Non-linear control algorithms, 2D overhead crane in the laboratory,

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Kỹ thuật điều khiển & Điện tử SETTING UP SOME NON-LINEAR CONTROL ALGORITHMS FOR 2D OVERHEAD CRANE IN THE LABORATORY Le Xuan Hai1*, Bui The Hao1, Tran Hai Dang1, Nguyen Van Thai1, Do Thi Tu Anh1, Ha Thi Kim Duyen2, Phan Xuan Minh1 Abstract: In this paper, some non-linear control algorithms have been verified through simulation and installed in atmega 32 microcontroller for 2D overhead crane system in the laboratory. The contribution of the paper is to evaluate the applicability of these laws and to create a practical research toolkit for students in the major of Automatic Control. The software of the proposed digital controllers has open structure to increase the ability of installing the new algorithms and the human-friendly interface on personal computer. Keyword: ATMEGA 32 micro controller, Overhead crane, PD law, E 2 law, PD law combined with E 2 , Anti-sway compensation nonlinear control law. 1. INTRODUCTION There are four kinds of crane: overhead crane, container crane, tower crane and jib crane. Overhead crane is widely used in the factory and seaports. Overhead crane makes loading and transporting work become more convenient and reduces work time. Because of the importance of this system in the industry, therefore the research for overhead crane system are always cared and developed. The focal point of this research is to verify performance and ability of several new control algorithms that is published in recent years through multi-functions digital controller that is installed in ATMEGA 32. These control algorithms are installed and implemented on real overhead crane model in the laboratory. The algorithms include: PD control law, PD combined with E 2 control law, PD combined with E 2 - kinetic energy compensation control law in [1] and antisway compensation nonlinear control law in [2]. The concept of this paper is divided into five parts: Introduction, Theory Fundamental, Design Multi-Functions Digital Controller, Experimental Result and Conclusions. 2. THEORY FUNDAMENTAL 2.1. Dynamic model of 2D overhead crane system A 2D-overhead crane is shown in figure 1: Figure 1. 2D Overhead crane model. 64 L. X. Hai, …, P. X. Minh, “Setting up some non-linear control… in the laboratory.” Nghiên cứu khoa học công nghệ Where: The mass of load is m p ( kg ) , the mass of trolley is mc (kg ) , the length of cable is L( m) and the angle of load is  (rad ) . To be simple, we assume that the friction of trolley equals zero. Additional, model of overhead crane needs to have some following assumption :The payload and trolley is connected by a cable that has no mass, the length of cable is fixed. The payload mass and the position of trolley are known exactly. The join between cable and trolley has no friction and does not revolve around the axis of the cable. The angle of load is limited:      . The model of 2D overhead crane is given bellow: M (q )q  Vm (q, q )q  G (q)  u (1) Where: T q  x   (2) 0 m p L sin   Vm  q, q     0 0  G  q   0 m p Lg sin    mc  m p M q    m p L cos  u t    F (3) T m p L cos   m p L2  T 0 Based on structure of M (q ) and Vm (q, q ) , we easily have a following relationship: (4)  T  M  q  / 2  Vm  q, q     0 In order to be convenient for analysis stability, the original model (1) can be rewritten as follows: q  M 1 (u  Vm  q   G ) (5)  m p L2   m p L cos  (6) Where: M 1 1   mc  m p sin 2   m p L2 m p L cos    mc  m p  Then, replacing (3) and (6) into (5), we obtain dynamic term below:  x   , F  m  m  (7)   1 2 (( F  m L sin  ) cos   ( m  m ) g sin  ) p c p Lm ( ) (8)   Where: Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 65 Kỹ thuật điều khiển & Điện tử m     mc  m p sin 2    0   ,   m p sin   L 2  g cos   Using (7), (8) can be rewritten as below: 1 g   cos   x  sin  L L To represent the energy of overhead crane, E (q, q ) is given as below: E  q, q   1 T q M  q  q  m p gL(1  cos  )  0 2 (9) (10) (11) (12) 2.2. Proposed control laws The purpose of this paper is to control trolley’s position from initial position to