Research Papers

Discrete-Time Adaptive Controller Based on Estimated Pseudopartial Derivative and Reaching Sliding Condition

[+] Author and Article Information
Chidentree Treesatayapun

Department of Robotic and Advanced Manufacturing,
Ramos Arizpe 25903, Mexico
e-mails: treesatayapun@gmail.com;

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 18, 2015; final manuscript received March 30, 2016; published online June 8, 2016. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 138(10), 101002 (Jun 08, 2016) (6 pages) Paper No: DS-15-1639; doi: 10.1115/1.4033408 History: Received December 18, 2015; Revised March 30, 2016

An adaptive controller based on sliding mode condition is developed with estimated pseudopartial derivative (PPD) of data-driven scheme. The controlled plant is considered as a class of unknown discrete-time systems with only output feedback, which allows the proposed controller to be applicable for practical plants operated by computerization systems. The convergence of estimated PPD is analyzed by Lyapunov direct method under reasonable assumptions. The control law is derived by the estimated PPD and reaching condition of sliding surface as a model-free of controlled plant. The performance of the proposed control scheme is validated by theoretical analysis and experimental system with direct current (DC) motor current control.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Hou, Z. S. , and Wang, Z. , 2013, “ From Model-Based Control to Data-Driven Control: Survey, Classification and Perspective,” Inf. Sci., 235(20), pp. 3–35. [CrossRef]
Zhang, C. L. , and Li, J. M. , 2015, “ Adaptive Iterative Learning Control of Non-Uniform Trajectory Tracking for Strict Feedback Nonlinear Time-Varying Systems With Unknown Control Direction,” Appl. Math. Modell., 39(10–11), pp. 2942–2950. [CrossRef]
Su, X. , Wu, L. , Shi, P. , and Song, Y. , 2012, “ H Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems,” IEEE Trans. Syst., Man, Cybern., Part B, 42(6), pp. 1574–1585. [CrossRef]
Wu, L. , Shi, P. , and Gao, H. , 2010, “ State Estimation and Sliding-Mode Control of Markovian Jump Singular Systems,” IEEE Trans. Autom. Control, 55(5), pp. 1213–1219. [CrossRef]
Liu, Y. J. , and Tong, S. , 2015, “ Adaptive NN Tracking Control of Uncertain Nonlinear Discrete-Time Systems With Nonaffine Dead-Zone Input,” IEEE Trans. Cybern., 45(3), pp. 497–505. [CrossRef] [PubMed]
Hou, Z. S. , 1994, “ The Parameter Identification, Adaptive Control and Model Free Learning Adaptive Control for Nonlinear Systems,” Ph.D. thesis, Northeastern University, Shenyang, China.
Zhu, Y. , and Hou, Z. S. , 2014, “ Data-Driven MFAC for a Class of Discrete-Time Nonlinear Systems With RBFNN,” IEEE Trans. Neural Networks Learn. Syst., 25(5), pp. 1013–2014. [CrossRef]
Treesatayapun, C. , 2015, “ Data Input-Output Adaptive Controller Based on IF–THEN Rules for a Class of Non-Affine Discrete-Time Systems: The Robotic Plant,” J. Intell. Fuzzy Syst., 28, pp. 661–668.
Treesatayapun, C. , 2014, “ Adaptive Control Based on IF–THEN Rules for Grasping Force Regulation With Unknown Contact Mechanism,” Rob. Comput. Integr. Manuf., 30(1), pp. 11–18. [CrossRef]
Chi, R. , Hou, Z. , and Jin, S. , 2015, “ A Data-Driven Adaptive ILC for a Class of Nonlinear Discrete-Time Systems With Random Initial States and Iteration-Varying Target Trajectory,” J. Franklin Inst., 352(6), pp. 2407–2424. [CrossRef]
