How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

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Stability properties of coupled impedance passive LTI systems

We study the stability of the feedback interconnection of two impedance passive linear time-invariant systems, of which one is finite-dimensional. The closed-loop system is well known to be impedance passive, but no stability properties follow from this alone. We are interested in two main issues: (1) the strong stability of the operator semigroup associated with the closed-loop system, (2) the input-output stability (meaning transfer function in H∞) of the closed-loop system. Our results are illustrated with the system obtained from the non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) model representing a vertical beam clamped at the bottom, with a rigid body having a large mass on top, connected with a trolley mounted on top of the rigid body, via a spring and a damper. Such an arrangement called a tuned mass damper (TMD), is used to stabilize tall buildings. We show that the SCOLE-TMD system is strongly stable on the energy state space and that the system is input-output stable from the horizontal force input to the horizontal velocity output

Strong stabilization of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilization of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform SCOLE system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilization theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilized. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor

Exponential stabilization of well-posed systems by colocated feedback

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