Spatial ℋ 2 control of a piezoelectric laminate beam: Experimental implementation

Dunant Halim, S. O.Reza Moheimani

Research output: Journal PublicationArticlepeer-review

60 Citations (Scopus)


The aim of this paper is to design and experimentally evaluate the performance of a feedback controller to suppress vibration of a flexible beam. The controller is designed to minimize the spatial ℋ 2 norm of the closed-loop system to ensure average reduction of vibration throughout the entire structure. Vibrations of the first six bending modes of the beam are to be controlled using a collocated piezoelectric actuator-sensor pair attached to the beam. Feedthrough terms are incorporated into the flexible-structure model to correct the locations of the in-bandwidth zeros. It is shown that the spatial ℋ 2 control has an advantage over the pointwise ℋ 2 control in minimizing the vibration of the entire structure. The spatial ℋ 2 controller minimizes the ℋ 2 norm of the entire structure more uniformly, while the pointwise ℋ 2 controller only has a local effect. The implemented spatial ℋ 2 controller is able to minimize the first six bending modes of the beam effectively. This spatial ℋ 2 control can also be applied to more general structural vibration suppression problems.

Original languageEnglish
Pages (from-to)533-546
Number of pages14
JournalIEEE Transactions on Control Systems Technology
Issue number4
Publication statusPublished - Jul 2002


  • Flexible structures
  • Intelligent structures
  • Piezoelectric transducers
  • Spatial ℋ norm
  • Vibration control
  • ℋ control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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