Research Papers

Proportional-Integral-Observer-Based Backstepping Approach for Position Control of a Hydraulic Differential Cylinder System With Model Uncertainties and Disturbances

[+] Author and Article Information
Fateme Bakhshande

Chair of Dynamics and Control,
University of Duisburg-Essen,
Duisburg 47057, NRW, Germany
e-mail: fateme.bakhshande@uni-due.de

Dirk Söffker

Chair of Dynamics and Control,
University of Duisburg-Essen,
Duisburg 47057, NRW, Germany
e-mail: soeffker@uni-due.de

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 1, 2017; final manuscript received June 21, 2018; published online July 23, 2018. Assoc. Editor: Umesh Vaidya.

J. Dyn. Sys., Meas., Control 140(12), 121006 (Jul 23, 2018) (10 pages) Paper No: DS-17-1063; doi: 10.1115/1.4040662 History: Received February 01, 2017; Revised June 21, 2018

This paper focuses on the design of an observer-based backstepping controller (BC) for a nonlinear hydraulic differential cylinder system. The system is affected by some uncertainties including modeling errors, external disturbances, and measurement noise. An observer-based control approach is proposed to assure suitable tracking performance and to increase robustness against unknown inputs. The task to estimate system states as well as unknown inputs is performed by a linear proportional-integral-observer (PIO). Input–output linearization is used to linearize the nonlinear system model to be used for the PIO structure. On the other hand, BC is utilized based on nonlinear system model to construct the Lyapunov function and to design the control input simultaneously. Stability or negativeness of the derivative of every-step Lyapunov function is fulfilled. Structural improvement regarding the combination of BC and PIO is the main aim of this contribution. This is supported by a novel stability proof and new conditions for the whole control loop with integrated PIO. Furthermore, parameter selection of BC is elaborately considered by defining a performance/energy criterion. A complete robustness evaluation considering different levels of additional measurement noise, modeling errors, and external disturbances is presented for the first time in this contribution. Experimental results validate the advantages of proposed observer-based approach compared to PIO-based sliding mode control (PIO-SMC) and industrial standard P-controller.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Jelali, M. , and Kroll, A. , 2003, Hydraulic Servo-Systems: Modelling, Identification and Control, Springer, London.
Mintsa, H. A. , Venugopal, R. , Kenné, J.-P. , and Belleau, C. , 2012, “ Feedback Linearization-Based Position Control of an Electrohydraulic Servo System With Supply Pressure Uncertainty,” IEEE Trans. Control Syst. Technol., 20(4), pp. 1092–1099. [CrossRef]
Marino, R. , and Tomei, P. , 1993, “ Robust Stabilization of Feedback Linearizable Time-Varying Uncertain Nonlinear Systems,” Automatica, 29(1), pp. 181–189. [CrossRef]
Mobayen, S. , and Baleanu, D. , 2016, “ Stability Analysis and Controller Design for the Performance Improvement of Disturbed Nonlinear Systems Using Adaptive Global Sliding Mode Control Approach,” Nonlinear Dyn., 83(3), pp. 1557–1565. [CrossRef]
Mobayen, S. , and Tchier, F. , 2016, “ An LMI Approach to Adaptive Robust Tracker Design for Uncertain Nonlinear Systems With Time-Delays and Input Nonlinearities,” Nonlinear Dyn., 85(3), pp. 1965–1978. [CrossRef]
Ferreira, A. , Bejarano, F. J. , and Fridman, L. M. , 2011, “ Robust Control With Exact Uncertainties Compensation: With or Without Chattering?,” IEEE Trans. Control Syst. Technol., 19(5), pp. 969–975. [CrossRef]
Liu, Y. , and Söffker, D. , 2014, “ Robust Control Approach for Input–Output Linearizable Nonlinear Systems Using High-Gain Disturbance Observer,” Int. J. Robust Nonlinear Control, 24(2), pp. 326–339. [CrossRef]
Khalil, H. K. , 1996, Nonlinear Systems, Vol. 3, Prentice Hall, Upper Saddle River, NJ.
Ginoya, D. , Shendge, P. D. , and Phadke, S. B. , 2013, “ Sliding Mode Control for Mismatched Uncertain Systems Using an Extended Disturbance Observer,” IEEE Trans. Ind. Electron., 61(4), pp. 1983–1992. [CrossRef]
Nakkarat, P. , and Kuntanapreeda, S. , 2009, “ Observer-Based Backstepping Force Control of an Electrohydraulic Actuator,” Control Eng. Pract., 17(8), pp. 895–902. [CrossRef]
