Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (6): 1982-1989.doi: 10.13229/j.cnki.jdxbgxb20200600

Previous Articles    

Moving horizon linear quadratic regulator control for ball and plate system with input constraints

Guang-xin HAN1(),Ju-le ZHAO2,Yun-feng HU3   

  1. 1.College of Information and Control Engineering，Jilin Institute of Chemical Technology，Jilin 132022，China
    2.College of Electrical Engineering，Northeast Electric Power University，Jilin 132011，China
    3.College of Communication Engineering，Jilin University，Changchun 130022，China
  • Received:2020-08-10 Online:2021-11-01 Published:2021-11-15

RICH HTML

 0   

PDF (PC)

103

Abstract:

This paper studies the trajectory tracking control of ball and plate system with actuator dynamic being considered. To realize precise trajectory tracking control, three steps are included as following. Firstly, according to the target trajectory, the feedforward control and target state are obtained using differential flatness technology. Secondly, tracking error system is established according to the target state and then a moving horizon Linear-Quadratic Regulator (LQR) controller is designed based on one of three fundamental principles of model predictive control. Thirdly, considering the practical constraints of control inputs, the target controller is achieved by solving Linear Matrix Inequalities（LMIs） under the condition of variable elliptic domain limits. Simulation results show that the closed-loop system has good trajectory tracking performance, steady state performance and robust performance under input constraints.

Key words: automatic control technology, ball and plate system, input constraints, differential flat, moving horizon linear quadratic regulator （LQR） control, variable elliptic domain limits

CLC Number: 

  • TP273

Fig.1

Quanser ball & plate experiment equipment"

Fig.2

Principle figure of direct servo system"

Fig.3

Comparing results before andafter model simplification"

Fig.4

Tracking of plum-type trajectory"

Fig.5

Trajectory tracking error"

Fig.6

Deviation of track tracking after amplification"

Fig.7

Control input of Moving horizon LQR"

Fig.8

Trajectory tracking under internal disturbance"

Fig.9

Trajectory tracking under external disturbance"

