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Research Papers

Discrete-Time Robust Control With an Anticipative Action for Preview Systems

[+] Author and Article Information
Asma Achnib

University Bordeaux,
Bordeaux INP,
CNRS, IMS, UMR 5218,
Talence 33405, France
Laboratoire Modélisation, Analyse et Commande
des Systèmes (MACS) - LR16ES22,
National Engineering School of Gabes,
University of Gabes,
Gabes 6072, Tunisia
e-mail: asma.achnib@u-bordeaux.fr

Tudor-Bogdan Airimitoaie

University Bordeaux,
Bordeaux INP,
CNRS, IMS, UMR 5218,
Talence 33405, France
e-mail: tudor-bogdan.airimitoaie@u-bordeaux.fr

Patrick Lanusse

University Bordeaux,
Bordeaux INP,
CNRS, IMS, UMR 5218,
Talence 33405, France
e-mail: patrick.lanusse@bordeaux-inp.fr

Sergey Abrashov

University Bordeaux,
Bordeaux INP,
CNRS, IMS, UMR 5218,
Talence 33405, France
e-mail: sergey.abrashov@u-bordeaux.fr

Mohamed Aoun

Laboratoire Modélisation, Analyse et Commande
des Systèmes (MACS) - LR16ES22,
National Engineering School of Gabes,
University of Gabes,
Gabes 6072, Tunisia
e-mail: mohamed.aoun@gmail.com

Manel Chetoui

Laboratoire Modélisation, Analyse et Commande
des Systèmes (MACS) - LR16ES22,
National Engineering School of Gabes,
University of Gabes,
Gabes 6072, Tunisia
e-mail: chetoui.manel@gmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received March 7, 2018; final manuscript received October 4, 2018; published online November 22, 2018. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 141(3), 031012 (Nov 22, 2018) (11 pages) Paper No: DS-18-1113; doi: 10.1115/1.4041711 History: Received March 07, 2018; Revised October 04, 2018

A discrete-time robust controller design method is proposed for optimal tracking of future references in preview systems. In the context of preview systems, it is supposed that future values of the reference signal are available a number of time steps ahead. The objective is to design a control algorithm that minimizes a quadratic error between the reference and the output of the system and at the same time achieves a good level of the control signal. The proposed solution combines a robust feedback controller with a feedforward anticipative filter. The feedback controller's purpose is to assure robustness of the closed-loop system to model uncertainties. Any robust control methodology can be used (such as μ-synthesis, qft, or crone control). The focus of this paper will be on the design of the feedforward action in order to introduce the anticipative effect with respect to known future values of the reference signal without hindering the robustness achieved through the feedback controller. As such, the model uncertainties are taken into account also in the design of the feedforward anticipative filter. The proposed solution is validated in simulation and on an experimental water tank level control system.

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References

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Figures

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Fig. 1

Feedforward − feedback control schema used for robust anticipative control

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Fig. 2

Sampling rate change in the implementation of the feedforward − feedback controller

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Fig. 3

Feedforward − feedback control schema used for robust anticipative control with sampling rate change and low-pass filter

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Fig. 4

Nichols chart of the uncertain parameters model G(q−1)

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Fig. 5

Feedback schema used in crone controller design

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Fig. 6

Sensitivity functions templates and obtained results: subscripts denote the nominal response (n), the highest response (M), and the minimum response (m)

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Fig. 7

Nichols chart comparison between the fractional and the rational open-loop: the nominal frequency responses are given by the solid lines. Responses of the augmented uncertainty domains enclose the nominal ones.

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Fig. 8

Evaluation of the rational crone controller: (a) step response and (b) control effort

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Fig. 9

Sensitivity functions from reference to control input using the nominal Gn (labeled Huydn) and the two extremum Gm (labeled Huydm) and GM (labeled HuydM) plant models (p=1)

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Fig. 10

Evaluation of the feedforward + feedback control schema (p = 1): (a) step response and (b) control effort

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Fig. 11

Sensitivity functions from reference to control input using the nominal Gn (labeled Huydn) and the two extremum Gm (labeled Huydm) and GM (labeled HuydM) plant models (p=8)

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Fig. 12

Evaluation of the feedforward + feedback control schema (p = 8): (a) step response and (b) control effort

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Fig. 13

Schema of the water level control test bench

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Fig. 14

Sensitivity functions from reference to control input using the nominal Gn and the two extremum Gm and GM plant models (p = 1)

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Fig. 15

Experimental results for the V102 manual valve wide open: control signal (upper plot), reference and output signals (lower plot)

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Fig. 16

Experimental results for the V102 manual valve partially open: control signal (upper plot), reference and output signals (lower plot)

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Fig. 17

Experimental results for the V102 manual valve completely closed: control signal (upper plot), reference and output signals (lower plot)

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