Improving of control overhead crane quality based on the fuzzy adaptive

Kỹ thuật điều khiển & Điện tử<br /> <br /> IMPROVING OF CONTROL OVERHEAD CRANE QUALITY<br /> BASED ON THE FUZZY ADAPTIVE SECOND ORDER SLIDING<br /> MODE CONTROL<br /> Le Xuan Hai, Quach Thai Quyen, Le Van Hung, Nguyen Van Thai,<br /> Vu Thi Thuy Nga*, Phan Xuan Minh<br /> Abstract: This paper proposes a fuzzy adaptive second order sliding mode<br /> controller for 2D overhead crane model to improve the quality of position<br /> tracking, anti-swing in case existence of external disturbances. The sliding<br /> surface parameters are adjusted by a fuzzy logic system to change the sliding<br /> surface in order to track faster and make the payload oscillation smaller. The<br /> simulation results show that the system quality is improved and the applicability<br /> of the proposed controller in industrial practice.<br /> Keywords: SOSMC, FASODMC, MIMO, HOSMC.<br /> <br /> 1. INTRODUCTION<br /> Crane is widely used to transport heavy load and hazardous materials in<br /> shipyards, factories and many kinds of industry. Therefore, researching on<br /> improving the control overhead crane quality is always implemented and<br /> developed by many researchers. Due to effect of the environment with unknown<br /> disturbances, sliding mode control on crane has been extremely attractive in recent<br /> years. High order control system are highly recommended and improved to<br /> increase the quality of controlling overhead crane system [1,4]. To solve the root<br /> problems for improving overhead crane system quality, both classic control and<br /> intelligent control are combined which is considered and researched [2,3,5].<br /> In this paper, a fuzzy adaptive second order sliding mode control is proposed to<br /> solve effectively the problem for overhead crane system. This control structure<br /> contains two sliding mode controller which have a parallel connection into a<br /> second order surface to control position and reduce sway angle of load at the same<br /> time. In order to adjust the parameters of sliding surface, a fuzzy logic system is<br /> used with inference rules are chosen by experience expert to help the system has<br /> suitable parameters to guarantee tracking trajectory faster and anti-sway angle of<br /> load under disturbance effect.<br /> This paper is divided into five parts: Introduction, Overhead Crane Dynamic<br /> model, Second Order Sliding Surface Construction, Sliding Surface Parameter<br /> Adjustment, Simulation and Results.<br /> 2. CONTENTS<br /> 2.1. Overhead crane dynamic model<br /> Overhead crane model is shown in figure 1 that includes: trolley and load.<br /> Where: mc , ml , l , u is the weight of trolley, the weight of load, the length of<br /> cable and impact force, respectively. Crane and load are considered like moving on<br /> Oxy plane.<br /> <br /> <br /> 20 L. X. Hai, … , P. X. Minh, “Improving of control overhead… sliding mode control.”<br /> Nghiên cứu khoa học công nghệ<br /> <br /> <br /> <br /> <br /> Fig 1. Overhead crane model.<br /> The dynamic equations are constructed based on Lagrange type II [6] :<br /> d  T  T <br />    Qi*  (1)<br /> dt  qi  qi qi<br /> Where: Qi* is generalized force, T is kinetic energy,  is potential energy, qi<br /> is generalized coordinate.