Research Papers

Flatness-Based Control of a Two Degrees-of-Freedom Platform With Pneumatic Artificial Muscles

[+] Author and Article Information
David Bou Saba

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: david.bou-saba@insa-lyon.fr

Paolo Massioni

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: paolo.massioni@insa-lyon.fr

Eric Bideaux

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: eric.bideaux@insa-lyon.fr

Xavier Brun

Laboratoire Ampère CNRS,
INSA Lyon,
Université de Lyon,
Villeurbanne, Cedex 69621, France
e-mail: xavier.brun@insa-lyon.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 15, 2018; final manuscript received September 6, 2018; published online October 5, 2018. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 141(2), 021003 (Oct 05, 2018) (10 pages) Paper No: DS-18-1024; doi: 10.1115/1.4041445 History: Received January 15, 2018; Revised September 06, 2018

Pneumatic artificial muscles (PAMs) are an interesting type of actuators as they provide high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods taking into account their complex and nonlinear dynamics. This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves. An overactuation is present as three muscles are controlled for only two degrees-of-freedom. The contribution of this work is twofold. First, whereas most of the literature approaches the control of systems of similar nature with sliding mode control, we show that the platform can be controlled with the flatness-based approach. This method is a nonlinear open-loop controller. In addition, this approach is model-based, and it can be applied thanks to the accurate models of the muscles, the platform and the servovalves, experimentally developed. In addition to the flatness-based controller, which is mainly a feedforward control, a proportional-integral (PI) controller is added in order to overcome the modeling errors and to improve the control robustness. Second, we solve the overactuation of the platform by an adequate choice for the range of the efforts applied by the muscles. In this paper, we recall the basics of this control technique and then show how it is applied to the proposed experimental platform. At the end of the paper, the proposed approach is compared to the most commonly used control method, and its effectiveness is shown by means of experimental results.

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Fig. 1

The experimental platform

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Fig. 2

Axonometric view and view from the top of the top plate, with definition of the axes x, y, z and the rotation angles θx and θy. M1, M2, and M3 are the attachment points of the three PAMs and define the three angular positions ϕ1, ϕ2, and ϕ3 given in the Nomenclature section.

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Fig. 3

Contraction force applied by a muscle as a function of the contraction εi and absolute pressure Pi

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Fig. 4

Mass flow of a servovalve as a function of voltage vi and absolute muscle pressure Pi

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Fig. 5

Value of z as function of x1 = θx and x2 = θy

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Fig. 6

Values of m as function of θx and θy

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Fig. 7

Global control scheme

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Fig. 8

Valid range of the efforts, bounded from below by Fmin and from above by Fmax for a given position of the platform, determined by the three contractions εi, i ∈ {1, 2, 3}

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Fig. 9

Simulation result of the evolution of the output F3 when the sliding mode control is used

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Fig. 10

Static setpoint tracking using the flatness-based control plus a PI

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Fig. 11

Muscle contractions for the setpoint tracking using the flatness-based control plus a PI

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Fig. 12

Trajectory tracking with simple PI control

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Fig. 13

Trajectory tracking with flatness-based control plus a PI

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Fig. 14

Pressures inside the PAMs during the flatness-based control plus PI experiment

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Fig. 15

Forces applied by the PAMs (estimated using Eq. (6) and the measurements of the pressures and the contractions) with flatness-based control plus a PI



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