Closed-loop input shaping for flexible structures using time-delay control

Research output: Contribution to journalArticle

Abstract

Input shaping techniques reduce the residual vibration inflexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller.

Original languageEnglish (US)
Pages (from-to)454-460
Number of pages7
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Volume122
Issue number3
StatePublished - Sep 2000

Fingerprint

Flexible structures
Time delay
time lag
Riccati equations
Linear matrix inequalities
Control theory
System stability
Closed loop systems
Feedback control
Stabilization
Degradation
impulses
Controllers
feedback control
Riccati equation
structural vibration
systems stability
control theory
commands
cancellation

Keywords

  • Flexible Structures
  • Input Shaping
  • Linear Matrix Inequality
  • Riccati Equation
  • Time-Delay Control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Instrumentation

Cite this

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title = "Closed-loop input shaping for flexible structures using time-delay control",
abstract = "Input shaping techniques reduce the residual vibration inflexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller.",
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N2 - Input shaping techniques reduce the residual vibration inflexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller.

AB - Input shaping techniques reduce the residual vibration inflexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller.

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