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Research Papers

On the Observability and the Observer Design of Differential Pneumatic Pistons

[+] Author and Article Information
Marco A. Arteaga-Pérez

Departamento de Control y Robótica,
DIE. Facultad de Ingeniería,
Universidad Nacional Autónoma de México,
Mexico City D.F. 04510, Mexico,
e-mail: marteagp@unam.mx

Alejandro Gutiérrez-Giles

Departamento de Control y Robótica,
DIE. Facultad de Ingeniería,
Universidad Nacional Autónoma de México,
Mexico City D.F. 04510, Mexico,
e-mail: alejandrogilesg@yahoo.com.mx

Jens Weist

Volkswagen AG,
Letter Box 1399/5,
Wolfsburg D-38436, Germany
e-mail: jens@jensweist.de

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 27, 2012; final manuscript received March 24, 2015; published online April 21, 2015. Assoc. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 137(8), 081006 (Aug 01, 2015) (25 pages) Paper No: DS-12-1204; doi: 10.1115/1.4030251 History: Received June 27, 2012; Revised March 24, 2015; Online April 21, 2015

In this paper, an observability analysis for differential pneumatic pistons is presented, together with the design and implementation of linear observers of the Luenberger type. To avoid as much as possible the knowledge of the system model parameters, the generalized proportional integral (GPI) approach is employed for the estimation of unmeasured variables. Experimental results show the good performance of the proposed scheme.

Copyright © 2015 by ASME
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References

Figures

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Fig. 1

Differential pneumatic piston structure

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Fig. 2

Experimental test bed

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Fig. 8

Input u1(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 9

Input u2(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 10

Input u2(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 12

Input u2(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 13

Input u2(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 14

Input u2(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 15

Input u3(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 16

Input u3(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 17

Input u3(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 18

Input u3(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 19

Input u3(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 20

Input u3(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 3

Input u1(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 4

Input u1(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 5

Input u1(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 6

Input u1(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 7

Input u1(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 11

Input u2(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 26

Input u4(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 27

Input u5(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 28

Input u5(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 29

Input u5(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 30

Input u5(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 21

Input u4(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 22

Input u4(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 23

Input u4(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 24

Input u4(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 25

Input u4(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 31

Input u5(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 32

Input u5(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 33

Input u6(t) without additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 34

Input u6(t) without additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 35

Input u6(t) with fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 36

Input u6(t) with fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 37

Input u6(t) with not fixed additional mass. (a) x3 (…), x∧3 (—) with GPIO and x∧3 (- - -) with SMO. (b) x4 (…), x∧4 (—) with GPIO and x∧4 (- - -) with SMO. (c) (x3-x∧3)/x3, (—) with GPIO and (- - -) with SMO. (d) (x4-x∧4)/x4, (—) with GPIO and (- - -) with SMO.

Grahic Jump Location
Fig. 38

Input u6(t) with not fixed additional mass. (a) x1 (…), x∧1 (—) with GPIO and x∧1 (- - -) with SMO. (b) x2 (…), x∧2 (—) with GPIO and x∧2 (- - -) with SMO. (c) x1-x∧1, (—) with GPIO and (- - -) with SMO. (d) x2-x∧2, (—) with GPIO and (- - -) with SMO.

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