Research Papers

Design and Analysis for Uncertain Repetitive Control Systems With Unknown Disturbances

[+] Author and Article Information
R. Sakthivel

Department of Mathematics,
Bharathiar University,
Coimbatore 641046, India
e-mail: krsakthivel@yahoo.com

K. Raajananthini

Department of Mathematics,
Anna University-Regional Campus,
Coimbatore 641046, India
e-mail: rjnanthini@gmail.com

P. Selvaraj

Department of Mathematics,
Anna University-Regional Campus,
Coimbatore 641046, India
e-mail: selvamath89@gmail.com

Y. Ren

Department of Mathematics,
Anhui Normal University,
Wuhu 241000, China
e-mail: brightry@hotmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 15, 2017; final manuscript received June 20, 2018; published online July 23, 2018. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(12), 121007 (Jul 23, 2018) (10 pages) Paper No: DS-17-1193; doi: 10.1115/1.4040663 History: Received April 15, 2017; Revised June 20, 2018

In this paper, the periodic tracking problem is considered for a class of continuous system with uncertainty, time-varying delay, and unknown bounded external disturbances. To be precise, in order to attenuate the unknown disturbance effectively, the equivalent-input-disturbance (EID) approach is incorporated into the developed algorithm. Then, the sufficient conditions that guarantee the asymptotic tracking performance of the system understudy are established based on the Lyapunov stability theorem. More precisely, Schur complement and free-weighting matrix approach are utilized to derive the main results. Moreover, the proposed EID-based modified repetitive controller (MRC) not only rejects the unknown external disturbance but also deals with the dead zone effect. Finally, two simulation examples are presented to verify the superiority of the proposed EID-based repetitive controller over the conventional repetitive controller.

