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Stability and convergence analysis of direct adaptive inverse control. (English) Zbl 1380.93150

Summary: In adaptive inverse control (AIC), adaptive inverse of the plant is used as a feed-forward controller. Majority of AIC schemes estimate controller parameters using the indirect method. Direct Adaptive Inverse Control (DAIC) alleviates the adhocism in adaptive loop. In this paper, we discuss the stability and convergence of DAIC algorithm. The computer simulation results are presented to demonstrate the performance of the DAIC. Laboratory scale experimental results are included in the paper to study the efficiency of DAIC for physical plants.

MSC:

93C40 Adaptive control/observation systems
93B40 Computational methods in systems theory (MSC2010)
93B35 Sensitivity (robustness)
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[1] Shafiq, M.; Shafiq, M. A., Direct adaptive inverse control, IEICE Electronics Express, 6, 5, 223-229 (2009) · doi:10.1587/elex.6.223
[2] Widrow, B.; Walach, E., Adaptive inverse control: a signal processing approach, Englewood Cliffs, NJ, USA: Prentice-Hall, Englewood Cliffs, NJ, USA
[3] Astrom, K. J.; Wittenmark, B., Adaptive Control (1994), Boston, MA, USA: Addison-Wesley Longman publishing Co. Inc, Boston, MA, USA · Zbl 0217.57903
[4] Landau, Y. D., Adaptive Control: The Model Reference Approach (1979), New |York, NY, USA: Marcel Dekker Inc., New |York, NY, USA · Zbl 0475.93002
[5] Widrow, B.; Bilello, M., Adaptive Inverse Control, Proceedings of the International symposium on Intelligent Control, IEEE
[6] Widrow, B.; Plett, G. L., Adaptive inverse control based on linear and nonlinear adaptive filtering, Proceedings of the International workshop on neural networks for Identification, Control, Robotics, and Signal Image processing, IEEE
[7] Widrow, B.; Plett, G. L., Nonlinear adaptive inverse control, Proceedings of the Decision and Control, IEEE
[8] Hizal, N. A., Improved adaptive model control, ARI—An International Journal for Physical and Engineering Sciences, 51, 181-190 (1999)
[9] Plett, G. L., Adaptive inverse control of linear and nonlinear systems using dynamic neural networks, IEEE Transactions on Neural Networks and Learning Systems, 14, 2, 360-376 (2003) · doi:10.1109/TNN.2003.809412
[10] Plett, G. L., Adaptive inverse control of unmodeled stable SISO and MIMO linear systems, International Journal of Adaptive Control and Signal Processing, 16, 4, 243-272 (2002) · Zbl 1048.93058 · doi:10.1002/acs.698
[11] Shafiq, M.; AL-Sunni, F. M.; Farooq, S. O., Adaptive control of nonlinear hammerstein model using NLMS filter, Proceedings of the International Conference on Electronics, Circuits and Systems, IEEE
[12] Salman, R., Neural networks of adaptive inverse control systems, Applied Mathematics and Computation, 163, 2, 931-939 (2005) · Zbl 1100.68604 · doi:10.1016/j.amc.2004.04.019
[13] Ming, L.; Cheng, Y.; Yu, S., An improved nonlinear adaptive inverse control systems based on filtered-\(ϵ\) LMS algorithm, Proceedings of the Chinese control conference, IEEE
[14] Anderson, B. D. O.; Dehghani, A., Challenges of adaptive control-past, permanent and future, Annual Reviews in Control, 32, 2, 123-135 (2008) · doi:10.1016/j.arcontrol.2008.06.001
[15] Karshenas, A. M.; Dunnigan, M. W.; Williams, B. W., Adaptive inverse control algorithm for shock testing, IEE Proceedings Control Theory and Applications, 147, 3, 267-276 (2000) · doi:10.1049/ip-cta:20000166
[16] Dias, F. M.; Mota, AM., Direct inverse control of a kiln, Proceedings of the Direct inverse control of a kiln
