Controllability and Observability

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 246)


This chapter is devoted to the analysis of the controllability and the observability. The goal pursued is to derive quantitative rather than qualitative measures which can be used in actuator and sensor placement. The chapter reviews some concepts which have been proposed to this end. The controllability and observability Gramians are introduced and a coordinate transformation is performed to define a set of internally balanced coordinates that can be used in model reduction. For the particular case of lightly damped flexible structures considered here, if modal coordinates are used, it turns out that the static gains of the various modes constitute a valuable aggregate information regarding the contribution of a mode to the input–output relationship, and can therefore be used in model reduction. The chapter concludes with a short list of references and a set of problems.


Controllability Observability Control canonical form PHB test Gramians Internally balanced coordinates Model reduction 


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Active Structures LaboratoryUniversité Libre de BruxellesBrusselsBelgium

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