desired position xd while the sway angle of load convergences to zero. Tracking error is defined as: e(t )  x  xd .Our purpose is to install these control laws on digital background. Because the control laws designation is shown detail in [1], [2] so we just introduce these mathematical structure of controller again. a. PD control law in [1]  k x  k p e F d (13) kE b. PD combined with E 2 control law in [1] k  ( , )  kd x  k p e  v m( ) F k kE E  v m( ) (14) c. PD combined with E 2 - kinetic energy compensation control law in [1]  kd x  k p e  kv ((  ,   m p sin  cos  x ) (15) F k E  kv d. Anti-sway compensation nonlinear control law for overhead crane in [2] F  m    e  2e  f    ( ,) (16)   3. DESIGN MULTI-FUNCTIONS DIGITAL CONTROLLER 3.1. 2D- Overhead crane model in the laboratory Real overhead crane system in the laboratory is shown in figure 2. This overhead crane model has RTG structure that is widely used in the seaports [5]. Crane is designed with its high is 2( m) , its width is 1.6( m) , the length of cable is 1.2( m) , the maximum load is 60( kg ) . Drive motor is asynchronous motor, three 66 L. X. Hai, …, P. X. Minh, “Setting up some non-linear control… in the laboratory.” Nghiên cứu khoa học công nghệ phases, 60 rpm, power 90W, has gear reducer. Driver motor is connected with industry inverter: OMRON 3G3JX. Figure 2. Real overhead crane in the laboratory. 3.2. Hardware of controller The controller is designed based on ATMEGA 32 micro-controller with technique specifications such as: 32Kbyte flash memory, 1Kbyte EEPROM, 2Kbyte SRAM, CPU speed is 16MHz, 2 counter/timer 8 bit, 1 counter/timer 16 bit, 4 PWM channels, 8 ADC 10 bit channels …The RS232 protocol is used to communicate with computer. The value from encoder is transported to controller in hard interrupt mode, the control signal is sent to inverter by adapter intergrated DAC in ATMEGA 32. Using MCP4922 IC to convert from digital control signal to analog control signal to send to inverter. Combined with relay module to control rotation direction of motor. Hardware controller is shown in figure 3 and HMI software is installed on PC. Figure 3. Hardware controller. 3.3. Design software Software designing includes three tasks:  Organize activity for micro-controller control overhead crane. Loop time is fixed: 25ms. Therefore, control loop time is performed by timer interrupt.  Design control program of control algorithms that is introduced in part 2.  Design HMI between controller and PC. In order to improve the performance of actuator for overhead crane, an internal speed control loop is designed and installed in micro-controller. This loop is Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 67 Kỹ thuật điều khiển & Điện tử designed based on overhead crane model that is constructed by experimental approach in [5] as follows: k 0.35124 G ( s)   (17) 1  T1s  (1  T2 s) (1  0.50912s)(1  0.035722s) 3.3.1. Control loop structure Control loop diagram in ATMEGA 32 is shown in figure 5. Read data from Encoder to CPU Communication with PC is implemented The control program is executed Send control signal to the inverter Figure 4. Control loop diagram. 3.3.2. Control program structure Start Adjust measurements value from Encoder Speed controller Observe Choice position controller PD controller PD combined with E2 and kinetic energy compensation controller PD combined with E2 controller Anti sway compensation nonlinear controller Send control signal to inverter End Figure 5. Control program structure. 68 L. X. Hai, …, P. X. Minh, “Setting up some non-linear control… in the laboratory.” Nghiên cứu khoa học công nghệ 4. EXPERIMENT RESULTS 4.1. PD controller Based on transfer function (17) and PD control law (13) combined with processing of collected data, the parameters of this controller are determined as follows: k p  228, kd  3.855, k E  0.01 Figure 6. Real position, control signal, angle of load with desired position is 1m. 2 4.2. PD combined with E controller Based on transfer function (17) and control law (14) combined with processing of collected data, the parameters of this controller are determined as follows: k p  50, kd  0.1253, k E  0.001, kv  50 Figure 7. Real position, control signal, angle of load with desired position is 1m. Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 69 Kỹ thuật điều khiển & Điện tử 4.3. PD combined with E2 and kinetic energy compensation controller Based on transfer function (17) and control law (15) combined with processing of collected data, the parameters of this controller are determined as follows: k p  50, kd  1.253, k E  0.001, kv  50 Figure 8. Real position, control signal, angle of load with desired position is 1m. 4.4. Anti-sway nonlinear controller The parameters of this controller are updated during experimental process. Collected data is sent to micro-controller then calculated and displayed on HMI screen. Figure 9. Real position, control signal, angle of load with desired position is 1m. 70 L. X. Hai, …, P. X. Minh, “Setting up some non-linear control… in the laboratory.” Nghiên cứu khoa học công nghệ Table 1. Performance of controllers comparison. Performance of controller Controller Settling time Overshoot Sway angle of load 17s 2% From -0.1 0.07 deg to PD combined with E2 controller 17s < 1% From -0.2 0.17 deg to PD combined with E2 – kinetic energy compensation controller 16s < 1% From -0.15 to 0.15 deg anti-sway compensation nonlinear controller 16s ≈ 0% From -0.18 to 0.17 deg PD controller 5. CONCLUSIONS The experimental results in the laboratory are shown that applicability of introduced controller in fact. Basic disadvantages is that settling time is long. In the near future, we are going to research other methods to resolve this problem. REFERENCES [1]. Y.Fang, E.Zergeroglu, W.E.Dixon, and D.M.Dawson, “Nonlinear Coupling Control Laws for an Overhead Crane System”.Proceedings of the 2001 IEEE International Conference on Control Applications, 2001, pp 639-644. [2]. Dongkyoung Chwa và Keum-Shik Hong, ”Nonlinear Control of 3-D Overhead Cranes: ENERGY-BASED DECOUPLING”.IFAC Proceedings Volumes16th IFAC World Congress, 2005, pp 275–280. [3]. Y. Fang, E.Zergeroglu, W.E.Dixon, and D.M.Dawson, ” Nonlinear Coupling Control Laws for an Underactuated Overhead Crane System”.IEEE/ASME TRANSACTIONS MECHATRONICS, VOL 8, NO.3, SEP. 2003, pp 418423. [4]. H.Chen, Y.Fang, N.Sun: “A Novel Emergency Braking Method with Payload Swing Suppression for Overhead Crane Systems”. ISNN 2016, LNCS 9719,pp. 242-249, 2016. [5]. Le Xuan Hai, Nguyen Van Thai, Bui Trong Duong, Vu Thi Thuy Nga, Thai Huu Nguyen, Phan Xuan Minh: “Implementation of a laboratory overhead crane control system”, Tạp chí NCKH-CNQS, số 44, tháng 8, năm 2016. Tạp chí Nghiên cứu KH&CN quân sự, Số 45, 10 - 2016 71 Kỹ thuật điều khiển & Điện tử [6]. Nguyễn Doãn Phước, Phan Xuân Minh, Hán Thành Trung, “Lý thuyết điều khiển phi tuyến”, Nhà xuất bản khoa học kỹ thuật, 2008. [7]. Nguyễn Doãn Phước “ Phân tích và điều khiển hệ phi tuyến”, Nhà xuất bản Bách khoa, 2012. TÓM TẮT CÀI ĐẶT MỘT SỐ THUẬT TOÁN ĐIỀU KHIỂN PHI TUYẾN TRÊN NỀN KỸ THUẬT SỐ CHO HỆ CẦN CẨU TREO 2D TRONG PHÒNG THÍ NGHIỆM Trong bài báo này, một số thuật toán điều khiển phi tuyến đã kiểm chứng qua mô phỏng được cài đặt trên vi điều khiển ATMEGA 32 cho hệ cần cẩu treo 2D trong phòng thí nghiệm nhằm đánh giá khả năng ứng dụng thực tế của các giải thuật này và tạo ra một công cụ nghiên cứu thực tiễn cho sinh viên chuyên ngành Điều khiển Tự động. Phần mềm của bộ điều khiển số này có cấu trúc mở để tăng thêm khả năng cài đặt thử nghiệm các giải thuật điều khiển mới và có giao diện người máy thân thiện trên máy tính cá nhân. Từ khóa: Vi điều khiển ATMEGA 32, Cần cẩu treo, Luật PD, luật E2, Luật PD kết hợp E2, Luật điều khiển phi tuyến bù chống lắc. Nhận bài ngày 12 tháng 08 năm 2016 Hoàn thiện ngày 25 tháng 10 năm 2016 Chấp nhận đăng ngày 26 tháng 10 năm 2016 Address: 1 Department of Automatic Control, School of Electrical Engineering, Ha Noi University of Science and Technology; 2 Department of Electrical, Hanoi University of Industry. * Email: xhaicuwc.edu.vn@gmail.com 72 L. X. Hai, …, P. X. Minh, “Setting up some non-linear control… in the laboratory.”
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