This paper presents an approximate analytical solution for the weakly nonlinear closed-loop dynamics of the sliding phase of a sliding mode controlled rotary inverted pendulum based on the multiple scale method. A locally stable nonlinear sliding mode control law with starting configurations above the horizontal line is presented for the rotary inverted pendulum. The analytical expressions derived from the nonlinear solution of the reduced-order closed-loop dynamics provide both qualitative and quantitative insight into the closed-loop response leading to proper selection of parameters that guarantee stabilization and improve controller performance. The approximate analytical solution is verified through comparison with the exact numerical solution. The control performance predicted by the analytical solution is experimentally demo.
Skip Nav Destination
Article navigation
March 2012
Technical Briefs
Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design
Hashem Ashrafiuon,
Hashem Ashrafiuon
Director, Center for Nonlinear Dynamics and Control Professor e-mail:
Search for other works by this author on:
Alan M. Whitman
Alan M. Whitman
Professor Emeritus
Department of Mechanical Engineering, Villanova University, Villanova
, PA 19085
Search for other works by this author on:
Hashem Ashrafiuon
Director, Center for Nonlinear Dynamics and Control Professor e-mail:
Alan M. Whitman
Professor Emeritus
Department of Mechanical Engineering, Villanova University, Villanova
, PA 19085J. Dyn. Sys., Meas., Control. Mar 2012, 134(2): 024503 (9 pages)
Published Online: December 30, 2011
Article history
Received:
February 2, 2011
Revised:
September 26, 2011
Online:
December 30, 2011
Published:
December 30, 2011
Citation
Ashrafiuon, H., and Whitman, A. M. (December 30, 2011). "Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design." ASME. J. Dyn. Sys., Meas., Control. March 2012; 134(2): 024503. https://doi.org/10.1115/1.4005358
Download citation file:
Get Email Alerts
Cited By
Data-Driven Tracking Control of a Cushion Robot With Safe Autonomous Motion Considering Human-Machine Interaction Environment
J. Dyn. Sys., Meas., Control (July 2025)
Dynamic Obstacle Avoidance Strategy for High-Speed Vehicles Via Constrained Model Predictive Control and Improved Artificial Potential Field
J. Dyn. Sys., Meas., Control (July 2025)
An Adaptive Sliding-Mode Observer-Based Fuzzy PI Control Method for Temperature Control of Laser Soldering Process
J. Dyn. Sys., Meas., Control
Related Articles
Adaptive Variable Structure Control of Linear Delayed Systems
J. Dyn. Sys., Meas., Control (December,2005)
Optimal Sliding Mode Cascade Control for Stabilization of Underactuated Nonlinear Systems
J. Dyn. Sys., Meas., Control (March,2012)
Robust Stabilization for a Class of Nonlinear Singularly Perturbed Systems
J. Dyn. Sys., Meas., Control (September,2011)
Block Control Principle for Mechanical Systems
J. Dyn. Sys., Meas., Control (March,2000)
Related Proceedings Papers
Related Chapters
Dynamic Simulations to Become Expert in Order to Set Fuzzy Rules in Real Systems
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
Design and Performance of PD and LQR Controller for Double Inverted Pendulum System
International Conference on Software Technology and Engineering (ICSTE 2012)
Smart Semi-Active Control of Floor-Isolated Structures
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17