Position control for ball and beam under linear algorithms

MINISTRY OF EDUCATION AND TRAINING HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING CAPSTONE PROJECT AUTOMATION AND CONTROL ENGINEERING POSITION CONTROL FOR BALL AND BEAM UNDER LINEAR ALGORITHMS LECTURER: NGUYEN VAN DONG HAI, PhD STUDENT: PHAM VAN CHINH HOANG DUY TAN SKL 0 Ho Chi Minh City, December 2022 HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION FACULTY FOR HIGH QUALITY TRAINING  GRADUATION THESIS POSITION CONTROL FOR BALL AND BEAM UNDER LINEAR ALGORITHMS Students: PHAM VAN CHINH 18151005 HOANG DUY TAN 18151034 Major: AUTOMATION AND CONTROL ENGINEERING Advisor: Nguyen Van Dong Hai, PhD Ho Chi Minh city, December 29, 2022 SOCIALIST REPUBLIC OF VIETNAM Independence-Freedom-Happiness ****** Ho Chi Minh City, December 29, 2022 SUBJECT PROJECT ASSIGNMENT Student name: Pham Van Chinh Student ID: 18151005 Student name: Hoang Duy Tan Student ID: 18151034 Major: Automation and control engineering Class: 18151CLA Advisor: PhD Nguyen Van Dong Hai Date of assignment: 6/9/2022 Date of submission: 30/12/2022 Project title: Position control for Ball and Beam system under linear algorithms Initial materials: They are provided by the advisor Content of the project: Calculation of the dynamical equation of the Ball and Beam system Simulating the ball and beam system on matlab Calculating the dynamics equation of the engine to apply to the real model Model building: Select hardware, select motor, H-bridge, 12V DC Power, Ball Run the PID algorithm: select the appropriate PID parameter Run the LQR algorithm: calculate the LQR and select the Q, R matrix values Optimize PID and LQR by GA algorithm Simulation and verification on real models Final product: Ball and Beam system in real model Graduation report book CHAIR OF THE PROGRAM ADVISOR (Sign with full name) (Sign with full name) SOCIALIST REPUBLIC OF VIETNAM Independence-Freedom-Happiness ****** Ho Chi Minh City, December 29, 2022 ADVISOR’S EVALUATION SHEET Student name: Pham Van Chinh Student ID: 18151005 Student name: Hoang Duy Tan Student ID: 18151034 Major: Automation and control engineering Class: 18151CLA Advisor: PhD Nguyen Van Dong Hai Project title: Position control for Ball and Beam system under linear algorithms EVALUATION Content of the project: Strengths: Weaknesses: Approval for oral defense? (Approved or denied) Overall evaluation: (Excellent, Good, Fair, Poor) Mark: …………….(in words: ) Ho Chi Minh City, December 29, 2022 ADVISOR (Sign with full name) SOCIALIST REPUBLIC OF VIETNAM Independence-Freedom-Happiness ****** Ho Chi Minh City, December 29, 2022 EVALUATION SHEET OF DEFENSE COMMITTEE MEMBER Student name: Pham Van Chinh Student ID: 18151005 Student name: Hoang Duy Tan Student ID: 18151034 Major: Automation and control engineering Class: 18151CLA Project title: Position control for Ball and Beam system under linear algorithms Name of Defense Committee Member: EVALUATION Content and workload of the project: Strengths: Weaknesses: Overall evaluation: (Excellent, Good, Fair, Poor): Mark: ……………….(in words: ) Ho Chi Minh City, December 29, 2022 COMMITTEE MEMBER (Sign with full name) GRADUATION THESIS Disclaimer Students hereby declare that this is my own research work and is under the scientific guidance of PhD Nguyen Van Dong Hai The research contents and results in this topic are honest and have not been published in any form before If I find any fault, I will take full responsibility for the content of my graduation thesis Ho Chi Minh City University of Technology and Education is not related to copyright and copyright infringements (if any) caused by me during the implementation Ho Chi Minh City, December 29, 2022 STUDENTS i GRADUATION THESIS Acknowledgements At the beginning, our group would like to express our sincere thanks to the teacher - PhD Nguyen Van Dong Hai for directly guiding us to carry out the graduation project, he enthusiastically guided,encouraged us throughout the process of implementing the topic and creating favorable conditions for us to successfully complete the graduation project Our group would also like to express our sincere thanks and deep gratitude to the teachers of the University of Technology Education, especially the teachers of the Faculty of High Quality Training for creating conditions for our group have time to projects Finally, our team would like to wish the teachers good health, success in their teaching path and bring many values to the next generations ii GRADUATION THESIS Table of Contents Disclaimer i Acknowledgements ii Table of Contents iii ABBRIVIATION vi Symbols vi Meaning vi B&b system vi Ball and beam system vi LQR vi Linear-Quadratic Regulator vi PID vi Proportional Integral Derivative vi List of Figures vii List of Tables x CHAPTER INTRODUCTION 1.1 Necessary 1.2 Overview 1.2.1 Decription about B&b system 1.2.2 Model and research completed over the world 1.3 Target 1.4 Approach 1.5.Research Methods 1.6 Research subjects CHAPTER 2: THEORETICAL BASIC AND SOLUTION CONTROL 2.1.1 Decription 2.1.2 Analyze and build mathematical models 2.1.3 Analyze and build mathematical models of motor 2.2 LQR Algorithm 11 2.2.1 Conception 11 2.2.2 LQR design 