Pseudo-downsampled iterative learning control
Bin Zhang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorCorresponding Author
Danwei Wang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore===Search for more papers by this authorKeliang Zhou
School of Electrical Engineering, Southeast University, Nanjing 210096, China
Search for more papers by this authorYongqiang Ye
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorYigang Wang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorBin Zhang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorCorresponding Author
Danwei Wang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore===Search for more papers by this authorKeliang Zhou
School of Electrical Engineering, Southeast University, Nanjing 210096, China
Search for more papers by this authorYongqiang Ye
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorYigang Wang
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, Singapore
Search for more papers by this authorAbstract
In this paper, a simple and effective multirate iterative learning control (ILC), referred as pseudo-downsampled ILC, is proposed to deal with initial state error. This scheme downsamples the tracking error and input signals collected from the feedback control system before they are used in the ILC learning law. The output of the ILC is interpolated to generate the input for the next cycle. Analysis shows that the exponential decay of the tracking error can be expected and convergence condition can be ensured by downsampling. Other advantages of the proposed pseudo-downsampled ILC include no need for a filter design and reduction of memory size and computation. Experimental results demonstrate the effectiveness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.
REFERENCES
- 1 Lee H-S, Bien Z. A note on convergence property of iterative learning controller with respect to sup norm. Automatica 1997; 33(8): 1591–1593.
- 2 Hillenbrand S, Pandit M. An iterative learning controller with reduced sampling rate for plant with variations of initial states. International Journal of Control 2000; 73: 882–889.
- 3 Moore KL. An observation about monotonic convergence of discrete-time, P-type iterative learning control. IEEE Symposium on Intelligence Control, Mexico, 2001; 45–49.
- 4 Longman RW. Iterative learning control and repetitive control for engineering practice. International Journal of Control 2000; 73(10): 930–954.
- 5 Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic System 1984; 1: 123–140.
- 6 Lee KH, Bien Z. Initial condition problem of learning control. IEE Proceedings—D 1991; 138: 525–528.
- 7 Zhang B, Wang D, Ye Y. Cutoff-frequency phase-in ILC to overcome initial position offsets. Proceedings of the IEEE International Conference on Control Applications, Taiwan, 2004; 983–988.
- 8 Chang C-K, Longman RW, Phan MQ. Techniques for improving transients in learning control systems. Advances in Astronautical Sciences 1992; 76: 2035–2052.
- 9 Park K-H, Bien Z. A study on iterative learning control with adjustment of learning interval for monotone convergence in the sense of sup-norm. Asian Journal of Control 2002; 4: 111–118.
10.1111/j.1934-6093.2002.tb00337.x Google Scholar
- 10 Zhang B, Wang D, Ye Y, Wang Y, Zhou K. Two-mode ILC with pseudo-downsampled learning in high frequency range. International Journal of Control 2007; 80: 349–362.
- 11 Ratcliffe J, Lewin P, Rogers E. Stable iterative learning control using cubic splines. Proceedings of the UKACC International Control Conference, Glasgow, Scotland, U.K., August 2006.
- 12 Ratcliffe J, Hatonnen J, Lewin P, Rogers E, Harte T, Owens D. P-type iterative learning control for systems that contain resonance. International Journal of Adaptive Control and Signal Processing 2005; 19: 769–796.
- 13 Ratcliffe J, Hatonnen J, Lewin P, Rogers E, Owens D. Repetitive control of synchronized operations for process applications. International Journal of Adaptive Control and Signal Processing 2007; 21(4): 300–325.
- 14 Heinzinger G, Fenwick D, Paden B, Miyazaki F. Stability of learning control with disturbances and uncertain initial conditions. IEEE Transactions on Automatic Control 1992; 37: 110–114.
- 15 Arimoto S, Naniwa T, Suzuki H. Robustness of P-type learning control with a forgetting factor for robot motions. Proceedings of the 29th Conference on Decision and Control, Honolulu, HI, U.S.A., December 1990; 2640–2645.
- 16 Saab SS. On the P-type learning control. IEEE Transactions on Automatic Control 1994; 39: 2298–2302.
- 17 Wang D. Convergence and robustness of discrete time nonlinear systems with iterative learning control. Automatica 1998; 34: 1445–1448.
- 18 Wang D. On D-type and P-type ILC designs and anticipatory approach. International Journal of Control 2000; 73: 890–901.
- 19 Sun M, Wang D. Iterative learning control with initial rectifying action. Automatica 2002; 38: 1177–1182.
- 20 Chen Y, Wen C, Xun J-X, Sun M. Initial state learning method for iterative learning control of uncertain time-varying systems. Proceedings of the 35th IEEE Conference on Decision and Control, vol. 4, Kobe, Japan, December 1996; 3996–4001.
- 21 Chen Y, Wen C, Gong Z, Sun M. An iterative learning controller with initial state learning. IEEE Transactions on Automatic Control 1999; 44: 371–376.
- 22 Kuc T-Y, Lee JS, Nam K. An iterative learning control theory for a class of nonlinear dynamic systems. Automatica 1992; 28: 1215–1221.
- 23 Owens DH. Iterative learning control—convergence using high gain feedback. Proceedings of the Conference on Decision and Control, Arizona, 1992; 2515–2546.
- 24 Lee H-S, Bien Z. Study on robustness of iterative learning control with non-zero initial error. International Journal of Control 1997; 64: 345–359.
- 25 Park K-H, Bien Z. A generalized iterative learning controller against initial state error. International Journal of Control 2000; 73(10): 871–881.
- 26 Elci H, Phan M, Longman RW, Juang J-N, Ugoletti R. Experiments in the use of learning control for maximum precision robot trajectory tracking. in Proceedings on Information Science and Systems, NJ, U.S.A., 1994; 951–958.
- 27 Sadegh N, Hu A, James C. Synthesis, stability analysis, and experimental implementation of a multirate repetitive learning controller. Journal of Dynamic Systems, Measurement, and Control—Transactions of the ASME 2002; 124: 668–674.
- 28 Longman RW, Wirkander S-L. Automated tuning concepts for iterative learning and repetitive control laws. Proceedings of the 37th CDC, FL, U.S.A., 1998; 192–198.
- 29 Zhang B, Wang D, Ye Y. Wavelet transform based frequency tuning ILC. IEEE Transactions on System, Man, and Cybernetics, Part B 2005; 35: 107–114.
- 30 Tomizuka M. Zero phase error tracking algorithm for digital control. Journal of Dynamic Systems, Measurement, and Control 1987; 109: 65–68.