Yao, J. , Jiao, Z. , and Ma, D. , 2014, “ Extended-State-Observer-Based Output Feedback Nonlinear Robust Control of Hydraulic Systems With Backstepping,” IEEE Trans. Ind. Electron., 61(11), pp. 6285–6293. [CrossRef]
Guo, Q. , min Yin, J. , Yu, T. , and Jiang, D. , 2017, “ Coupled-Disturbance-Observer-Based Position Tracking Control for a Cascade Electro-Hydraulic System,” ISA Trans., 68, pp. 367–380. [CrossRef] [PubMed]
Bakhshande, F. , and Söffker, D. , 2017, “ Robust Control Approach for a Hydraulic Differential Cylinder System Using a Proportional-Integral-Observer-Based Backstepping Control,” American Control Conference (ACC), Seattle, WA, May 24–26, pp. 3102–3107.
Shafai, B. , and Saif, M. , 2015, “ Proportional-Integral-Observer in Robust Control, Fault Detection, and Decentralized Control of Dynamic Systems,” Control and Systems Engineering, Vol 27, A. In: El-Osery A., Prevost J., eds., Springer, Cham, Swizterland, pp. 13–43. [CrossRef] [PubMed] [PubMed]
Bakhshande, F. , and Söffker, D. , 2015, “ Proportional-Integral-Observer: A Brief Survey With Special Attention to the Actual Methods Using ACC Benchmark,” IFAC-PapersOnLine, 48(1), pp. 532–537. [CrossRef]
Liu, Y. , and Söffker, D. , 2012, “ Variable High-Gain Disturbance Observer Design With Online Adaption of Observer Gains Embedded in Numerical Integration,” Math. Comput. Simul., 82(5), pp. 847–857. [CrossRef]
Söffker, D. , Yu, T. J. , and Müller, P. C. , 1995, “ State Estimation of Dynamical Systems With Nonlinearities by Using Proportional-Integral-Observer,” Int. J. Syst. Sci., 26(9), pp. 1571–1582. [CrossRef]
Johnson, C. D. , 1976, “ Theory of Disturbance Accommodating Controllers,” Control Dyn. Syst., 12, pp. 387–489. [CrossRef]
Hippe, P. , and Wurmthaler, C. , 1985, Zustandsregelung: Theoretische Grundlagen und anwendungsorientierte Regelungskonzepte, Springer, Springer-Verlag, Berlin.
Johnson, C. D. , 1968, “ Optimal Control of the Linear Regulator With Constant Disturbances,” IEEE Trans. Autom. Control, 13(4), pp. 416–421. [CrossRef]
Johnson, C. D. , 1971, “ Accommodation of External Disturbances in Linear Regulator and Servomechanism Problems,” IEEE Trans. Automatic Control, 16(6), pp. 635–644. [CrossRef]
Davison, E. J. , 1972, “ The Output Control of Linear Time-Invariant Multivariable Systems With Unmeasurable Arbitrary Disturbances,” IEEE Trans. Autom. Control, 17(5), pp. 621–630. [CrossRef]
Bakhshande, F. , 2018, “ Observer-Based Robust Nonlinear Control Design,” Ph.D. thesis, Universität Duisburg-Essen, Fakultät für Ingenieurwissenschaften Maschinenbau und Verfahrenstechnik, Duisburg, Germany.
Müller, P. C. , and Başpinar, C. , 2000, “ Convergence of Nonlinearity Estimations by Linear Estimators,” J. Appl. Math. Mech., 80(S2), pp. 325–326.
Krstić, M. , Kanellakopoulos, I. , and Kokotović, P. , 1992, “ Adaptive Nonlinear Control Without Overparametrization,” Syst. Control Lett., 19(3), pp. 177–185. [CrossRef]
Kanellakopoulos, I. , Kokotovic, P. V. , and Morse, A. S. , 1991, “ Systematic Design of Adaptive Controllers for Feedback Linearizable Systems,” IEEE Trans. Autom. Control, 36(11), pp. 1241–1253. [CrossRef]
Wu, J. , Chen, W. , Yang, F. , Li, J. , and Zhu, Q. , 2015, “ Global Adaptive Neural Control for Strict-Feedback Time-Delay Systems With Predefined Output Accuracy,” Inf. Sci., 301, pp. 27–43. [CrossRef]
Wu, J. , Li, J. , and Chen, W. , 2014, “ Semi-Globally/Globally Stable Adaptive NN Backstepping Control for Uncertain MIMO Systems With Tracking Accuracy Known a Priori,” J. Franklin Inst., 351(12), pp. 5274–5309. [CrossRef]
Wu, J. , Chen, W. , and Li, J. , 2015, “ Fuzzy-Approximation-Based Global Adaptive Control for Uncertain Strict-Feedback Systems With a Priori Known Tracking Accuracy,” Fuzzy Sets Syst., 273, pp. 1–25. [CrossRef]
Tran, D. T. , Jeong, K. , Jun, G. , Kiro, J. S. , Kiro, M. J. , and Ahn, K. K. , 2017, “ Adaptive Gain Back-Stepping Sliding Mode Control for Electrohydraulic Servo System With Uncertainties,” 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), Jeju, South Korea, 28 June–1 July, pp. 534–539. http://www.urai2017.org/
Chen, F. , Jiang, R. , Zhang, K. , Jiang, B. , and Tao, G. , 2016, “ Robust Backstepping Sliding-Mode Control and Observer-Based Fault Estimation for a Quadrotor UAV,” IEEE Trans. Ind. Electron., 63(8), pp. 5044–5056. https://ieeexplore.ieee.org/abstract/document/7448915/