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Costa-Castello, R. , Olm, J. M. , and Ramos, G. A. , 2011, “ Design and Analysis Strategies for Digital Repetitive Control Systems With Time-Varying Reference/Disturbance Period,” Int. J. Control, 84(7), pp. 1209–1222. [CrossRef]
Niu, B. , Karimi, H. R. , Wang, H. , and Liu, Y. , 2017, “ Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method,” IEEE Trans. Syst. Man Cybern. Syst., 47(7), pp. 1371–1382. [CrossRef]
Zhou, Q. , Wang, L. , Wu, C. , Li, H. , and Du, H. , 2017, “ Adaptive Fuzzy Control for Nonstrict-Feedback Systems With Input Saturation and Output Constraint,” IEEE Trans. Syst. Man Cybern. Syst., 47(1), pp. 1–12. [CrossRef]
Zhou, L. , and She, J. , 2015, “ Design of a Robust Output-Feedback-Based Modified Repetitive-Control System,” Int. J. Syst. Sci., 46(5), pp. 808–817. [CrossRef]
Fedele, G. , and Ferrise, A. , 2016, “ On the Uncertainty on the Phase of a Stable Linear System in the Periodic Disturbance Cancellation Problem,” IEEE Trans. Autom. Control, 61(9), pp. 2720–2726. [CrossRef]
Jafari, S. , Ioannou, P. , Fitzpatrick, B. , and Wang, Y. , 2015, “ Robustness and Performance of Adaptive Suppression of Unknown Periodic Disturbances,” IEEE Trans. Autom. Control, 60(8), pp. 2166–2171. [CrossRef]
Chen, X. , and Tomizuka, M. , 2014, “ New Repetitive Control With Improved Steady-State Performance and Accelerated Transient,” IEEE Trans. Control Syst. Technol., 22(2), pp. 664–675. [CrossRef]
Sun, M. X. , Yu, L. J. , and He, H. G. , 2013, “ Discrete Adaptive Repetitive Control: Convergence Analysis and Implementation,” Acta Autom. Sin., 39(4), pp. 400–406. [CrossRef]
Chung, C. H. , and Chen, M. S. , 2012, “ A Robust Adaptive Feed Forward Control in Repetitive Control Design for Linear System,” Automatica, 48(1), pp. 183–190. [CrossRef]
Kurniawan, E. , Cao, Z. , and Man, Z. , 2014, “ Design of Robust Repetitive Control With Time-Varying Sampling Periods,” IEEE Trans. Ind. Electron., 61(6), pp. 2834–2841. [CrossRef]
Joo, Y. , Park, G. , Back, J. , and Shim, H. , 2015, “ Embedding Internal Model in Disturbance Observer With Robust Stability,” IEEE Trans. Autom. Control, 61(10), pp. 3128–3133. [CrossRef]
Guo, B. Z. , and Zhou, H. C. , 2015, “ The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance,” IEEE Trans. Autom. Control, 60(1), pp. 143–157. [CrossRef]
Na, J. , Grino, R. , Costa-Castello, R. , Ren, X. , and Chen, Q. , 2010, “ Repetitive Controller for Time-Delay Systems Based on Disturbance Observer,” IET Control Theory Appl., 4(11), pp. 2391–2404. [CrossRef]
Song, J. , Song, S. , Guo, Y. , and Zhou, H. , 2015, “ Nonlinear Disturbance Observer-Based Fast Terminal Sliding Mode Guidance Law With Impact Angle Constraints,” Int. J. Innovative Comput. Inf. Control, 11(3), pp. 787–802. http://www.ijicic.org/ijicic-14-06012.pdf
Hao, R. , Wang, J. , Zhao, J. , and Wang, S. , 2016, “ Observer-Based Robust Control of 6-DOF Parallel Electrical Manipulator With Fast Friction Estimation,” IEEE Trans. Autom. Sci. Eng., 13(3), pp. 1399–1408. [CrossRef]
Li, J. , Ren, H. P. , and Zhong, Y. R. , 2015, “ Robust Speed Control of Induction Motor Drives Using First-Order Auto-Disturbance Rejection Controllers,” IEEE Trans. Ind. Appl., 51(1), pp. 712–720. [CrossRef]
Flores, J. L. , Avalos, J. L. B. , Ramirez, H. S. , and Ordaz, M. A. C. , 2012, “ Robust Passivity-Based Control of a Buckboost-Converter/DC-Motor System: An Active Disturbance Rejection Approach,” IEEE Trans. Ind. Appl., 48(6), pp. 2362–2371. [CrossRef]
Mendez, A. H. , Flores, J. L. , Ramirez, H. S. , Castellanos, J. F. G. , and Aguilar, G. M. , 2017, “ A Backstepping Approach to Decentralized Active Disturbance Rejection Control of Interacting Boost Converters,” IEEE Trans. Ind. Appl., 53(4), pp. 4063–4072. [CrossRef]
Li, C. X. , Gu, G. Y. , Yang, M. J. , and Zhu, L. M. , 2017, “ High-Speed Tracking of a Nanopositioning Stage Using Modified Repetitive Control,” IEEE Trans. Autom. Sci. Eng., 14(3), pp. 1467–1477. [CrossRef]
Zhao, S. , and Gao, Z. , 2014, “ Modified Active Disturbance Rejection Control for Time-Delay Systems,” ISA Trans., 53(4), pp. 882–888. [CrossRef] [PubMed]
Ahn, C. K. , Shi, P. , and Basin, M. V. , 2015, “ Two-Dimensional Dissipative Control and Filtering for Roesser Model,” IEEE Trans. Autom. Control, 60(7), pp. 1745–1759. [CrossRef]
Wu, M. , Xu, B. , Cao, W. , and She, J. , 2014, “ Aperiodic Disturbance Rejection in Repetitive-Control Systems,” IEEE Trans. Control Syst. Technol., 22(3), pp. 1044–1051. [CrossRef]
She, J. , Fang, M. X. , Ohyama, Y. , Hashimoto, H. , and Wu, M. , 2008, “ Improving Disturbance-Rejection Performance Based on an Equivalent-Input-Disturbance Approach,” IEEE Trans. Ind. Electron., 55(1), pp. 380–389. [CrossRef]
Zhou, L. , She, J. , Wu, M. , He, Y. , and Zhou, S. , 2014, “ Estimation and Rejection of Aperiodic Disturbance in a Modified Repetitive-Control System,” IET Control Theory. Appl., 8(10), pp. 882–889. [CrossRef]
Yang, X. , Wu, L. , Lam, H. K. , and Su, X. , 2014, “ Stability and Stabilization of Discrete-Time T-S Fuzzy Systems With Stochastic Perturbation and Time-Varying Delay,” IEEE Trans. Fuzzy Syst., 22(1), pp. 124–138. [CrossRef]
Li, H. , Jing, X. , and Karimi, H. R. , 2014, “ Output-Feedback-Based H Control for Vehicle Suspension Systems With Control Delay,” IEEE Trans. Ind. Electron., 61(1), pp. 436–446. [CrossRef]
