Many dynamic systems of practical interest have inherent time delays and thus are governed by delay differential equations (DDEs). Because DDEs are infinite dimensional, time-delayed systems may be difficult to stabilize using traditional controller design strategies. We apply the Galerkin approximation method using a new pseudo-inverse-based technique for embedding the boundary conditions, which results in a simpler mathematical derivation than has been presented previously. We then use the pole placement technique to design closed-loop feedback gains that stabilize time-delayed systems and verify our results through comparison to those reported in the literature. Finally, we perform experimental validation by applying our method to stabilize a rotary inverted pendulum system with inherent sensing delays as well as additional time delays that are introduced deliberately. The proposed approach is easily implemented and performs at least as well as existing methods.
Skip Nav Destination
Article navigation
Research-Article
Pole Placement for Time-Delayed Systems Using Galerkin Approximations
Shanti S. Kandala,
Shanti S. Kandala
Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
Search for other works by this author on:
Thomas K. Uchida,
Thomas K. Uchida
Department of Bioengineering,
Stanford University,
James H. Clark Center,
318 Campus Drive,
Stanford, CA 94305
Stanford University,
James H. Clark Center,
318 Campus Drive,
Stanford, CA 94305
Search for other works by this author on:
C. P. Vyasarayani
C. P. Vyasarayani
Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
e-mail: vcprakash@iith.ac.in
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
e-mail: vcprakash@iith.ac.in
Search for other works by this author on:
Shanti S. Kandala
Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
Thomas K. Uchida
Department of Bioengineering,
Stanford University,
James H. Clark Center,
318 Campus Drive,
Stanford, CA 94305
Stanford University,
James H. Clark Center,
318 Campus Drive,
Stanford, CA 94305
C. P. Vyasarayani
Department of Mechanical and
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
e-mail: vcprakash@iith.ac.in
Aerospace Engineering,
Indian Institute of Technology Hyderabad,
Kandi,
Sangareddy, Telangana 502285, India
e-mail: vcprakash@iith.ac.in
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 27, 2018; final manuscript received December 24, 2018; published online January 29, 2019. Assoc. Editor: Dumitru I. Caruntu.
J. Dyn. Sys., Meas., Control. May 2019, 141(5): 051012 (10 pages)
Published Online: January 29, 2019
Article history
Received:
February 27, 2018
Revised:
December 24, 2018
Citation
Kandala, S. S., Uchida, T. K., and Vyasarayani, C. P. (January 29, 2019). "Pole Placement for Time-Delayed Systems Using Galerkin Approximations." ASME. J. Dyn. Sys., Meas., Control. May 2019; 141(5): 051012. https://doi.org/10.1115/1.4042465
Download citation file:
Get Email Alerts
Cited By
Integral Sliding Mode Disturbance Observer-Based Preview Repetitive Control
J. Dyn. Sys., Meas., Control (July 2024)
Global-Position Tracking Control for Multi-Domain Bipedal Walking with Underactuation
J. Dyn. Sys., Meas., Control
Surge-Elimination Strategy for Aero-Engine Transient Control
J. Dyn. Sys., Meas., Control (July 2024)
Safe Reinforcement Learning-Based Balance Control for Multi-Cylinder Hydraulic Press
J. Dyn. Sys., Meas., Control (July 2024)
Related Articles
Pole Placement for Delay Differential Equations With Time-Periodic Delays Using Galerkin Approximations
J. Comput. Nonlinear Dynam (September,2021)
Oscillation Control of Quay-Side Container Cranes Using Cable-Length Manipulation
J. Dyn. Sys., Meas., Control (March,2007)
Analytic Bounds for Instability Regions in Periodic Systems With Delay via Meissner’s Equation
J. Comput. Nonlinear Dynam (January,2012)
Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Coefficients
J. Comput. Nonlinear Dynam (March,2015)
Related Proceedings Papers
Related Chapters
A Design Method for Modified Smith Predictors for Non-Minimum-Phase Time-Delay Plants with Feedback Connected Multiple Time-Delays
Intelligent Engineering Systems through Artificial Neural Networks Volume 18
Pre-Accidental Situations Highlighted by RECUPERARE Method and Data (PSAM-0029)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
Modeling in Biomedical Engineering
Intelligent Engineering Systems through Artificial Neural Networks, Volume 16