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Adaptive Robust Tracker Design for Nonlinear Sandwich Systems Subject to Saturation Nonlinearities

Published online by Cambridge University Press:  22 June 2020

Meysam Azhdari  and
Tahereh Binazadeh Open the ORCID record for Tahereh Binazadeh [Opens in a new window]
Meysam Azhdari
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, P.O. Box 71555-313, Shiraz, Iran
Tahereh Binazadeh*
Affiliation:
Department of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, P.O. Box 71555-313, Shiraz, Iran
*
*Corresponding author. E-mail: binazadeh@sutech.ac.ir
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Summary

This paper addresses the tracking problem for uncertain nonlinear sandwich systems that consist of two nonlinear subsystems and saturation nonlinearity, which is sandwiched between the subsystems. The considered sandwich system is also subject to a nonsymmetric input saturation constraint. Due to the nonsmooth characteristics of sandwiched saturation nonlinearity and also the input saturation function, the design procedure deals with hard challenges. To overcome these difficulties, a recursive approach is suggested that consists of two phases. For the implementation of the proposed approach, a tracking problem is solved in each phase. In the first phase, the second subsystem with sandwiched saturation nonlinearity is considered and the output tracking problem of the desired time-varying reference signal is solved using backstepping method. The outcome of the first phase is the desired reference signal that should be tracked by the first subsystem in the next phase. In the second phase, the robust control input is designed for the first subsystem by employing adaptive sliding mode technique such that, despite the nonsymmetric input saturation constraint, model uncertainty and external disturbances, the output of the first subsystem follows the desired signal that is obtained in the previous phase. The simulation results for a mechanical sandwich system are illustrated to verify the effectiveness of the proposed control method.

