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Research Papers

# Sliding Mode Control of a 2DOF Planar Pneumatic Manipulator

[+] Author and Article Information
Michaël Van Damme

Robotics and Multibody Mechanics Research Group, Department of Mechanical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgiummichael.vandamme@vub.ac.be

Bram Vanderborght, Ronald Van Ham, Björn Verrelst, Frank Daerden, Dirk Lefeber

Robotics and Multibody Mechanics Research Group, Department of Mechanical Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium

A SISO system is said to be in controllability canonical form (see for instance Ref. 65, Chap. 6) if its dynamics can be written as

$x(n)=f(x)+b(x)u$
with $u$ as the scalar control input, $x$ the scalar output, $x=[xẋ⋯x(n−1)]T$ as the state vector, and $f(x)$ and $b(x)$ as nonlinear functions of the state. Note that no derivatives of the control input $u$ are present.

The scalar function $Lfh(x)=(∂h∕∂x)f$ stands for the Lie derivative of the scalar function $h$ with respect to the vector field $f(x)$. $Lf2h(x)=LfLfh(x)=Lf(Lfh)(x)$. $Lf0h(x)=h(x)$. See for instance Refs. 65,73 for more information.

A polynomial with real positive coefficients and roots, which are either negative or pairwise conjugate with negative real parts.

J. Dyn. Sys., Meas., Control 131(2), 021013 (Feb 09, 2009) (12 pages) doi:10.1115/1.3023132 History: Received February 05, 2008; Revised August 27, 2008; Published February 09, 2009

## Abstract

This paper presents a sliding mode controller for a 2DOF planar pneumatic manipulator actuated by pleated pneumatic artificial muscle actuators. It is argued that it is necessary to account for the pressure dynamics of muscles and valves. A relatively detailed system model that includes pressure dynamics is established. Since the model includes actuator dynamics, feedback linearization was necessary to design a sliding mode controller. The feedback linearization and subsequent controller design are presented in detail, and the controller’s performance is evaluated, both in simulation and experimentally. Chattering was found to be quite severe, so the introduction of significant boundary layers was required.

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## Figures

Figure 3

A PPAM shown for three different values of contraction

Figure 4

ft0 (dimensionless force function)

Figure 6

Antagonistic setup

Figure 7

Torque functions

Figure 10

Schematic representation of the manipulator. All distances and angles used in the calculations are indicated.

Figure 1

The manipulator. The series arrangement of pleated pneumatic artificial muscles is clearly visible.

Figure 2

The inverse elbow configuration

Figure 5

Force exerted by a PPAM with l0∕R=6 and l0=6cm for different gauge pressures

Figure 8

Simulation results for tracking a circular trajectory: (a) shows the desired and the actual trajectory for one revolution and (b) shows the position error for three revolutions

Figure 9

Measurements taken while tracking a circular trajectory: (a) shows the desired and the actual trajectory for one revolution and (b) shows the measured position error for three revolutions

## Errata

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