12 2.3 PID Controller 13 2.3.4 Integrated Controller 17 2.3.5 Stability 17 iii CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL The system illustrate the good respondent with the set point when trying to track and reach the setpoint with the low time Square wave control GA-PID parameter: Kp_ball 68.1334 Kd_ball 23.9348 Ki_ball Kp_beam 81.9487 Kd_beam 2.4819 Ki_beam Fig 28 Square wave control GA-PID result 5.3.1 GA-PID vs GA-LQR in real model Fig 29 Result of GA-LQR simulation 76 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL State steady error, State steady time and Undershoot respectively: State steady error 0.0116( m) Settling time 3.148( s ) Undershoot 0% From Fig 24 and Fig 30, it can be seen that the steady state error of GA-PID is smaller than that of GA-LQR, and the settling time of GA-LQR is larger than that of GA-PID 5.4 Filter survey In the experimental control system, we easily encounter the case of noise occurring Students get ADC noise when reading the position of the ball on the beam Filters are required to reduce system noise 5.4.1 Median filter Parameters using median filter in combination with PD: Median filter Kp_ball Kd_ball Kp_beam Kd_beam 15 62.3080 44.8061 95.2322 7.1875 The standard parameters of the PD combined with the median filter produces the Fig 30 result: Fig 30 Result of median filter (standard median filter) State steady error, State steady time and Undershoot respectively: • State steady error: 0.0187 (m) • State steady time: 7.283 (s) • Undershoot: 23.99% Parameters when increasing median filter: 77 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL Median filter Kp_ball Kd_ball Kp_beam Kd_beam 25 62.3080 44.8061 95.2322 7.1875 The system generates the outcomes indicated in Fig 31 when the median filter is raised (equal 25) from the starting values shown in Fig 30: Fig 31 Result of median filter (increase median filter) State steady error, State steady time and Undershoot respectively: • State steady error: 0.0008 (m) • State steady time: 5.265 (s) • Undershoot: 29.55% Parameters when increasing median filter: Median filter Kp_ball Kd_ball Kp_beam Kd_beam 35 62.3080 44.8061 95.2322 7.1875 Keep the PD parameters unchanged and keep increasing the median filter to 35, the result is shown in Fig 32: Fig 32 Result of median filter (increase median filter) 78 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL State steady error, State steady time and Undershoot respectively: • State steady error: 0.0154 (m) • State steady time: 4.254 (s) • Undershoot: 31.92% Parameters when increasing median filter: Median filter Kp_ball Kd_ball Kp_beam Kd_beam 45 62.3080 44.8061 95.2322 7.1875 Maintaining the PD parameters while raising the median filter to 45 yields the result displayed in Fig 33: Fig 33 Result of median filter (increase median filter) State steady error, State steady time and Undershoot respectively: • State steady error: (m) • State steady time: 3.758 (s) • Undershoot: 22.5% Parameters when increasing median filter: Median filter Kp_ball Kd_ball Kp_beam Kd_beam 55 62.3080 44.8061 95.2322 7.1875 The result shown in Fig 34 is obtained by maintaining the PD parameters and increasing the median filter to 45: 79 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL Fig 34 Result of median filter (increase median filter) State steady error, State steady time and Undershoot respectively: • State steady error: 0.01 (m) • State steady time: 4.542 (s) • Undershoot: 38.96% With the same control law, the same controller and the same model, the median filter gives positive results on each metric: with a low parameter filter (25), the filter gives the result : time When the number of filter values is increased, the median helps to filter out the system noises, making the system work more accurately and reducing the steady-state time and reaching the optimal level (median filter = 45) the system gives an accurate result when the steady-state error is approximately zero, and the setup time is also reduced compared with filters with a lower filter range But if the filter range is selected 5.4.2 Lowpass filter Change the parameters of the pass band filter and the result is as shown in Fig 35: Fig 35 Result of changing the pass band lowpass filter 80 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL The outcome is as indicated in Fig 36 when the parameters of the stop band filter are changed: Fig 36 Result of changing the stop band lowpass filter The result of altering the parameters of the ripple filter is shown in Fig Fig 37: Fig 37 Result of changing the ripple lowpass filter Fig 38 depicts what happens when the parameters of the atennuation filter are changed: 81 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL Fig 38 Result of changing the atennuation lowpass filter If the pass band filter is too low, it will filter out the desired signal, the signals will be interrupted and there will be jumps due to the signal loss Increasing the stop band increases the system's response, reducing the transport delay time for better system performance, faster setup and smaller fluctuations The system allow the signal with the frequency higher than the signal attenuation pass Cause the