Guaranteed Cost Preview and Repetitive Control for Uncertain Linear Discrete Time-Delay Systems

doi:10.16182/j.issn1004731x.joss.19-0617

Abstract

Abstract: For a class of uncertain linear discrete time-delay systems, a design method for guaranteed cost preview and repetitive controller is proposed . By introducing a repetitive controller in the forward channel to improve the tracking accuracy of the system, L-order difference operators are used to construct an augmented error system that contains preview information but does not include time delay, and the design problem of guaranteed cost preview and repetitive controller is converted into an output feedback adjustment problem. Using the Lyapunov stability theory and the linear matrix inequality method, the sufficient conditions for guaranteeing the asymptotic stability of the closed-loop system are obtained. A numerical simulation is presented to illustrate the validity of the proposed method.

Key words: discrete time-delay system, preview control, repetitive control, guaranteed cost, linear matrix inequality

CLC Number:

Lan Yonghong, He Jinlin. Guaranteed Cost Preview and Repetitive Control for Uncertain Linear Discrete Time-Delay Systems[J]. Journal of System Simulation, 2021, 33(3): 529-538.

References

[1] Liu Z X, Lu S.Stabilization Analysis for Discrete-Time Systems with Time Delay[J]. Applied Mathematics and Computation (S0096-3003), 2010, 216(7): 2024-2035.
[2] 孙俊娜. 不确定线性时滞系统的鲁棒容错控制[D]. 沈阳: 东北大学, 2011.
Sun Junna.Robust Fault-tolerant Control for UncertainLinear Time-delay Systems[D]. Shenyang: Northeastern University, 2011.
[3] Zhou B.Input Delay Compensation of Linear Systems with both State and Input Delays by Nested Prediction[J]. Automatica (S0005-1098), 2014, 50(5): 1434-1443.
[4] Liao Y L, Liao F C.Design of Preview Controller for Linear Continuous-time Systems with Input Delay[J]. International Journal of Control, Automation, and Systems (S1598-6446), 2018, 16(3): 1080-1090.
[5] 廖福成, 江上正, 土谷武士, 等. 一般型数字最优预见伺服系统的设计[J]. 应用数学和力学, 1996, 17(5): 405-417.
Liao Fucheng, Egami Tadashi, Tsuchiga Takeshi, et al.On General Type of Digital Optimal Preview Servo System[J]. Applied Mathematics and Mechanics, 1996, 17(5): 405-417.
[6] Zhen Z Y.Research Development in Preview Control Theory and Applications[J]. Acta Astronautica (S0094-5765), 2016, 42(2): 172-188.
[7] Wu P, Wu W.Walking Pattern Generation of Dual-arm Mobile Robot Using Preview Controller[J]. Research Journal of Applied Science, Engineering and Technology (S1388-0764), 2012, 4(20): 4098-4104.
[8] 李相儒, 米根锁. 基于最优预见控制的高速列车速度控制器研究[J]. 测控技术, 2019, 38(3): 144-148.
Li Xiangru, Mi Gensuo.Study on Speed Controller of High Speed Train Based on Optimal Preview Control[J]. Measurement & Control Technology, 2019, 38(3): 144-148.
[9] Hui P, Yan W, Xu Z, et al.Robust State-feedback Control Design for Active Suspension System with Time-varying Input Delay and Wheelbase Preview Information[J]. Journal of the Franklin Institute (S0016-0032), 2019, 24(8): 145-155.
[10] 廖福成, 苏晓洁, 廖永龙. 不确定离散时滞系统的H_∞保性能预见控制[J]. 工程科学学报, 2016, 38(7): 1008-1016.
