Feedback approach to design fast iterative learning controller for a class of time-delay systems

The design of a fast iterative learning controller for a class of linear time-varying continuous systems with multiple time delays is discussed. A feedback iterative learning control (ILC) scheme is considered from the point of view of the two-dimensional (2D) system. To this end, a time-varying 2D error system is developed in the form of the continuous-discrete Roesser model, and its solution is summarised in terms of norm inequality. Based on this 2D error system, a sufficient convergence criterion is provided to ensure that the feedback ILC scheme drives the output tracking error to zero after just one iteration. Furthermore, by exploiting some prediction results with an observer, a new ILC scheme is derived only using feedforward controllers, which can equivalently achieve the learning performance of the feedback ILC scheme. The simulation results show that the proposed ILC schemes can provide fast updating laws to improve the tracking performance of the control systems.

[1]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[2]  Suguru Arimoto,et al.  Bettering operation of Robots by learning , 1984, J. Field Robotics.

[3]  S. Bhattacharyya,et al.  Iterative learning for trajectory control , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[4]  R. Carroll,et al.  Two-dimensional model and algorithm analysis for a class of iterative learning control systems , 1990 .

[5]  Tae-Yong Kuc,et al.  An iterative learning control of robot manipulators , 1991, IEEE Trans. Robotics Autom..

[6]  D. Owens.  Iterative learning control-Convergence using high gain feedback , 1992, Proceedings of the 1992 IEEE International Symposium on Intelligent Control.

[7]  J. Kurek,et al.  Iterative learning control synthesis based on 2-D system theory , 1993, IEEE Trans. Autom. Control..

[8]  D. Owens.  Universal iterative learning control using adaptive high-gain feedback , 1993 .

[9]  M. Phan,et al.  Discrete frequency based learning control for precision motion control , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[10]  Chong-Ho Choi,et al.  Iterative learning control in feedback systems , 1995, Autom..

[11]  Jian-Xin Xu,et al.  Current iteration tracking error assisted iterative learning control of uncertain nonlinear discrete-time systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  Y. Chen,et al.  A robust high-order P-type iterative learning controller using current iteration tracking error , 1997 .

[13]  Yangquan Chen,et al.  Analysis of a high-order iterative learning control algorithm for uncertain nonlinear systems with state delays , 1998, Autom..

[14]  Dong-Hwan Hwang,et al.  Design of an iterative learning controller for a class of linear dynamic systems with time-delay , 1998 .

[15]  Yong Fang,et al.  An iterative learning control method for continuous-time systems based on 2-D system theory , 1998 .

[16]  Tommy W. S. Chow,et al.  Iterative Learning Control of Linear Discrete-Time Multivariable Systems , 1998, Autom..

[17]  Eric Rogers,et al.  Analysis of Linear Iterative Learning Control Schemes - A 2D Systems/Repetitive Processes Approach , 2000, Multidimens. Syst. Signal Process..

[18]  Richard W. Longman,et al.  Iterative learning control and repetitive control for engineering practice , 2000 .

[19]  Hikaru Inooka,et al.  Prediction-based Iterative Learning Control (PILC) for Uncertain Dynamic Nonlinear Systems Using System Identification Technique , 2000, J. Intell. Robotic Syst..

[20]  Mingxuan Sun,et al.  Iterative Learning Control Design for Uncertain Dynamic Systems with Delayed States , 2000 .

[21]  Mingxuan Sun,et al.  Initial condition issues on iterative learning control for non-linear systems with time delay , 2001, Int. J. Syst. Sci..

[22]  K. Moore,et al.  An observation about monotonic convergence in discrete-time, P-type iterative learning control , 2001, Proceeding of the 2001 IEEE International Symposium on Intelligent Control (ISIC '01) (Cat. No.01CH37206).

[23]  Optimal hedging point control for a failure-prone manufacturing system , 2001 .

[24]  Samer S. Saab,et al.  A discrete-time stochastic learning control algorithm , 2001, IEEE Trans. Autom. Control..

[25]  Mingxuan Sun,et al.  Closed‐loop iterative learning control for non‐linear systems with initial shifts , 2002 .

[26]  Hikaru Inooka,et al.  Experience-Based Iterative Learning Controllers for Robotic Systems , 2002, J. Intell. Robotic Syst..

[27]  Svante Gunnarsson,et al.  Time and frequency domain convergence properties in iterative learning control , 2002 .

[28]  Hikaru Inooka,et al.  A Learning Control for a Class of Linear Time Varying Systems Using Double Differential of Error , 2003, J. Intell. Robotic Syst..

[29]  Jay H. Lee,et al.  Iterative learning control-based batch process control technique for integrated control of end product properties and transient profiles of process variables , 2003 .

[30]  Kevin L. Moore,et al.  Monotonic convergent iterative learning controller design based on interval model conversion , 2005, IEEE Transactions on Automatic Control.

[31]  An open-closed-loop PID-type iterative learning control algorithm for uncertain time-delay systems , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[32]  Kevin L. Moore,et al.  Monotonically convergent iterative learning control for linear discrete-time systems , 2005, Autom..

[33]  Tommy W. S. Chow,et al.  Iterative learning control for linear time-variant discrete systems based on 2-D system theory , 2005 .

[34]  Tommy W. S. Chow,et al.  2-D system theory based iterative learning control for linear continuous systems with time delays , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  A.G. Alleyne,et al.  A survey of iterative learning control , 2006, IEEE Control Systems.

[36]  Xisheng Zhan.  Application and Design of a Robust Iterative Learning Controller for Uncertain Time-delay Systems , 2006, 2006 IEEE International Conference on Information Acquisition.

[37]  Zhi Wang,et al.  An iterative learning controller for reduction of repetitive runout in disk drives , 2006, IEEE Transactions on Control Systems Technology.

[38]  Gong-You Tang,et al.  PD-type iterative learning control for nonlinear time-delay system with external disturbance 1 1 This project was supported by the National Natural Science Foundation of China (60074001) and the Natural Science Foundation of Shandong Province (Y2000G02). , 2006 .

[39]  Kevin L. Moore,et al.  Stability analysis of discrete-time iterative learning control systems with interval uncertainty , 2007, Autom..

[40]  Abdelhamid Tayebi.  Analysis of two particular iterative learning control schemes in frequency and time domains , 2007, Autom..

[41]  Jie Wu,et al.  Robust iterative learning control for uncertain systems with both state and input delay , 2007, 2007 IEEE International Conference on Grey Systems and Intelligent Services.

[42]  Kevin L. Moore,et al.  Iterative Learning Control: Brief Survey and Categorization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[43]  Kevin L. Moore,et al.  A New Arimoto-Type Algorithm to Estimate States for Repetitive Processes: Iterative Learning Observer (ILO) , 2007, 2007 IEEE 22nd International Symposium on Intelligent Control.