Smith predictorlike designs for compensation of arbitrarily long input delays are commonly available only for finite-dimensional systems. Only very few examples exist, where such compensation has been achieved for partial differential equation (PDE) systems, including our recent result for a parabolic (reaction-diffusion) PDE. In this paper, we address a more challenging wave PDE problem, where the difficulty is amplified by allowing all of this PDE’s eigenvalues to be a distance to the right of the imaginary axis. Antidamping (positive feedback) on the uncontrolled boundary induces this dramatic form of instability. We develop a design that compensates an arbitrarily long delay at the input of the boundary control system and achieves exponential stability in closed-loop. We derive explicit formulae for our controller’s gain kernel functions. They are related to the open-loop solutions of the antistable wave equation system over the time period of input delay (this simple relationship is the result of the design approach).
Skip Nav Destination
e-mail: krstic@ucsd.edu
Article navigation
Research Papers
Dead-Time Compensation for Wave/String PDEs
Miroslav Krstic
Miroslav Krstic
Professor
Department of Mechanical and Aerospace Engineering,
e-mail: krstic@ucsd.edu
University of California
, San Diego La Jolla, CA 92093-0411
Search for other works by this author on:
Miroslav Krstic
Professor
Department of Mechanical and Aerospace Engineering,
University of California
, San Diego La Jolla, CA 92093-0411e-mail: krstic@ucsd.edu
J. Dyn. Sys., Meas., Control. May 2011, 133(3): 031004 (13 pages)
Published Online: March 23, 2011
Article history
Received:
December 6, 2008
Revised:
April 5, 2010
Online:
March 23, 2011
Published:
March 23, 2011
Citation
Krstic, M. (March 23, 2011). "Dead-Time Compensation for Wave/String PDEs." ASME. J. Dyn. Sys., Meas., Control. May 2011; 133(3): 031004. https://doi.org/10.1115/1.4003638
Download citation file:
Get Email Alerts
Offline and online exergy-based strategies for hybrid electric vehicles
J. Dyn. Sys., Meas., Control
Optimal Control of a Roll-to-Roll Dry Transfer Process With Bounded Dynamics Convexification
J. Dyn. Sys., Meas., Control (May 2025)
In-Situ Calibration of Six-Axis Force/Torque Transducers on a Six-Legged Robot
J. Dyn. Sys., Meas., Control (May 2025)
Active Data-enabled Robot Learning of Elastic Workpiece Interactions
J. Dyn. Sys., Meas., Control
Related Articles
Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions
J. Dyn. Sys., Meas., Control (December,2005)
Compensation of Time-Varying Input and State Delays for Nonlinear Systems
J. Dyn. Sys., Meas., Control (January,2012)
Transparency and Stability Robustness in Two-Channel Bilateral Telemanipulation
J. Dyn. Sys., Meas., Control (September,2001)
Delay-Independent Observer-Based Control for a Class of Neutral Systems
J. Dyn. Sys., Meas., Control (December,2004)
Related Proceedings Papers
Related Chapters
Pre-Accidental Situations Highlighted by RECUPERARE Method and Data (PSAM-0029)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
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
Stability of a Class of Nonlinear Stochastic Large-Scale Systems with Time Delay
International Symposium on Information Engineering and Electronic Commerce, 3rd (IEEC 2011)