Liao Fucheng, Su Xiaojie, Liao Yonglong.Preview Control of H_∞ Guarantee Performance for Uncertain Discrete Time-Delay Systems[J]. Journal of Engineering Science, 2016, 38(7): 1008-1016.
[11] Wang C R, Wu H N.Off-Policy Reinforcement Learning for Optimal Preview Tracking Control of Linear Discrete-Time systems with Unknown Dynamics[C]// 2018 Chinese Automation Congress (CAC). IEEE, 2018, 65(8): 1402-1407.
[12] Johannes N S, Fabian C.Preview H_∞ Control of a Hybrid Suspension System[J]. IFAC Papers On Line (S0123-4265), 2019, 52(5): 456-468.
[13] Liao F, Li L.Robust Preview Control for Uncertain Discrete-time Systems based on LMI[J]. Optim Control Appl Meth (S0143-2087), 2017, 44(5): 22-32.
[14] 游志青, 胡育文. 采用重复控制技术的逆变器仿真研究[J]. 机械制造与自动化, 2002, 15(3): 37-40.
You Zhiqing, Hu Yuwen.Research on Inverter Simulation Using Repeated Control Technology[J]. Machinery Manufacturing & Automation, 2002, 15(3): 37-40.
[15] Rodriguez H, Pons J L, Ceres R A.ZPET-Repeptitive Speed Controller for Ultrasonic Motors[J]. Proc. of the IEEE International Conference on Robotics and Automation, 2016, 4(3): 3654-3659.
[16] Federico C, Alessandro M.A Stability Analysis Based on Dissipativity of Linear and Nonlinear Repetitive Control[J]. Engineering with Computers (S0177-0667), 2019, 52(2): 325-339.
[17] 季传坤, 钱俊兵. 基于重复滑膜控制PMSM的矢量控制系统[J]. 电子科技, 2019, 32(1): 52-57.
Ji Chuankun, Qian Junbing.Vector Control System Based on Repetitive Synovial Control PMSM[J]. Electronic Science and Technology, 2019, 32(1): 52-57.
[18] Wang X H, Pan Z F, Thi T G H. New Repetitive Current Controller for PWM Rectifier[J]. Journal of Electrical Engineering (S1300-0632), 2018, 51(4): 45-56.
[19] Yuan S G, Zhou B, Ye Q, et al.Discrete-time Repetitive Control Systems Design Method based on Two-dimensional Model[J]. Natural Science (S1875-5100), 2012, 38(1): 60-65.
[20] 唐巍, 张春来. 最优预见重复控制及其稳定条件[J]. 舰载武器, 1999, 25(1): 38-48.
Tang Wei, Zhang Chunlai.Optimal Foreseeable Repeated Control and Its Stability Conditions[J]. Shipborne Weapons, 1999, 25(1): 38-48.
[21] Yoshiro H.New LMI-based Conditions for Preview Feedforward Synthesis[J]. Control Engineering Practice (S0967-0661), 2019, 21(5): 90-95.
[22] Flores J V, Pereira L F A, Bonan G, et al. A Systematic Approach for Robust Repetitive Controller Design[J]. Control Engineering Practice (S0967-0661), 2016, 54(2): 214-222.
[23] Chang X H, Zhang L, Park J H.Robust Static Output Feedback H_∞ Control for Uncertain Fuzzy Systems[J]. Fuzzy Sets and Systems (S0165-0114), 2015, 45(2): 87-104.
[24] Nasiri A, Nguang S K, Swain A, et al.Robust Output Feedback Controller Design of Discrete-time Takagi-Sugeno Fuzzy Systems: a Non-monotonic Lyapunov Approach[J]. Applied Mathematical Modelling (S0307-904X), 2016, 10(5): 545-553.
[25] 付成宏, 吴敏, 何勇, 等. 基于二维模型的保性能离散重复控制系统设计[J]. 系统工程与电子技术, 2012, 12(8): 1685-1690.
Fu Chenghong, Wu Min, He Yong, et al.Design of Guaranteed Performance Discrete Repetitive Control System Based on Two-Dimensional Model[J]. Systems Engineering and Electronics, 2012, 12(8): 1685-1690.