0
Research Papers

Optimal Sliding Mode Cascade Control for Stabilization of Underactuated Nonlinear Systems

[+] Author and Article Information
Kenneth R. Muske

Department of Chemical Engineering,  Villanova University, Villanova, PA 19085

Hashem Ashrafiuon1

Department of Mechanical Engineering, Center for Nonlinear Dynamics and Control,  Villanova University, Villanova, PA 19085hashem.ashrafiuon@villanova.edu

Sergey Nersesov

Department of Mechanical Engineering, Center for Nonlinear Dynamics and Control,  Villanova University, Villanova, PA 19085

Mehdi Nikkhah2

Department of Mechanical Engineering, Center for Nonlinear Dynamics and Control,  Villanova University, Villanova, PA 19085

1

Corresponding author.

2

Currently a postdoctoral research fellow at Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA 02139.

J. Dyn. Sys., Meas., Control 134(2), 021020 (Jan 12, 2012) (11 pages) doi:10.1115/1.4005367 History: Received July 23, 2010; Revised September 06, 2011; Accepted September 12, 2011; Published January 12, 2012; Online January 12, 2012

This paper presents an optimal sliding mode cascade control for stabilization of a class of underactuated nonlinear mechanical systems. A discrete-time, nonlinear model predictive control structure is used to optimally select and update the parameters of the sliding mode control surfaces at specified intervals in order to achieve a desired performance objective. The determination of these surface parameters is subject to constraints that arise from the stability conditions imposed by the sliding mode control law and the physical limits on the system such as input saturation. Nominal stability of the optimal cascade control structure is demonstrated and its robust performance is illustrated using an experimental rotary inverted pendulum system.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 2

The rotary inverted pendulum

Grahic Jump Location
Figure 3

Comparison of simulation and experimental results; (top) pendulum arm angle (middle), rotating arm angle (bottom), control input voltage

Grahic Jump Location
Figure 4

Comparison of experimental initial feasible design (base case), one-time optimization (initial optimal), and MPC cascade control (MPC cascade) for the minimum-energy problem; (top) pendulum arm angle, (middle) rotating arm angle, (bottom) control input voltage

Grahic Jump Location
Figure 5

Experimental reaching and sliding phases with the surface changes for the minimum-energy MPC cascade controller

Grahic Jump Location
Figure 6

Comparison of experimental initial feasible design (base case), one-time optimization (initial optimal), and MPC cascade control (MPC cascade) for the minimum-time problem; (top) pendulum arm angle (middle), rotating arm angle (bottom), control input voltage

Grahic Jump Location
Figure 10

Initial one-time optimization-minimum time

Grahic Jump Location
Figure 11

MPC cascade controller-minimum time

Grahic Jump Location
Figure 1

Cascade controller block diagram

Grahic Jump Location
Figure 8

Initial one-time optimization-minimum energy

Grahic Jump Location
Figure 9

MPC cascade controller-minimum energy

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In