Grahic Jump Location
Fig. 1

Hydraulic differential cylinder system. (a) Test rig of hydraulic differential cylinder system at the chair of dynamics and control (UDuE): 1—proportional control valve, 2—oil supply in chamber A, 3—oil supply in chamber B, 4—moving mass, and 5—load cylinder (used as external disturbance). (b) Sketch of the hydraulic differential cylinder system.

Grahic Jump Location
Fig. 2

Input–output linearization of the nonlinear system model

Grahic Jump Location
Fig. 3

Estimation results using linear high gain PIO in the case of P-controller (experimental results): (a) Estimation of cylinder position η1, (b) estimation of cylinder velocity η2, (c) estimation of cylinder acceleration η3, and (d) estimation of transformed unknown input d̃

Grahic Jump Location
Fig. 4

Block diagram of the proposed PIO-BC method

Grahic Jump Location
Fig. 5

Block diagram of experimental setup at the chair of dynamics and control (UDuE)

Grahic Jump Location
Fig. 6

Comparison of design parameters by means of criterion (39) to find and tune the parameters of PIO-BC (case I)

Grahic Jump Location
Fig. 7

Experimental results with sinusoidal signal as reference signal (case I): (a) position control error and (b) estimation of unknown input in original coordinate

Grahic Jump Location
Fig. 8

Comparison of different control methods (PIO-SMC, PIO-BC, and P-controller) by means of criterion (39): (a) considering different levels of additional noise and (b) considering model uncertainties and unknown effects

Grahic Jump Location
Fig. 9

Comparison of convergence speed for different control methods (PIO-SMC, PIO-BC, and P-controller) considering caseI: (a) step signal as reference and (b) sinusoidal signal as reference



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