=ZE, Ak3=PS; k=1,2), and the basic domain is [-1, +1] Output variable contains five constants (c1 c2 c3 c4 c5) = (-2, -1, 0, 1, 2), the basic domain is [-2,+2] The establishment of the input of the triangular membership function is shown in Figure The IF-THEN rules of the fuzzy controllers are designed as shown in Table Figure The membership function of input variables Table The IF-THEN rules ex (e ) u1 ex (e ) NS ZE PS PS ZE -1 NS -2 -1 The output signal ui (i=1,2) is determined as the formula of Takagi-Sugeno [14] h c i i u1 i 1 (7) hi i 1 hi Ai je (ex ). Ai je (ex ) ; i 1,2, ; Where: x (8) x Here, jex ( jex ) 1, 2,3 is the index of fuzzy sets hc i i u2 i 1 (9) h i i 1 hi Ai je (e ). Ai je (e ) ; i 1,2, ; (10) Journal of Military Science and Technology, No 48A, - 2017 71 Electronics and Automation Here, je ( je ) 1, 2,3 is the index of fuzzy sets 3.2 Design FLC for the second layer The second layer has one FLC with two input variables u1andu2, output variable is control signal u Each input variable includes five fuzzy sets (Ak1=NM, Ak2=NS, Ak3=ZE, Ak4=PS, Ak5=PM; k=1,2) with the basic domain is [-2,+2] The establishment of the input of the triangular membership function is shown in Figure The constants for output’s variable is chosen by (c1 c2 c3 c4 c5 c6 c7 c8 c9) =(-4 -3 -2 -1 4) and the basic domain is [100,+100] The IF-THEN rules of the fuzzy controllers are shown in Tab Figure The membership function of input variable Table The IF-THEN rules u1 u u2 NM NS ZE PS PM PM PS -1 ZE -2 -1 NS -3 -2 -1 NM -4 -3 -2 -1 The control signal u is determined as the formula of Takagi-Sugeno [14] 25 h c i i u i 1 25 (11) h i i 1 Where: hi Ai ju (u1 ). Ai ju (u ) ; (12) Here, ju1 ( ju2 ) 1, 2,3, 4,5 is the index of fuzzy sets 72 V.T.T.Nga, L.X.Hai,…,“Anti-swing tracking control for 2D overhead crane…” Research SIMULATION RESULTS To verify the performances of the proposed proposed control structure the simulation is done for overhead crane systemwith the following parameters: Table The parameters of overhead crane system Specification Value Trolley mass ( mc ) 20 (kg) Payload mass ( ml ) (kg) Cable length ( l ) (m) Gravitational (g) 9.81 ( m / s ) 4.1 Simulation without disturbance affect Simulations are executed with Matlab-Simulink software The simulation results are shown in Figure Figure 5a performances displacement trolley, Figure 5b performances tracking error, Figure 5c, 5d show the sway angle of payload and control signal, respectively From the simulation results, it can be seen that the trolley arrived at the desired position in nearly seconds, and swing angle is less than 0.1 (rad) (a) (b) (c) (d) Figure Simulation results without disturbance effect 4.2 Simulation with disturbance affect Journal of Military Science and Technology, No 48A, - 2017 73 Electronics and Automation The disturbance is added from 1(s) to 1.1(s) The position of trolley, tracking error, control signal and swing angle are shown in Figure 6a, 6b, 6c, 6d, respectively In this case, the proposed controller stills ensuring the quality of system, with trajectory tracking and reduction of load swing angle Hence, using the DLFLC for crane system is better to reduce disturbance (a) (b) (c) (d) Figure Simulation results with disturbance effect EXPERIMENTAL RESULTS Based on the simulation result, experimentation is setup to identify the effectiveness of the proposed controller The hardware system is structured based on the system presented in [17] The controller is programed on Atmega32 microcontroller chip, communicates with computer via port RS232, human machine interface is designed by C# Window Form and sampling time is 25 miliseconds Figure descibes the overhead crane model in laboratory.In which, the system comprises a cart of mass mc moving on a rail of mass ml Below the trolley is a winch which yields a force u to tune the length l of the suspended rope Furthermore, the system includes three-phase asynchronous motors connected with the inverter and encoder; this makes the whole system similar to that in industry The three-phase deceleration motor with a breaking system is controlled by the inverter OMRON 3G3JX due to its compact size and easy use This inverter is simple but satisfies the requirement The incremental optical encoder used in the experiment is Rotary Encoder E40S6-1024-3T-24 with voltage of 12V DC – 24V DC 74 V.T.T.Nga, L.X.Hai,…,“Anti-swing tracking