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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

Professor
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.

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Figures

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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.

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Fig. 2

Input–output linearization of the nonlinear system model

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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

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Fig. 4

Block diagram of the proposed PIO-BC method

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Fig. 5

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

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Fig. 6

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

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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

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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

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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

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