<br /> The kinetic and potential energies of the crane system are presented in the<br /> following equation:<br /> 1 1<br /> T   mc  ml  x 2  ml l 2 2  ml lx cos  (2)<br /> 2 2<br />   mgl cos <br /> T<br />   mc  ml  ml l cos <br /> x<br /> d  T <br />      mc  ml   x  ml l cos   ml l 2 sin <br /> dt  x <br />  T<br />  0;  0; Qx*  u<br /> x x<br /> x  ml l cos   ml l 2 sin   u<br />  (mc  ml )  (3)<br /> T<br />   ml l 2  ml lx cos <br /> <br /> d  T  2  <br />    ml l   ml lx cos   ml x sin <br /> dt   <br />  T<br />  ml gl sin  ;   ml lx sin  ; Q *  0<br />  <br /> <br />  l  <br /> x cos    g sin  (4)<br /> From equation (3) and (4), dynamic model of overhead crane is obtained as<br /> followed:<br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 21<br />  Kỹ thuật điều khiển & Điện tử<br /> <br /> x  ml l cos   ml l 2 sin   u<br />  mc  ml  <br />   (5)<br />  l  <br /> x cos    g sin <br /> 2.2. Second order surface construction<br /> x4    x x    . The<br /> T T<br /> Defining the state variable: X   x1 x2 x3<br /> parts of sate variable are position, velocity of trolley, sway angle and velocity of<br /> sway angle of load, respectively. The equation (3) can be rewriten as the the state<br /> space model belows:<br /> x1  x2<br /> x2  f1 ( X )  g1 ( X )u<br /> (6)<br /> x3  x4<br /> x4  f 2 ( X )  g 2 ( X )u<br /> Where :<br /> ml l sin   ml g sin  cos  1<br /> f1 ( X )  g1 ( X ) <br /> mc  ml sin 2  mc  ml sin 2 <br /> (7)<br /> m l 2 sin  cos   (mc  ml ) g sin  cos <br /> f2 ( X )   l g2 ( X )  <br />  mc  ml sin 2   l  mc  ml sin 2   l<br />  x  x   x  xd   x  xd <br /> Error e(t ) is defined as follows : e(t )   1 d     <br />  x3   d     d    <br /> Where: xd and  d are the desired position and the sway angle of load, in this<br /> case  d  0 . The state space model with error ex  e1 , e  e3 as belows:<br /> e1  e2<br /> e2  f1 ( X )  g1 ( X )u  <br /> xd<br /> (8)<br /> e3  e4<br /> e4  f 2 ( X )  g 2 ( X )u<br /> The purpose of overhead crane control system is to move the load from initial<br /> position to desired position without sway. Hence, using two sliding surfaces is to<br /> separate the system as follows :<br /> s1  c1e1  e2<br /> (9)<br /> s2  c2 e3  e4<br /> Therefore, the second order surface is defined as :<br /> s   s1   s2 (10)<br /> With c1 , c2 ,  and  are the positive constants. Apply the index accessibility<br /> rule s   k1 sgn( s )  k2 s   s1   s2 , the control law is inferred :<br /> <br /> <br /> 22 L. X. Hai, … , P. X. Minh, “Improving of control overhead… sliding mode control.”<br /> Nghiên cứu khoa học công nghệ<br /> <br />  f1 ( X )   f 2 ( X )   c1e2   c2 e4   xd  k1 sgn( s )  k2 s<br /> u (11)<br />  g1 ( X )   g 2 ( X )<br /> However, ovehead crane system appears a highly frequent oscillation in the<br /> control law because of the sgn(s) function . To cut down the oscillation, this paper<br /> uses the saturation function sat(s) instead of using the sgn(s) function in the<br /> equation (9). The sat ( s ) function is defined as :<br /> sgn( s ), s  1<br /> sat ( s )   (12)<br />  s , s 1<br /> Therefore, u is now as :<br />  f1 ( X )   f 2 ( X )   c1e2   c2 e4   xd  k1sat ( s )  k2 s<br /> u (13)<br />  g1 ( X )   g 2 ( X )<br /> 2.3. Second order surface construction<br /> In the previous researches, the parameters  ,  of the second order sliding<br /> surface are chosen to be positive. However, in this paper, the relationship of  and<br />  is displayed by a coefficient k1 as follows:   k1 where k1  0.6<br /> Since then, the signal control u is rewriten as :<br />  f ( X )   f 2 ( X )   c1e2  k1 c2 e4   xd  k1sat ( s )  k2 s<br /> u 1 (14)<br />  g1 ( X )  k1 g 2 ( X )<br /> Accordingly, the second order sliding surface in (10) depend on the value  .