noise can be random number, sometimes number can repeat regularly , to prevent that the higher attenuation can chosen but the sinal can not exceeding the frequency of ball position when it reaches state steady set point 5.5 Interface To control and monitor the system process, students program an interface to that The figure below is the system monitoring and control interface: Fig 39 The interface to observe the operation of system 82 CHAPTER BUILDING THE CONTROLLERS ON THE REAL MODEL (1) (2) (3) (4) It contains the name of the connected port and the desired Baud rate of the port Connect and disconnect Setpoint setting, run and stop system Interface for monitoring a system 5.6 Compare PID with PID-GA The difference between Fig 20 and Fig 21 clearly shows that the effect of GA is very large for the PID controller when finding good parameters gives positive results in almost the whole system is complete The feedback signals of the system have a large positive reflection as the steady-state error decreases from 0.0541(m) (Fig 20) to 0.0371(m) (Fig 21) and 0.0094(m) (Fig 22) and both the settling time was also significantly improved when it takes from 7,589(s) (Fig 20) to reach balanced state to only 2,544(s) (Fig 21) and 2.402(s) (Fig 22) 83 CHAPTER CONCLUSION CHAPTER 6: CONCLUSION 6.1 Conclusion Through the project, it can be seen that the LQR, PID and GA control methods are capable of stably controlling The Ball and Beam system with Deviated Axis Algorithms can control and balance the ball on the beam almost exactly This demonstrates high applicability in real-world applications The parameters in the control algorithm between the real model and the simulation not seem to be the same In the real model, there will be many problems of friction, noise due to many internal and external influences, and the processing ability of microcontrollers, motors, and H-bridges, Before building the real model, students will simulate first to ensure that the algorithms can be applied to this model After successful simulation, students will proceed to make a real model and adjust the parameters to suitable the model 6.2 Improvement The development direction of students is to continue to improve the problems of hardware as well as control algorithms to make the model more complete, and at the same time apply a new algorithm that combines fuzzy and neural control (fuzzy neural control (FNC)) to demonstrate the feasibility of the algorithm and optimize the system For sensor could be substitute by Ultrasonic sensors to reduce noise, which usually happens with the high frequency cause by the ball move out of the beam, help to improve performent The advance algorithms can be applied to the system such as Adaptive Control because in the process of researching the parameters of the system always change, with them the response can be fit with the different states CHAPTER CONCLUSION REFERENCES [1] D P B M P R D R D K Vipulkumar D Jadhav, Design and Implementation of Ball and Beam Control System, International Journal of Innovative Research in Science, Engineering and Technology [2] G B.-B Carlos G Bolívar-Vincenty, Modelling the Ball-and-Beam System, from Newtonian Mechanics and from Lagrange Methods., Twelfth [3] F A Salem, "Mechatronics Design of Ball and Beam System," pp Education and Research ISSN 2224-5774 (Paper) ISSN 2225-0492 (Online), Vol.3, No.4, 2013 [4] Quanser, Quanser, Ball and Beam, Experiment Quanser Consulting, 1991 [5] N V D Hai, XÂY DỰNG BỘ ĐIỀU KHIỂN NHÚNG TUYẾN TÍNH HĨA VÀO RA CHO HỆ XE CON LẮC NGƯỢC, HCM, 2011 [6] H T HOANG, HỆ THỐNG ĐIỀU KHIỂN THÔNG MINH, HCM: ĐẠI HỌC QUỐC GIA THÀNH PHỒ HCM, 2006 [7] L W Yakov Frayman, A dynamically-constructed fuzzy neural controller for direct model reference adaptive control of multi-input-multi-output nonlinear processes, Soft Computing, Springer Nature,, 2002 [8] A F J A M M H A a Mohammad Keshmiri, MODELING AND CONTROL OF BALL AND BEAM SYSTEM, 2012 [9] D M T V D D H T N N M H N V D H N T O Nguyen Minh Tam, Method of Sliding mode control for Ball and Beam systems, HCM: HCM University of Technology and Education, 2016 APPENDIX APPENDIX Appendix 1: Ball and beam system control source code using Matlab Simulink State diagram: Fig 15 Code diagram Appendix 2: Pinout, datasheet and specification of motor Pinout of stepper motor: Fig 3.16: Nema 17 stepper motor 86 APPENDIX The datasheet of the stepper motor: Fig 17 Nema 17 specifications Fig 18 Torque holding of nema 17 Fig 19 DC motor jgb37-520 87 APPENDIX Fig 20 Table testing Jgb37-520 Fig 21 Servo Motor Jgb37-520 wiring diagram Appendix 3: Real life shape and working principle of Ultra sonic sensor HC SR04 Fig 22 Ultra sonic sensor HC SR04 88 APPENDIX The ultrasonic sensor SR04 uses the principle of ultrasonic wave reflection The sensor consists of modules.1 module emitting ultrasonic waves and module receiving reflected ultrasonic waves The sensor will first emit an ultrasonic wave with a frequency of 40khz If there is an obstacle in the way, the ultrasonic wave will reflect back and affect the receiving module By measuring the time from transmitting to receiving waves, we will calculate the distance from the sensor to the obstacle 89 S K L 0