Esmaeli, A. , 2016, “ Stability Analysis and Control of Microgrids by Sliding Mode Control,” Electr. Power Energy Syst., 78(1), pp. 22–28. [CrossRef]
Pai, M. C. , 2014, “ Global Synchronization of Uncertain Chaotic Systems Via Discrete-Time Sliding Mode Control,” Appl. Math. Comput., 227(1), pp. 663–671.
Khandekar, A. A. , Malwatkar, G. M. , and Patre, B. M. , 2013, “ Discrete Sliding Mode Control for Robust Tracking of Higher Order Delay Time Systems With Experimental Application,” ISA Trans., 52(1), pp. 36–44. [CrossRef] [PubMed]
Castanos, F. , and Fridman, L. , 2006, “ Analysis and Design of Integral Sliding Manifolds for Systems With Unmatched Perturbations,” IEEE Trans. Autom. Control, 51(5), pp. 853–858. [CrossRef]
Hwang, C. L. , and Chen, Y. M. , 2004, “ Discrete Sliding-Mode Tracking Control of High-Displacement Piezoelectric Actuator Systems,” ASME J. Dyn. Syst., Meas., Control, 126(4), pp. 721–731. [CrossRef]
Boban, V. , Branislava, P. D. , and Cedomir, M. , 2010, “ Improved Discrete-Time Sliding-Mode Position Control Using Euler Velocity Estimation,” IEEE Trans. Ind. Electron., 57, pp. 3840–3847. [CrossRef]
Atia, M. R. A. , Haggag, S. A. , and Kamal, A. M. M. , 2016, “ Enhanced Electromechanical Brake-by-Wire System Using Sliding Mode Controller,” ASME J. Dyn. Syst., Meas., Control, 138(4), p. 041003. [CrossRef]
Bai, R. , 2015, “ Neural Network Control-Based Adaptive Design for a Class of DC Motor Systems With the Full State Constraints,” Neurocomputing, 168(1), pp. 65–69. [CrossRef]
Rubaai, A. , Castro-Sitiriche, M. J. , and Ofoli, A. R. , 2008, “ Design and Implementation of Parallel Fuzzy PID Controller for High-Performance Brushless Motor Drives: An Integrated Environment for Rapid Control Prototyping,” IEEE Trans. Ind. Appl., 44(4), pp. 1090–1098. [CrossRef]
Dhanya, K. , Panicker, M. , and Mol, R. , 2013, “ Hybrid PI-Fuzzy Controller for Brushless DC Motor Speed Control,” IOSR J. Electr. Electron. Eng., 8(6), pp. 33–43. [CrossRef]
Bharatkar, S. S. , Yanamshetti, R. , Chatterjee, D. , and Ganguli, A. K. , 2011, “ Dual-Mode Switching Technique for Reduction of Commutation Torque Ripple of Brushless DC Motor,” IET Electr. Power Appl., 5(1), pp. 193–202. [CrossRef]
Fakham, H. , Djemai, M. , and Busawon, K. , 2008, “ Design and Practical Implementation of Aback-EMF Sliding-Mode Observer for a Brushless DC Motor,” IET Electr. Power Appl., 2(6), pp. 353–361. [CrossRef]
Mozaffari-Niapour, S. , Tabarraie, M. , and Feyzi, M. , 2012, “ Design and Analysis of Speed-Sensorless Robust Stochastic L-Induced Observer for High-Performance Brushless DC Motor Drives With Diminished Torque Ripple,” Energy Convers. Manage., 64(1), pp. 482–498. [CrossRef]


Grahic Jump Location
Fig. 1

Discrete-time system and digital computerization control: DC motor

Grahic Jump Location
Fig. 3

Estimated PPD θ̂(k)

Grahic Jump Location
Fig. 2

Control system block diagram

Grahic Jump Location
Fig. 4

Learning rate of PPD estimator η̂(k)

Grahic Jump Location
Fig. 5

Estimated output ŷ(k)

Grahic Jump Location
Fig. 6

Tracking performance y(k)

Grahic Jump Location
Fig. 7

Control effort u(k)

Grahic Jump Location
Fig. 8

Phase plane trajectory

Grahic Jump Location
Fig. 9

Illustration of Theorem 4.1



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In