<br /> To select a suitable sliding surface, we recommend a fuzzy logic system to appoint<br /> the coefficient  of this surface. The information got from the error position e1 and<br /> the first derivative positon e1 is used to adjust  . The sets of input fuzzy which<br /> are chosen to fuzzise are A (the error position e1 ) and B (the derivation e1 ).<br /> The generalized fuzzy system is built according to the linear method [7] which<br /> includes 3 fuzzy sets for each of input variables: -1 0 1 and 5 fuzzy sets for output<br /> variables: -2 1 0 1 2. Defined, i is the set for A variable, j is the set for the B<br /> variable, k is the set for output variable, so the generalized linear rule always be<br /> satisfied: i  j  k  0 .<br /> The rule is defined in the table belows:<br /> <br /> <br /> <br /> <br /> The structure of control second order generalized sliding system is shown in fig 2.<br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 23<br />  Kỹ thuật điều khiển & Điện tử<br /> <br /> <br /> <br /> <br /> Fig 2. The control structure.<br /> 3. SIMULATION RESULT<br /> To verify the effectiveness of this proposed method. Fuzzy adaptive second<br /> order sliding mode control (FASOSMC) is used for overhead crane system with the<br /> following parameters: mc  6(kg ) , ml  3(kg ) , g  9.8(m / s 2 ) , L  1(m) . The<br /> desired position is xd  3(m) and the selected parameters of FASOSMC are:<br /> k  3.5 , k1  0.6 , c1  2 , c2  0.01 ,   3.85 .<br /> The simulation is aim to give some estimations :<br />  The effectiveness of FASOSMC compared to SOSMC<br />  The ablility in against disturbance of FASOSMC<br /> Simulation 1 : Compare the quality of FASOSMC to SOSMC<br /> <br /> <br /> <br /> <br /> Figure 3a. The position of trolley. Figure 3b. The velocity of trolley.<br /> <br /> <br /> <br /> <br /> Figure 3c. The angle of load . Figure 3d. The angle velocity of load.<br /> <br /> <br /> 24 L. X. Hai, … , P. X. Minh, “Improving of control overhead… sliding mode control.”<br /> Nghiên cứu khoa học công nghệ<br /> <br /> The results are shown in figure 3. Inside, figure 3a shows the position of trolley<br /> when using two above controllers. Similarly, figure 3b, 3c, 3d show the velocity of<br /> trolley, the sway angle of load, the sway angle velocity of load, respectively.<br /> Table 1. The quality comparison.<br /> Settling time Overshoot Maximum angle of load<br /> Controller<br /> (s) (%) (rad)<br /> SOSMC 5 6.7 0.9<br /> FASOSMC 2.5 0 0.4<br /> <br /> The simulation results show that the quality of controlling system which using<br /> FASOSMC is better than using SOSMC, trolley tracks the desired trajectory faster<br /> and the sway angle of load is smaller.<br /> Simulation 2: Overhead crane with FASOSMC under disturbance affect<br /> The parameters of both the crane system and the controlling system are kept<br /> unchanged. However, the disturbance is added from 2(s) to 2.1(s) and the<br /> amplitude is 120. Here are the results of both with and without disturbance of<br /> FASOSMC in figure 4 below:<br /> <br /> <br /> <br /> <br /> Figure 4a. The position of trolley. Figure 4b. The velocity of trolley.<br /> <br /> <br /> <br /> <br /> Figure 4c. The sway angle of load. Figure 4d. The angle velocity of load.<br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 25<br />  Kỹ thuật điều khiển & Điện tử<br /> <br /> Table 2. The quality of overhead crane system under disturbance effect.