[17] Shafiq, M., Internal model control structure using adaptive inverse control strategy, ISA Transactions®, 44, 3, 353-362 (2005) · doi:10.1016/S0019-0578(07)60209-2
[18] Du, G.; Zhan, X.; Zhang, W.; Zhong, S., Improved filtered-\(ε\) adaptive inverse control and its application on nonlinear ship maneuvering, Journal of Systems Engineering and Electronics, 17, 4, 788-792 (2006) · Zbl 1158.93407 · doi:10.1016/S1004-4132(07)60017-6
[19] Wang, X.; Shen, T.; Wang, W., An approach for echo cancellation system based on improved, Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing, IEEE
[20] Ryu, B.-S.; Lee, J.-K.; Kim, J.; Lee, C.-W., The performance of an adaptive noise canceller with DSP processor, Proceedings of the 40th Southeastern Symposium on System Theory, IEEE · doi:10.1109/SSST.2008.4480186
[21] Shubao, S.; Siyang, S.; Nan, C.; Minglong, X., Structure and control strategy for a piezoelectric inchworm actuator equipped with MEMS ridges, Sensors and Actuators A: Physical, 264, 9, 40-50 (2017)
[22] Gang, S.; Xiang, L.; Zhencai, Z.; Yu, T.; Weidong, Z.; Shanzeng, L., Acceleration tracking control combining adaptive control and off-line compensators for six-degree-of-freedom electro-hydraulic shaking tables, ISA Transactions, 70, 9, 322-337 (2017)
[23] Astrom, K. J.; Wittenmark, B., Computer controlled systems: theory and design (1996), Prentice-Hall
[24] Astrom, K. J.; Hagander, P.; Sternby, J., Zeros of sampled systems, Proceedings of the IEEE Conference on Decision and Control including the Symposium on Adaptive Processes, IEEE
[25] Ishitobi, M., Properties of zeros of a discrete-time system with fractional order hold, Proceedings of the IEEE Conference on Decision and Control, IEEE · Zbl 1279.35049
[26] Bai, E. W.; Dasgupta, S., A minimal k-step delay controller for robust tracking of non-minimum phase systems, Proceedings of the IEEE Conference on Decision and Control, IEEE
[27] Wang, X.; Chen, D., Causal inversion of non-minimum phase systems, Proceedings of the IEEE Conference on Decision and Control, IEEE
[28] Yao, J.; Wang, X.; Hu, S.; Fu, W., Adaline neural network-based adaptive inverse control for an electro-hydraulic servo system, Journal of Vibration and Control, 17, 13, 2007-2014 (2011) · doi:10.1177/1077546310395972
[29] Ahmed, M.; Lachhab, N.; Svaricek, F., Non-model based adaptive control of electro-hydraulic servo systems using prefilter inversion, Proceedings of the 9th International Multi-Conference on Systems, Signals and Devices (SSD), IEEE · doi:10.1109/SSD.2012.6197984
[30] Shafiq, M. A., Predicting the compressive strength of concrete using neural network and kernel ridge regression, Proceedings of the Future Technologies Conference (FTC), IEEE · doi:10.1109/FTC.2016.7821698
[31] Shafiq, M. A., Direct adaptive inverse control of nonlinear plants using neural networks, Proceedings of the Future Technologies Conference (FTC), IEEE · doi:10.1109/FTC.2016.7821699
[32] Shafiq, M.; Shafiq, M. A.; Ahmed, N., Closed loop direct adaptive inverse control for linear plants, The Scientific World Journal, 2014 (2014) · doi:10.1155/2014/658497
[33] Slock, D. T. M., On the Convergence Behavior of the LMS and the Normalized LMS Algorithms, IEEE Transactions on Signal Processing, 41, 9, 2811-2825 (1993) · Zbl 0800.94093 · doi:10.1109/78.236504
[34] Bershad, N. J., Analysis of the normalized LMS algorithm with gaussian inputs, IEEE Transactions on Signal Processing, 34, 4, 793-806 (1986) · doi:10.1109/TASSP.1986.1164914
[35] Smith Julius, O. (2007), W3K Publishing
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