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Research Papers

Controller Design and Stability Analysis of Output Pressure Regulation in Electrohydrostatic Actuators

[+] Author and Article Information
Masoumeh Esfandiari

Department of Mechanical Engineering,
University of Manitoba,
75A Chancellors Circle,
Winnipeg, MB R3T 5V6, Canada

Nariman Sepehri

Fellow ASME,
Department of Mechanical Engineering,
University of Manitoba,
75A Chancellors Circle,
Winnipeg, MB R3T 5V6, Canada,
e-mail: Nariman.Sepehri@umanitoba.ca

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received September 18, 2017; final manuscript received November 10, 2018; published online December 19, 2018. Assoc. Editor: Zongxuan Sun.

J. Dyn. Sys., Meas., Control 141(4), 041008 (Dec 19, 2018) (10 pages) Paper No: DS-17-1476; doi: 10.1115/1.4042028 History: Received September 18, 2017; Revised November 10, 2018

In this paper, a robust fixed-gain linear output pressure controller is designed for a double-rod electrohydrostatic actuator using quantitative feedback theory (QFT). First, the family of frequency responses of the system is identified by applying an advanced form of fast Fourier transform on the open-loop input–output experimental data. This approach results in realistic frequency responses of the system, which prevents the generation of unnecessary large QFT templates, and consequently contributes to the design of a low-order QFT controller. The designed controller provides desired transient responses, desired tracking bandwidth, robust stability, and disturbance rejection for the closed-loop system. Experimental results confirm the desired performance met by the QFT controller. Then, the nonlinear stability of the closed-loop system is analyzed considering the friction and leakage, and in the presence of parametric uncertainties. For this analysis, Takagi–Sugeno (T–S) fuzzy modeling and its stability theory are employed. The T–S fuzzy model is derived for the closed-loop system and the stability conditions are presented as linear matrix inequalities (LMIs). LMIs are found feasible and thus the stability of the closed-loop system is proven for a wide range of parametric uncertainties and in the presence of friction and leakages.

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Figures

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Fig. 1

Experimental setup: (a) photograph of experimental test-bench and (b) electrohydrostatic actuator interacting with environment

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Fig. 2

Output pressure of the experimental setup (solid line) and simulation model using the dynamics given in Eqs. (1)(9) (dashed line): (a) open-loop response to input signal of u = 0.15 V and (b) open-loop response to input signal of u = 0.1 V.

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Fig. 3

(a) Typical linear swept-frequency input signal, u, (b) corresponding output pressure, PL. Hydraulic actuator is operating against a spring having stiffness of 82 kN/m, and carrying a 12.3 kg mass.

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Fig. 4

Family of frequency responses of experimental electrohydrostatic actuator with output pressure, PL, and input voltage, u, for different masses (12.3, 13.4, and 14.5 kg) and different spring stiffnesses (82 and 125 kN/m): (a) magnitude (dB), (b) phase (deg), and (c) coherence coefficient. Acceptable frequency response range is shown between arrows.

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Fig. 5

Two degrees-of-freedom QFT control system

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Fig. 6

Plant templates at design frequencies, ω (rad/s) for electrohydrostatic actuator. The parameter uncertainties are load mass (12.3, 13.4, and 14.5 kg) and environment stiffnesses (82 and 125 kN/m). Circles represent frequency response of nominal plant.

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Fig. 8

Frequency responses of closed-loop system using controller (15): (a) response before adding prefilter and (b) response after adding prefilter (16)

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Fig. 9

(a) Normalized output pressure responses using springs having 82 and 125 kN/m stiffnesses, and carrying 12.3 or 14.5 kg loads—desired inputs are within 1–3 MPa; the gray region covers acceptable responses within upper and lower bounds in Eq. (14), (b) corresponding control signals, and (c) corresponding error signals between desired and actual output pressures.

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Fig. 10

(a) 3 Hz sinusoidal output pressure tracking, interacting with 82 kN/m spring—the desired peak values are shown by horizontal dashed lines, (b) corresponding control signal, and (c) corresponding piston displacement. Solid lines represent the results of experimental setup. Dashed lines are the simulation results using the nonlinear model given in Eqs. (1)(9).

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Fig. 11

(a) 5 Hz sinusoidal output pressure tracking, interacting with 125 kN/m spring—the desired peak values are shown by dashed lines, (b) the corresponding control signal, and (c) the corresponding piston displacement. Solid lines represent the results of experimental setup. Dashed lines are the simulation results using the nonlinear model given in Eqs. (1)(9).

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