<br /> Settling Overshoot Maximum sway angle of load<br /> FASOSMC<br /> time (s) (%) (rad)<br /> With disturbance 2.5 0 0.4<br /> Without disturbance 5 5 0.4<br /> <br /> The system reaches the setting point right after 6s in the case with and without<br /> disturbance. Hence, using FASOSMC for overhead crane system is better to reduce<br /> disturbance.<br /> <br /> <br /> 4. CONCLUSIONS<br /> The simulation results show that FASOSMC as mentioned improves the quality<br /> of the overhead crane control system. With the simple control structure, FASOSMC<br /> is easy to be installed in digital technology.<br /> Acknowledgement: This research is funded by the Hanoi University of Science and<br /> Technology (HUST) under project number T2016-PC- 107.<br /> <br /> <br /> <br /> REFERENCES<br /> [1]. Chiou, J.S, Lium M.T, “Numerical Simulation for Fuzzy-PID Controller and<br /> Helping EP Reproduction with PSO hybrid algorithm”, Simulation Modeling<br /> Practice and Theory 17,1555-1565 (2009).<br /> [2]. Liu, D., J., Zhao, D., Wang, “Adaptive Sliding Mode Fuzzy Control for Two<br /> Dimensional Overhead Crane”, Mechatronics 15, 505-522 (2005).<br /> [3]. Shu, K., -K, Jen, C., -L, Shang, L., -J, “Design of Sliding Mode Controller for<br /> Anti-swing Control of Overhead Cranes”, IECON Annual Conference of<br /> IEEE Industrial Electronics Society, pp. 147-152 (2005).<br /> [4]. Wang, J., Li, H., Karray, F., Basir, O., “Real World Implementation of Fuzzy<br /> Anti-Swing Control for a Behavior-Based Intelligent Crane System”, IEEE<br /> International Conference on Intelligent Robots and Systems, vol.2, pp. 1192-<br /> 1197. IEEE Press.Las Vegas (2003).<br /> [5]. Chang, CY., Hsu, K.C, Chiang, K.H, Huang, G.E, “Enhanced Adaptive<br /> Sliding Mode Fuzzy Control for Position and Anti-Swing Control of the<br /> Overhead Crane System”, IEEE International Conference on Systems, Man,<br /> and Cybermetics, vol.2, pp. 922-997, IEEE Press Taipei (2006).<br /> [6]. Nguyễn Văn Khang, “Cơ học kỹ thuật”, Nhà xuất bản Giáo dục (2009).<br /> [7]. Phan Xuân Minh, Nguyễn Doãn Phước, “Lý thuyết điều khiển mờ”, Nhà xuất<br /> bản Khoa học và Kỹ thuật (2006).<br /> <br /> <br /> 26 L. X. Hai, … , P. X. Minh, “Improving of control overhead… sliding mode control.”<br /> Nghiên cứu khoa học công nghệ<br /> <br /> TÓM TẮT<br /> NÂNG CAO CHẤT LƯỢNG ĐIỀU KHIỂN CẦN CẨU TREO BẰNG ĐIỀU<br /> KHIỂN TRƯỢT BẬC HAI THÍCH NGHI MỜ<br /> Bài báo đề xuất bộ điều khiển trượt bậc hai thích nghi mờ cho hệ cần cẩu<br /> treo 2D nhằm nâng cao chất lượng bám của xe, chống lắc cho tải trong<br /> trường hợp có nhiễu tác động. Các tham số của mặt trượt được chỉnh định<br /> bằng một hệ logic mờ nhằm thay đổi mặt trượt để hệ bám nhanh hơn và giảm<br /> thiểu lắc của tải. Các kết quả mô phỏng cho thấy chất lượng hệ thống được<br /> cải thiện đáng kể và có khả năng ứng dụng trong công nghiệp.<br /> Từ khóa: Điều khiển trượt bậc hai (SOSMC), Điều khiển trượt bậc hai thích nghi mờ (FASOSMC), Nhiều vào<br /> nhiều ra (MIMO), Điều khiển trượt bậc cao (HOSMC).<br /> <br /> <br /> Nhận bài ngày 05 tháng 8 năm 2016<br /> Hoàn thiện ngày 25 tháng 10 năm 2016<br /> Chấp nhận đăng ngày 26 tháng 10 năm 2016<br /> <br /> <br /> Address: 1Ha Noi University of Science and Technology.<br /> *<br /> Email: nga.vuthithuy@hust.edu.vn.<br /> <br /> <br /> <br /> <br /> Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 27<br />