Abstract
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.
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References
Ackermann J (1985) Sampled-data control systems. Springer, Berlin
Franklin GF, Powell JD, Emami-Naeini A (1986) Feedback control of dynamic systems. Addison-Wesley, Reading
Gawronski WK (2004) Advanced structural dynamics and active control of structures. Springer, Berlin
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):768
Hughes PC (1987) Space structure vibration modes: how many exist? Which ones are important? IEEE Control Syst Mag 7:22–28
Junkins JL, Kim Y (1993) Introduction to dynamics and control of flexible structures. In: AIAA education series
Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs
Kim Y, Junkins JL (1991) Measure of controllability for actuator placement. AIAA J Guid Control Dyn 14(5):895–902
Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley, New York
Moore BC (1981) Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Trans Autom Control AC-26(1):17–32
Skelton RE, Hughes PC (1980) Modal cost analysis for linear matrix second-order systems. ASME J Dyn Syst Meas Control 102:151–158
Wiberg DM (1971) State space and linear systems. McGraw-Hill Schaum’s outline series in engineering
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Preumont, A. (2018). Controllability and Observability. In: Vibration Control of Active Structures. Solid Mechanics and Its Applications, vol 246. Springer, Cham. https://doi.org/10.1007/978-3-319-72296-2_12
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DOI: https://doi.org/10.1007/978-3-319-72296-2_12
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