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Flatness-based control of a two-degree-of-freedom platform with pneumatic artificial muscles

David Bou Saba, Paolo Massioni, Eric Bideaux, Xavier Brun

TL;DR

This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves, and shows that the platform can be controlled with the flatness-based approach, a nonlinear open-loop controller.

Abstract

Pneumatic artificial muscles are a quite interesting type of actuators which have a very high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods which can take into account their complex dynamic, which is highly nonlinear. This paper consider a model of two-degree-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves, which mimics a simplified version of a Stewart platform. For this testbed, a model-based control approach is proposed, based on accurate first principle modeling of the muscles and the platform and on a static model for the servovalve. The employed control method is the so-called flatness-based control introduced by Fliess. The paper first recalls the basics of this control technique and then it shows how it can be applied to the proposed experimental platform; being flatness-based control an open-loop kind of control, a proportional-integral controller is added on top of it in order to add robustness with respect to modelling errors and external perturbations. At the end of the paper, the effectiveness of the proposed approach is shown by means of experimental results. A clear improvement of the tracking performance is visible compared to a simple proportional-integral controller.

Flatness-based control of a two-degree-of-freedom platform with pneumatic artificial muscles

TL;DR

This paper considers a two degrees-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves, and shows that the platform can be controlled with the flatness-based approach, a nonlinear open-loop controller.

Abstract

Pneumatic artificial muscles are a quite interesting type of actuators which have a very high power-to-weight and power-to-volume ratio. However, their efficient use requires very accurate control methods which can take into account their complex dynamic, which is highly nonlinear. This paper consider a model of two-degree-of-freedom platform whose attitude is determined by three pneumatic muscles controlled by servovalves, which mimics a simplified version of a Stewart platform. For this testbed, a model-based control approach is proposed, based on accurate first principle modeling of the muscles and the platform and on a static model for the servovalve. The employed control method is the so-called flatness-based control introduced by Fliess. The paper first recalls the basics of this control technique and then it shows how it can be applied to the proposed experimental platform; being flatness-based control an open-loop kind of control, a proportional-integral controller is added on top of it in order to add robustness with respect to modelling errors and external perturbations. At the end of the paper, the effectiveness of the proposed approach is shown by means of experimental results. A clear improvement of the tracking performance is visible compared to a simple proportional-integral controller.

Paper Structure

This paper contains 14 sections, 1 theorem, 27 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation and definitions
  3. The pneumatic platform
  4. Description
  5. Model
  6. Control objectives
  7. Model analysis and control
  8. Flatness and flatness-based control
  9. Complete state-space model
  10. Flatness of the model
  11. Control law
  12. Solving the overactuation
  13. Experimental results
  14. Conclusion

Key Result

Theorem 4

If a system of equations $\dot{x}=f(x)+g(x)u$ with $u \in \mathbb{R}^m$ is flat (Definition def:fla) with respect to a flat output $y =h(x)\in \mathbb{R}^m$ with characteristic coefficients $\rho_i$, and if the matrix $\Delta(x)$ is invertible (at least locally), then it is possible to track a given

Figures (11)

  • Figure 1: The experimental platform.
  • Figure 2: Axonometric view and view from the top of the top plate, with definition of the axes $x$, $y$, $z$ and the rotation angles $\theta_x$ and $\theta_y$. $M_1$, $M_2$ and $M_3$ are the attachment points of the three pneumatic artificial muscles.
  • Figure 3: Traction force applied by a muscle as a function of the contraction $\varepsilon_i$ and absolute pressure $P_i$.
  • Figure 4: Mass flow of a servovalve as a function of voltage $v_i$ and absolute muscle pressure $P_i$.
  • Figure 6: Values of $m$ as function of $\theta_x$ and $\theta_y$.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Definition 1: Flat system - adapted from fliess1995flatness
  • Definition 2: Characteristic index
  • Definition 3: Coupling matrix
  • Theorem 4: Adapted from fliess1995flatness