Abstract
The chapter begins with a discussion of the mechanisms involved in the active tendon control of strings and cables; the Integral Force Feedback (IFF with collocated actuator/sensor pairs) is then applied and confirmed by a basic experiment, even at the parametric resonance. Next, the linear theory of the decentralized active damping of cable structures with IFF is developed and closed-loop analytical results are established; the Beta controller is introduced to recover the static stiffness of the cables. The analytical results are confirmed by a set of experiments on a guyed truss and on a space truss representative of an interferometer. Next, a laboratory mock-up representative of a cable-stayed bridge during its construction phase is used to study the control of the parametric resonance of uncontrolled stay cables. A successful large scale experiment conducted on a mock-up of 30 m controlled with hydraulic actuators is also described. The final part of the chapter is devoted to the active damping of suspension bridges using active stay cables; it is applied numerically to the model of a pedestrian bridge and confirmed experimentally on a laboratory mock-up. The chapter concludes with a list of references.
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Notes
- 1.
the excitation u appears as a parameter in the differential equation.
- 2.
To establish the vibration absorbing properties of Eq. (15.2) when T is the dynamic component of the tension in the cable, one can show that the dynamic contribution to the total energy, resulting from the vibration around the static equilibrium position, is a Lyapunov function. Thus, the stability is guaranteed if we assume perfect sensor and actuator dynamics. Note that the fact that the global stability is guaranteed does not imply that all the vibration modes are effectively damped. In fact, from a detailed examination of the dynamic equations (e.g., [1, 9, 10]), it appears that not all the cable modes are controllable with this actuator and sensor configuration. The odd numbered in-plane modes (in the gravity plane) can be damped substantially because they are linearly controllable by the active tendon (inertia term in Fig. 15.2c) and linearly observable from the tension in the cable; all the other cable modes are controllable only through active stiffness variation (parametric excitation in Fig. 15.2), and observable from quadratic terms due to cable stretching. However, these weakly controllable modes are never destabilized by the control system, even at the parametric resonance, when the natural frequency of the structure is twice that of the cable.
- 3.
piezoelectric force sensors have a built-in high-pass filter.
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Preumont, A. (2018). Tendon Control of Cable Structures. 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_15
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