Controllability and Observability
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.
KeywordsControllability Observability Control canonical form PHB test Gramians Internally balanced coordinates Model reduction
- 2.Franklin GF, Powell JD, Emami-Naeini A (1986) Feedback control of dynamic systems. Addison-Wesley, ReadingGoogle Scholar
- 4.Hamdan AMA, Nayfeh AH, (1989) Measure of modal controllability and observability for first and second order linear systems. AIAA J Guid Control Dyn 12(5):768Google Scholar
- 6.Junkins JL, Kim Y (1993) Introduction to dynamics and control of flexible structures. In: AIAA education seriesGoogle Scholar
- 10.Moore BC (1981) Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Trans Autom Control AC-26(1):17–32Google Scholar
- 12.Wiberg DM (1971) State space and linear systems. McGraw-Hill Schaum’s outline series in engineeringGoogle Scholar