1 Huang Jiang-shuai, Wen Cang-yun, Wang Wei, et al. Global stable tracking control of underactuated ships with input saturation[J]. Systems & Control Letters, 2015, 85: 1-7.
2 Shojaei K.Neural adaptive robust control of underactuated marine surface vehicles with input saturation[J]. Applied Ocean Research, 2015, 53: 267-278.
3 陈谋, 杨青运, 周砚龙, 等. 近空间飞行器鲁棒受限控制技术[M]. 北京:国防工业出版社,2017.
4 Wang Chen, Han Guang-xin. Variable structure PID control of four-tank system with input constaints[C]∥2018 International Conference on New Material and Intelligent Manufacturing, Jilin, China, 2018: 377-380.
5 于树友, 常欢, 孟凌宇, 等. 基于扰动观测器的轮式移动机器人滚动时域路径跟踪控制[J]. 吉林大学学报: 工学版, 2021, 51(3):1097-1105.
Yu Shu-you, Chang Huan, Meng Ling-yu, et al. Disturbance observer based moving horizon control for path following problems of wheeled mobile robots[J]. Journal of Jilin University (Engineering and Technology Edition), 2021, 51(3): 1097-1105.
6 Shaojaei K. Observer-based neural adaptive formation control of autonomous surface vessels with limited torque[J]. Robotics & Autonomous Systems, 2016, 78(C): 83-96.
7 Sun Ming-xiao, Luan Tian-tian, Liang Li-hua. RBF neural network compensation-based adaptive control for lift-feedback system of ship fin stabilizers to improve anti-rolling effect[J]. Ocean Engineering, 2018, 163(1): 307-321.
8 孙丽颖, 王新, 白锐. 考虑输入约束的半主动悬架非线性自适应控制[J]. 控制与决策, 2018, 33(11): 2099-2103.
Sun Li-ying, Wang Xin, Bai Rui. Nonlinear adaptive control for semi-active suspension with input constraints[J]. Control and Decision, 2018, 33(11): 2099-2103.
9 韩光信, 胡云峰. 轮式机器人执行机构动态跟踪优化控制研究[J]. 计算机仿真, 2016, 33(12): 300-304.
Han Guang-xin, Hu Yun-feng. Study on actuator dynamics tracking optimization control of wheeled mobile robots[J]. Computer Simulation, 2016, 33(12): 300-304.
10 曹洋洋, 林意, 王智博, 等. 基于双曲正切函数约束的时间序列建模表示[J]. 计算机工程与应用, 2018, 54(18): 82-89.
Cao Yang-yang, Lin Yi, Wang Zhi-bo, et al. Time series modeling representation based on hyperbolic tangent function constraints[J]. Computer Engineering and Applications, 2018, 54(18):82-89.
11 Chen Hao-lan, Zhou Jun, Zhou Min, et al. Nussbaum gain adaptive control scheme for moving mass reentry hypersonic vehicle with actuator saturation[J]. Aerospace Science and Technology, 2019, 91: 357-371.
12 Zhang Li-li, Chen Bing, Lin Chong. Adaptive neural consensus tracking control for a class of 2-order multi-agent systems with nonlinear dynamics[J]. Neurocomputing, 2020, 404: 84-92.
13 Koksal N, An H, Fidan B. Backstepping-based adaptive control of a quadrotor UAV with guaranteed tracking performance[J]. ISA Transactions, 2020, 105: 98-110.
14 翟晨汐,李洪兴.板球系统的直接自适应模糊滑模控制[J]. 计算机仿真, 2016, 33(2): 383-388, 432.
Zhai Chen-xi, Li Hong-xing. Direct adaptive fuzzy sliding mode control for ball and plate system[J], Computer Simulation, 2016,33(2): 383-388, 432.
15 张英慧. 板球系统自适应控制算法与实验研究[D]. 长春:吉林大学通信工程学院, 2013.
Zhang Ying-hui. On the adaptive control algorithm and experimentation of ball and plate system[D]. Changchun:College of Communication, Jilin University, 2013.
16 韩京元, 田彦涛, 孔英秀, 等. 板球系统自适应解耦滑模控制[J]. 吉林大学学报:工学版, 2014, 44(3): 718-725.
Han Jing-yuan, Tian Yan-tao, Kong Ying-xiu, et al. Adaptive decoupled sliding mode control for the ball and plate system [J]. Journal of Jilin University (Engineering and Technology Edition), 2014, 44(3): 718-725.
17 Didier H, Simone N, Mohab S E D. SPECTRA—a maple library for solving linear matrix inequalities in exact arithmetic[J]. Optimization Methods and Software, 2017, 34(1): 62-78.
18 鲜永菊,扶坤荣,吴周青,等.一个新三维混沌系统及其自适应滑模同步控制[J].重庆邮电大学学报:自然科学版, 2020, 32(2): 278-286.
Xian Yong-ju, Fu Kun-rong, Wu Zhou-qing,et al. A new 3-D chaotic system and its adaptive sliding mode synchronization control[J]. JJournal of Chongqing University of Posts and Telecommunications(Natural Science Edition),2020, 32(2): 278-286.
19 曹伟,徐凤霞,张剑飞,等.网络控制系统中迭代学习控制算法的鲁棒收敛性分析[J].重庆邮电大学学报:自然科学版,2020,32(1):15-22.