Keywords

Saturation nonlinearityNonlinear sandwich systemsBack-stepping approachAdaptive sliding modeLyapunov stabilityRobotic system
Type
Articles
Information
Robotica , Volume 39 , Issue 3 , March 2021 , pp. 452 - 467
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Taware, A. and Tao, G., Control of Sandwich Nonlinear Systems (Springer Science & Business Media, Berlin, Germany, 2003).Google Scholar
Zhou, Z., Tan, Y., Xie, Y. and Dong, R., “State estimation of a compound non-smooth sandwich system with backlash and dead zone,” Mech. Syst. Sig. Process. 83, 439–449 (2017).CrossRefGoogle Scholar
Hamedani, M. H., Zekri, M. and Sheikholeslam, F., “Adaptive impedance control of uncertain robot manipulators with saturation effect based on dynamic surface technique and self-recurrent wavelet Neural Networks,” Robotica 37(1), 161–188 (2019).CrossRefGoogle Scholar
Li, Y.-X. and Yang, G.-H., “Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems with actuator faults and unknown dead zones,” IEEE Trans. Syst., Man, Cyber. Syst. 47(5), 729–740 (2017).CrossRefGoogle Scholar
Zhang, Q., Tan, L. and Xu, G., “Evaluating transient performance of servo mechanisms by analysing stator current of PMSM,” Mech. Syst. Sig. Process. 101, 535–548 (2018).CrossRefGoogle Scholar
Senjyu, T., Kashiwagi, T. and Uezato, K., “Position control of ultrasonic motors using MRAC and dead-zone compensation with fuzzy inference,” IEEE Trans. Power Electron. 17(2), 265–272 (2002).CrossRefGoogle Scholar
Zhou, Z., Tan, Y., Dong, R. and He, H., Non-smooth observer for mechanical systems based on sandwich model with backlash,” International Conference on Intelligent Robotics and Applications, Berlin, Heidelberg (2020) pp. 611–621.Google Scholar
Tan, Y., Dong, R. and Li, R., “Recursive identification of sandwich systems with dead zone and application,” IEEE Trans. Control Syst. Technol. 17(4), 945–951 (2009).Google Scholar
Zhou, Z., Tan, Y., Xie, Y. and Dong, R., “Soft measurement of states of sandwich system with dead zone and its application,” Measurement 78, 219–234 (2016).CrossRefGoogle Scholar
Taware, A., Control of Sandwich Nonlinear Systems Doctoral dissertation (University of Virginia, Charlottesville, VA, 2001).Google Scholar
Choi, H.-S., “Robust control of robot manipulators with torque saturation using fuzzy logic,” Robotica 19(6), 631–639 (2001).CrossRefGoogle Scholar
Jafari, E. and Binazadeh, T., “Modified composite nonlinear feedback control for output tracking of nonstep signals in singular systems with actuator saturation,” Int. J. Robust Nonlinear Control. 28(16), 4885–4899 (2018).CrossRefGoogle Scholar
Edalati, L., Sedigh, A. K., Shooredeli, M. A. and Moarefianpour, A., “Asymptotic tracking control of strict-feedback non-linear systems with output constraints in the presence of input saturation,” IET Control Theory Appl. 12(6), 778–785 (2018).CrossRefGoogle Scholar
Jafari, E. and Binazadeh, T., “Observer-based improved composite nonlinear feedback control for output tracking of time-varying references in descriptor systems with actuator saturation,” ISA Trans. 91, 1–10 (2019).CrossRefGoogle ScholarPubMed
Tarbouriech, S., Queinnec, I. and Prieur, C., “Stability analysis and stabilization of systems with input backlash,” IEEE Trans. Automat. Control 59(2), 488–494 (2014).CrossRefGoogle Scholar
Tarbouriech, S., Prieur, C. and Queinnec, I., “Stability analysis for linear systems with input backlash through sufficient LMI conditions,” Automatica 46(11), 1911–1915 (2010).CrossRefGoogle Scholar
Binazadeh, T. and Bahmani, M., “Design of robust controller for a class of uncertain discrete-time systems subject to actuator saturation,” IEEE Trans. Auto. Control 62(3), 1505–1510 (2019).CrossRefGoogle Scholar
Caverly, R. J., Zlotnik, D. E. and Forbes, J. R., “Saturated control of flexible-joint manipulators using a Hammerstein strictly positive real compensator,” Robotica 34(6), 1367–1382 (2016).CrossRefGoogle Scholar
Jafari, E. and Binazadeh, T., “Robust output regulation in discrete-time singular systems with actuator saturation and uncertainties,” IEEE Trans. Circuits Syst. II: Express Briefs 67(2), 340–344 (2020).CrossRefGoogle Scholar
Wang, X., Stoorvogel, A. A., Saberi, A., Grip, H. F., Roy, S. and Sannuti, P., “Stabilization of a class of sandwich systems via state feedback,” IEEE Trans. Autom. Control 55(9), 2156–2160 (2010).CrossRefGoogle Scholar
Wang, X., Stoorvogel, A. A., Saberi, A., Grip, H. F. and Sannuti, P., “Stabilization of nonlinear sandwich systems via state feedback—Discrete-time systems,” Int. J. Robust Nonlinear Control 21(16), 1841–1864 (2011).CrossRefGoogle Scholar
Stoorvogel, A. A., Wang, X., Saberi, A. and Sannuti, P., Stabilization of sandwich non-linear systems with low-and-high gain feedback design,” IEEE Proceedings of the 2010 American Control Conference, Baltimore, Maryland, USA (2010) pp. 4217–4222.Google Scholar
