Brief Observer-controller design for cranes via Lyapunov equivalence

Authors:
Alessandro Giua;Carla Seatzu;Giampaolo Usai
Affiliations:
Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Piazza dArmi - 09123 Cagliari, Italy;Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Piazza dArmi - 09123 Cagliari, Italy;Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Piazza dArmi - 09123 Cagliari, Italy
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

We consider a linearized parameter-varying model of a planar crane and show how a controller can be designed, following the state-feedback stabilization technique for time-varying systems proposed by Wolovich. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. We also show that an observer can be designed applying Wolovich procedure to the dual system of the plant. The proposed procedure leads to the computation of the desired time-varying gains for controller and observer in a parameterized form. The results of several simulations with data taken from a real container crane, are also shown.