Cao Wei, Xu Feng-xia, Zhang Jian-fei,et al. Robust convergence of iterative learning control for networked control systems[J]. Journal of Chongqing University of Posts and Telecommunications(Natural Science Edition), 2020, 32(1): 15-22.
20 刘志林, 张军, 原新. 复杂系统的应用鲁棒预测控制[M]. 北京:电子工业出版社,2017.
21 赵聚乐, 韩光信. 基于粒子群优化的板球系统双闭环滑模控制[J]. 吉林化工学院学报, 2020, 37(1):63-67.
Zhao Ju-le, Han Guang-xin. Double closed loop sliding mode control of ball and plate system based on particle swarm optimization[J]. Journal of Jilin Institute of Chemical Technology, 2020, 37(1): 63-67.
[1] Shu-you YU,Huan CHANG,Ling-yu MENG,Yang GUO,Ting QU. Disturbance observer based moving horizon control for path following problems of wheeled mobile robots [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(3): 1097-1105.
[2] Ai-guo WU,Jun-qing HAN,Na DONG. Adaptive sliding mode control based on ultra⁃local model for robotic manipulator [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(5): 1905-1912.
[3] Wei WANG,Jian-ting ZHAO,Kuan-rong HU,Yong-cang GUO. Trajectory tracking of robotic manipulators based on fast nonsingular terminal sliding mode [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(2): 464-471.
[4] Fu LIU,Yi AN,Bo DONG,Yuan-chun LI. Decentralized energy guaranteed cost decentralized optimal control of reconfigurable robots based on ADP [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 342-350.
[5] Xing-tian QU,Xue-xu WANG,Hui-chao SUN,Kun ZHANG,Long-wei YAN,Hong-yi WANG. Fuzzy self⁃adaptive PID control for fused deposition modeling 3D printer heating system [J]. Journal of Jilin University(Engineering and Technology Edition), 2020, 50(1): 77-83.
[6] Miao-miao MA,Jun-jun PAN,Xiang-jie LIU. Model predictive load frequency control of microgrid with electrical vehicles [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(5): 1644-1652.
[7] Shu⁃you YU,Lei TAN,Wu⁃yang WANG,Hong CHEN. Control of active four wheel steering vehicle based ontriple⁃step method [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(3): 934-942.
[8] Hai⁃ying WEN,Xiang REN,Wei⁃liang XU,Ming CONG,Wen⁃long QIN,Shu⁃hai HU. Bionic design and experimental test of temporomandibular joint for masticatory robot [J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(3): 943-952.
[9] GU Wan-li,WANG Ping,HU Yun-feng,CAI Shuo,CHEN Hong. Nonlinear controller design of wheeled mobile robot with H∞ performance [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1811-1819.
[10] LI Zhan-dong,TAO Jian-guo,LUO Yang,SUN Hao,DING Liang,DENG Zong-quan. Design of thrust attachment underwater robot system in nuclear power station pool [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(6): 1820-1826.
[11] WANG De-jun, WEI Wei-li, BAO Ya-xin. Actuator fault diagnosis of ESC system considering crosswind interference [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(5): 1548-1555.
[12] YAN Dong-mei, ZHONG Hui, REN Li-li, WANG Ruo-lin, LI Hong-mei. Stability analysis of linear systems with interval time-varying delay [J]. Journal of Jilin University(Engineering and Technology Edition), 2018, 48(5): 1556-1562.
[13] TIAN Yan-tao, ZHANG Yu, WANG Xiao-yu, CHEN Hua. Estimation of side-slip angle of electric vehicle based on square-root unscented Kalman filter algorithm [J]. 吉林大学学报(工学版), 2018, 48(3): 845-852.
[14] ZHANG Shi-tao, ZHANG Bao, LI Xian-tao, WANG Zheng-xi, TIAN Da-peng. Enhancing performance of FSM based on zero phase error tracking control [J]. 吉林大学学报(工学版), 2018, 48(3): 853-858.
[15] WANG Lin, WANG Hong-guang, SONG Yi-feng, PAN Xin-an, ZHANG Hong-zhi. Behavior planning of a suspension insulator cleaning robot for power transmission lines [J]. 吉林大学学报(工学版), 2018, 48(2): 518-525.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright © Journal of Jilin University(Engineering and Technology Edition), All Rights Reserved.
Tel: +86-431-85095297　Fax: +86-431-85094074　E-mail: xbgxb@jlu.edu.cn
Powered by Beijing Magtech Co. Ltd