Grip, H. F., Saberi, A., Stoorvogel, A. A., Wang, X. and Roy, S., Semiglobal stabilization of sandwich systems by dynamic output feedback,” IEEE Proceedings of the 2010 American Control Conference, Baltimore, Maryland, USA (2010) pp. 4229–4234.Google Scholar
Luo, N., Tan, Y. and Dong, R., “Observability and controllability analysis for sandwich systems with -zone,” Int. J. Control Autom. Syst. 14(1), 188–197 (2016).CrossRefGoogle Scholar
Taware, A., Tao, G. and Teolis, C., “Design and analysis of a hybrid control scheme for sandwich nonsmooth nonlinear systems,” IEEE Trans. Autom. Control 47(1), 145–150 (2002).CrossRefGoogle Scholar
Song, J., Zuo, Z. and Ding, Z., “Backstepping control of sandwich-like non-linear systems with deadzone non-linearity,” IET Control Theory Appl. 11(17), 3122–3129 (2017).CrossRefGoogle Scholar
Saberi, A., Stoorvogel, A. A. and Sannuti, P., Internal and External Stabilization of Linear Systems with Constraints (Springer Science & Business Media, Berlin, Germany, 2012).CrossRefGoogle Scholar
Zheng, Y., Wen, C. and Li, Z., “Robust adaptive asymptotic tracking control of uncertain nonlinear systems subject to nonsmooth actuator nonlinearities,” Int. J. Adapt. Control Signal Process 27(1–2), 108–121 (2013).CrossRefGoogle Scholar
Du, H., Shao, H. and Yao, P., “Adaptive neural network control for a class of low-triangular-structured nonlinear systems,” IEEE Trans. Neural Net. 17(2), 509–514 (2006).CrossRefGoogle Scholar
Ma, J., Zheng, Z. and Li, P., “Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation,” IEEE Trans. Cybern. 45(4), 728–741 (2015).CrossRefGoogle ScholarPubMed
Li, Y., Tong, S. and Li, T., “Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation,” Neural Comput. Appl. 23(5), 1207–1216 (2013).CrossRefGoogle Scholar
Ge, S. S. and Wang, J., “Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients,” IEEE Trans. Autom. Control 48(8), 1463–1469 (2003).Google Scholar
Mohammadpour, S. and Binazadeh, T., “Robust adaptive synchronization of chaotic systems with nonsymmetric input saturation constraints,” J. Comput. Nonlinear Dyn. 13(1), 011005 (2018).CrossRefGoogle Scholar
Hao, L.-Y. and Yang, G.-H., “Fault tolerant control for a class of uncertain chaotic systems with actuator saturation,” Nonlinear Dyn. 73(4), 2133–2147 (2013).CrossRefGoogle Scholar
Hu, Q., “Adaptive output feedback sliding-mode -* manoeuvring and vibration control of flexible spacecraft with input saturation,” IET Control Theory Appl. 2(6), 467–478 (2008).CrossRefGoogle Scholar
Levant, A., “Higher-order sliding modes, differentiation, and output-feedback control,” Int. J. Control 76(9–10), 924–941 (2003).CrossRefGoogle Scholar
Pan, Y., Wang, H., Li, X. and Yu, H., “Adaptive command-filtered backstepping control of robot arms with compliant actuators,” IEEE Trans. Control Syst. Technol. 26(3), 1149–1156 (2017).CrossRefGoogle Scholar
Farrell, J. A., Polycarpou, M., Sharma, M. and Dong, W., “Command filtered backstepping,” IEEE Trans. Autom. Control 54(6), 1391–1395 (2009).CrossRefGoogle Scholar
Binazadeh, T. and Shafiei, M., “Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach,” Mechatronics 23(7), 888–892 (2013).CrossRefGoogle Scholar
Shafiei, M. and Binazadeh, T., “Application of partial sliding mode in guidance problem,” ISA Trans. 52(2), 192–197 (2013).CrossRefGoogle ScholarPubMed
Aminsafaee, M. and Shafiei, M.H., “A robust approach to stabilization of 2-DOF underactuated mechanical systems,” Robotica, 1–18. (2020) doi: 10.1017/S0263574720000053.Google Scholar
Shiravani, F. and Shafiei, M.H., “Robust output regulation via sliding mode control and disturbance observer: Application in a forced Van Der Pol chaotic oscillator,” J. Dyn. Syst. Measure. Control 139(9), 091015 (6 pages) (2017).CrossRefGoogle Scholar
Binazadeh, T., Shafiei, M. H. and Rahgoshay, M. A., “Robust stabilization of a class of nonaffine quadratic polynomial systems: Application in magnetic ball levitation system,” J. Comput. Nonlinear Dyn. 10(1), 014501 (4 pages), (2015).CrossRefGoogle Scholar
Khalil, H. K., Nonlinear Control (Pearson, New York, 2015).Google Scholar
Chenarani, H. and Binazadeh, T., “Flexible structure control of unmatched uncertain nonlinear systems via passivity-based sliding mode technique,” Iranian J. Sci. Technol., Trans. Elect. Engin. 41(1), 1–11 (2017).Google Scholar
Yang, Z. and Zhang, H., “A fuzzy adaptive tracking control for a class of uncertain strick-feedback nonlinear systems with dead-zone input,” Neurocomputing 272, 130–135 (2018).CrossRefGoogle Scholar
Chiang, C.-C. and Liu, C.-C., “Output feedback tracking control of uncertain nonlinear systems with non-symmetric dead-zone input,” IEEE International Conference on Fuzzy Systems (2012) pp. 1–8.Google Scholar
Wen, C., Zhou, J., Liu, Z. and Su, H., “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Trans. Autom. Control. 56(7), 1672–1678 (2011).CrossRefGoogle Scholar