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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.

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References

Ning, S., and Bone, G. M., 2002, “High Steady-State Accuracy Pneumatic Servo Positioning System With PVA/PV Control and Friction Compensation,” IEEE International Conference on Robotics and Automation, Washington, DC, pp. 2824–2829.
Ning, S., and Bone, G. M., 2005, “Experimental Comparison of Two Pneumatic Servo Position Control Algorithms,” IEEE International Conference on Mechatronics and Automation, Niagara Falls, ON, Canada.
Sawodny, O., and Hildebrandt, A., 2002, “Aspects of the Control of Differential Pneumatic Cylinders,” 10th German Japanese Seminar on Problems in Dynamical Systems, Kanazawa, Japan.
Shen, X., Zhang, J., Barth, E. J., and Goldfarb, M., 2006, “Nonlinear Model-Based Control of Pulse Width Modulated Pneumatic Servo Systems,” ASME J. Dyn. Syst. Meas. Control, 128(3), pp. 663–669. [CrossRef]
Guenther, R., Perondi, E. A., DePieri, E. R., and Valdiero, A. C., 2006, “Cascade Controlled Pneumatic Positioning System With LuGre Model Based Friction Compensation,” J. Braz. Soc. Mech. Sci. Eng., 28(1), pp. 48–57. [CrossRef]
Zhu, Y., 2006, “Control of Pneumatic Systems for Free Space and Interaction Tasks With System and Environmental Uncertainties,” Ph. D. dissertation, School of Vanderbilt University, Nashville, TN.
Goettert, M., and Neumann, R., 2007, “Bahnregelung Servopneumatischer Antriebe—Ein Vergleich von Linearen und Nichtlinearen Reglern,” Autmoatisierungs Tech., 2, pp. 69–74.
Weist, J., Arteaga Pérez, M. A., de la Cruz, L. R., and Hebisch, H., 2011, “Model Free Control for Differential Pneumatic Pistons: Experimental Comparison,” Int. J. Control, 84(1), pp. 138–164. [CrossRef]
Bigras, P., and Khayati, K., 2002, “Nonlinear Observer for Pneumatic System With Non Negligible Connection Port Restriction,” American Control Conference, pp. 3191–3195. [CrossRef]
Pandian, S. R., Takemura, F., Hayakawa, Y., and Kawamura, S., 2002, “Pressure Observer–Controller Design for Pneumatic Cylinder Actuators,” IEEE/ASME Trans. Mechatronics, 7(4), pp. 490–499. [CrossRef]
Wu, J., Goldfarb, M., and Barth, E., 2003, “The Role of Pressure Sensors in the Servo Control of Pneumatic Actuators,” American Control Conference, Vol. 2, pp. 1710–1714.
Wu, J., Goldfarb, M., and Barth, E., 2004, “On the Observability of Pressure in a Pneumatic Servo Actuator,” ASME J. Dyn. Syst. Meas. Control, 126(4), pp. 921–924. [CrossRef]
Gulati, N., and Barth, E. J., 2005, “Non-Linear Pressure Observer Design for Pneumatic Actuators,” 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Monterey, CA, July 24–28, pp. 783–788. [CrossRef]
Fliess, M., Marquez, R., Delaleau, E., and Sira-Ramírez, H., 2002, “Correcteurs Proportionnels Intègraux Généralisés,” ESAIM: Control Optim. Calculus Var., 7(2), pp. 23–41. [CrossRef]
Sira-Ramírez, H., Ramírez-Neria, M., and Rodríguez-Ángeles, A., 2010, “On the Linear Control of Nonlinear Mechanical Systems,” 49th IEEE Conference on Decision and Control, Atlanta, GA, Dec. 15–17, pp. 1999–2004. [CrossRef]
Goettert, M., and Neumann, R., 1999, “Nichtlineare Regelungskonzepte für Servopneumatische Roboter,” Deutsch-Polnisches Seminar Inovation und Fortschritt in der Fluidtechnik, Zakopane, Poland.
Sobczyk, M. R., and Perondi, E. A., 2006, “Variable Structure Cascade Control of a Pneumatic Positioning System,” ABCM Symposium Series in Mechatronics, Vol. 2, pp. 27–34.
Beater, P., 2007, Pneumatic Drives, Springer-Verlag, Berlin. [CrossRef]
Diop, S., and Fliess, M., 1991, “Nonlinear Observability, Identifiability and Persistent Trajectories,” 36th IEEE Conference on Decision and Control, Brighton, Dec. 11–13. [CrossRef]
Hermann, R., and Krener, A. J., 1977, “Nonlinear Controllability and Observability,” IEEE Trans. Autom. Control, 22(5), pp. 728–740. [CrossRef]

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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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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