control for 2D overhead crane…” Research Figure laboratory The 3D overhead crane in laboratory Figure Experimental Experiment results results Figure includes the position of trolley control signal and swing angle of payload with desired position is 1m Experiment results show the applicability of the proposed controller in the real time system The overhead crane arrived at the expected position in nearly 20 seconds and the angle of the load is less than 0.1 degrees in absolute value, and nearly it decreases to CONCLUSION This paper presented a control scheme for 22 D D overhead crane system by using double layer fuzzy logic controller Not only have simpl simplee structure, easy to be installed in digital Journal of Military Science and Technology, No No 48A, 48A - 2017 75 Electronics and Automation technology, the presented controller also doesn’t require accurately knowledge about system Both simulation and experiment results show that the controller is effective to move the trolley with lower payload oscillation and perfectly capable of using in industry applications ACKNOWLEDGEMENT: This research is funded by the Hanoi University of Science and Technology (HUST) under project number T2016-PC- 107 REFERENCES [1] J Yu, F.L Lewis, T Huang, “Nonlinear feedback control of a gantry crane”, American Control Conference, Proceedings of the 1995, Jun 1995 [2] Park H., Chwa D and Hong K S.,“A feedback linearization control of container cranes: Varying rope length”, Int J Control Autom Syst (4), pp 379 – 387, Aug 2007 [3] W Wang, J Q Yi, D B Zhao, D T Liu,“Anti-swing control of overhead cranes based on sliding-mode method”, Control theory and Applications, pp1013-1016, Sep.2004 [4] H Lee, Y Liang, and D Segura, “A sliding-mode antiswing trajectory control for overhead cranes with high-speed load hoisting”, Trans ASME, J Dyn Syst Meas Control, vol 128, no 4, pp 842–845, Dec 2006 [5] Benhidjeb A, Gissinger GL, “Fuzzy control of an overhead crane performance comparison with classic control”, Control EngPract,pg 1687-1696, Volume 3, Issue 12, Dec 1995 [6] M Mahfouf, C H Kee, M F Abbod and D A Linkens, “Fuzzy Logic Based AntiSway Control Design for Overhead Cranes”, Neural Computing &Applications, Volume 9, Issue 1, pp 38–43, May 2000 [7] Nalley Michael J., Trabia Mohamed B., “Control of overhead cranes using a fuzzy logic controller“, Journal of Intelligent and Fuzzy Systems, vol 8, no 1, pp 1-18, 2000 [8] Cheng-Yuan Chang, “Adaptive Fuzzy Controller of the Overhead Cranes With Nonlinear Disturbance”, IEEE Transactions on Industrial Informatics, pg 164 - 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132, Sep 1985 [17] Hai L X., Thai N V., Duong B T., Nga V T T., Nguyen T H., Minh P X “Implementation of a laboratory overhead crane control”, Journal of military scientific research and technology, No14, Aug 2016 TÓM TẮT ĐIỀU KHIỂN BÁM QUỸ ĐẠO VÀ CHỐNG RUNG LẮC CHO CẦN CẨU TREO 2D BẰNG BỘ ĐIỀU KHIỂN MỜ HAI LỚP Bài báo đề xuất phương pháp điều khiển đơn giản hiệu cho cần cẩu treodựa sở hệ logic mờ Một điều khiển mờ hai lớp đề xuất nhằm đảm bảo bám vị trí đặt xe,đồng thời giảm thiểu rung lắc cho tải khắc phục nhiễu tác động vào hệ thống Kết mô thực nghiệm cho thấy hiệu điều khiển đề xuất, xe đẩy bám vị trí đặt nhanh giảm góc lắc tải có nhiễu tác động Từ khóa: Position Control, Payload Anti-swing, Fuzzy Logic Controller (FLC), Overhead Crane, Double layer Fuzzy Logic Controller (DLFLC) Received date, 14th February 2017 Revised manuscript, 25th March 2017 Published on 26th April 2017 Author affiliations: Department of Automatic Control, Hanoi University of Science and Technology; Department of Electronics, Hanoi University of Industry ; *Correspondingauthor: xhaicuwc.edu.vn@gmail.com Journal of Military Science and Technology, No 48A, - 2017 77 ... góc lắc tải có nhiễu tác động Từ khóa: Position Control, Payload Anti- swing, Fuzzy Logic Controller (FLC), Overhead Crane, Double layer Fuzzy Logic Controller (DLFLC) Received date, 14th February... Industrial Informatics, pg 164 - 172, May 2007 [9] Lifu Wang, Hongbo Zhang, Zhi Kong, Anti- swing Control of Overhead Crane Based on Double Fuzzy Controllers , The 27th Chinese Control and Decision... the index of fuzzy sets 72 V.T.T.Nga, L.X.Hai,…, Anti- swing tracking control for 2D overhead crane ” Research SIMULATION RESULTS To verify the performances of the proposed proposed control structure