Samidurai, R. , Manivannan, R. , Ahn, C. K. , and Karimi, H. R. , 2018, “ New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays,” IEEE Trans. Syst. Man Cybern. Syst., 48(4), pp. 485–499. [CrossRef]
Zeng, H. B. , He, Y. , Wu, M. , and She, J. , 2015, “ Free-Matrix Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay,” IEEE Trans. Autom. Control, 60(10), pp. 2768–2772. [CrossRef]
Li, H. , Wang, J. , Lam, H. K. , Zhou, Q. , and Du, H. , 2016, “ Adaptive Sliding Mode Control for Interval Type-2 Fuzzy Systems,” IEEE Trans. Syst. Man Cybern. Syst., 46(12), pp. 1654–1663. [CrossRef]
Lam, H. K. , 2012, “ Stabilization of Nonlinear Systems Using Sampled-Data Output-Feedback Fuzzy Controller Based on Polynomial-Fuzzy-Model-Based Control Approach,” IEEE Trans. Syst. Man Cybern., Part B, 42(1), pp. 258–267. [CrossRef]
Li, Y. X. , and Yang, G. H. , 2017, “ Robust Adaptive Fault-Tolerant Control for a Class of Uncertain Nonlinear Time Delay Systems,” IEEE Trans. Syst. Man Cybern. Syst., 47(7), pp. 1554–1563. [CrossRef]
Su, X. , Shi, P. , Wu, L. , and Basin, M. V. , 2014, “ Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems,” IEEE Trans. Cybern., 44(12), pp. 2470–2483. [CrossRef] [PubMed]
Na, J. , Ren, X. , Costa-Castello, R. , and Guo, Y. , 2014, “ Repetitive Control of Servo Systems With Time Delays,” Rob. Auton. Syst., 62(3), pp. 319–329. [CrossRef]
Li, J. , and Yue, H. , 2015, “ Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems With Unknown Time-Varying Delays,” Appl. Math. Comput., 256, pp. 514–528.
Sakthivel, R. , Mathiyalagan, K. , and Marshal Anthoni, S. , 2012, “ Robust Stability and Control for Uncertain Neutral Time Delay Systems,” Int. J. Control, 85(4), pp. 373–383. [CrossRef]
Kwon, O. M. , Park, M. J. , Park, J. H. , Lee, M. , and Cha, E. J. , 2013, “ Analysis on Robust H Performance and Stability for Linear Systems With Interval Time-Varying State Delays Via Some New Augmented Lyapunov-Krasovskii Functional,” Appl. Math. Comput., 224, pp. 108–122.
Tong, S. , Zhang, L. , and Li, Y. , 2016, “ Observed-Based Adaptive Fuzzy Decentralized Tracking Control for Switched Uncertain Nonlinear Large-Scale Systems With Dead Zones,” IEEE Trans. Syst. Man Cybern. Syst., 46(1), pp. 37–47. [CrossRef]
Medvedeva, I. V. , and Zhabko, A. P. , 2015, “ Synthesis of Razumikhin and Lyapunov-Krasovskii Approaches to Stability Analysis of Time-Delay Systems,” Automatica, 51, pp. 372–377. [CrossRef]
Liu, R. J. , Liu, G. P. , Wu, M. , She, J. , and Nie, Z. Y. , 2014, “ Robust Disturbance Rejection in Modified Repetitive Control System,” Syst. Control Lett., 70, pp. 100–108. [CrossRef]
Zhou, L. , She, J. , and Wu, M. , 2014, “ A One-Step Method of Designing an Observer-Based Modified Repetitive-Control System,” Int. J. Syst. Sci., 46(14), pp. 2617–2627. [CrossRef]
Zhou, L. , She, J. , Wu, M. , and He, Y. , 2013, “ Design of a Robust Observer-Based Modified Repetitive-Control System,” ISA Trans., 52(3), pp. 375–382. [CrossRef] [PubMed]
Wu, M. , Zhou, L. , and She, J. , 2011, “ Design of Observer-Based Robust Repetitive-Control System,” IEEE Trans. Autom. Control, 56(6), pp. 1452–1457. [CrossRef]
Weiss, G. , and HaKfele, M. , 1999, “ Repetitive Control of MIMO Systems Using H Design,” Automatica, 35(7), pp. 1185–1199. [CrossRef]
Seuret, A. , and Gouaisbaut, F. , 2013, “ Wirtinger-Based Integral Inequality: Application to Time-Delay Systems,” Automatica, 49(9), pp. 2860–2866. [CrossRef]
Mathiyalagan, K. , Park, J. H. , Sakthivel, R. , and Marshal Anthoni, S. , 2014, “ Delay Fractioning Approach to Robust Exponential Stability of Fuzzy Cohen-Grossberg Neural Networks,” Appl. Math. Comput., 230, pp. 451–463.
Zhou, L. , She, J. , and Zhou, S. , 2014, “ A 2D System Approach to the Design of a Robust Modified Repetitive-Control System With a Dynamic Output-Feedback Controller,” Int. J. Appl. Math. Comput. Sci., 24(2), pp. 325–334. [CrossRef]
She, J. , Makino, K. , Ouyang, L. , and Hashimoto, H. , 2014, “ Estimation of Normalized Longitudinal Force for an Electric Cart Using Equivalent-Input-Disturbance Approach,” IEEE Trans. Veh. Technol., 63(8), pp. 3642–3650. [CrossRef]
She, J. , Xin, X. , and Pan, Y. , 2011, “ Equivalent-Input-Disturbance Approach-Analysis and Application to Disturbance Rejection in Dual-Stage Feed Drive Control System,” IEEE Trans. Mechatronics, 16(2), pp. 330–340. [CrossRef]


Grahic Jump Location
Fig. 1

Block diagram of the EID-based MRC system

Grahic Jump Location
Fig. 3

State responses for uncertain system in the presence of disturbance without EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 4

State responses for uncertain system in the presence of disturbance with EID: (a) tracking performance of closed-loop system with EID (9) and (b) error

Grahic Jump Location
Fig. 5

Simulation results for uncertain system in the presence of dead-zone without EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 6

Simulation results for uncertain system in the presence of dead-zone with EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 7

Simulation result for different r(t) with T = 4

Grahic Jump Location
Fig. 8

Tracking error of the system with EID-based controller and disturbance observer based controller in Ref. [13]: (a) the output of the system y(t) with EID-based controller and disturbance observer based controller in Ref. [13], the reference input r(t) and (b) error



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