Digital control of cable vibration with time delay
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Digital control of cable vibration with time delay László E. Kollár1 Received: 4 June 2020 / Revised: 1 October 2020 / Accepted: 5 October 2020 © The Author(s) 2020
Abstract A simplified model for active control of vibration of a suspended cable is proposed. The model is constructed so that it considers the dynamic characteristics of the cable at the location where a vibration absorber is attached together with the absorber itself. The control is applicable for attenuating high-frequency, low-amplitude cable vibration due to periodic excitation that may model the wind effect. The methodology to choose control parameters is based on the dynamics of the vibration absorber and the stability analysis of the controlled system. The model takes into account the time delay that is always present in digital control due to sampling. Results reveal that the application of active control reduces vibration amplitude significantly provided that samples are taken in short time intervals. Increasing time delay reduces the effects of control and above a critical value, the vibration amplitude becomes even greater than without control. The importance of time delay grows with increasing excitation frequency, which means a limitation of the application of the control methodology developed. This limitation concerns the highest excitation frequencies. Keywords Control · Delay · Modelling · Vibration
1 Introduction Cable structures are often exposed to natural phenomena that induce cable vibration. The main application areas where such problems occur are power transmission lines and cablestayed bridges. The sources of cable vibration include wind, ice accretion, ice shedding, or impact of another body. The characteristics of the resulting vibration depends on the inducing mechanism. The regular shedding of vortices due to wind results in high-frequency, low-amplitude vibration, the so-called aeolian vibration. Another type of wind-induced vibration, the galloping, is a movement-induced excitation, which leads to high-amplitude, low-frequency vibration. Vibration with a great jump height of the cable may also be caused by shedding of heavy ice chunks from the suspended cable, although the vibration decays due to structural damping. The present paper focuses on high-frequency, lowamplitude vibration. The aeolian vibration is characterized by frequency in the range of 3–150 Hz and by amplitude in the range of cable
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László E. Kollár [email protected] Savaria Institute of Technology, ELTE Eötvös Loránd University, Budapest, Károlyi G. tér 4, Szombathely 9700, Hungary
diameter [1, 2]. The forces developing during such vibration are relatively small; therefore, quick damage in the cable structure is not probable. However, frequent occurrence of this high-frequency vibration leads to reduced reliability and lifespan due to fatigue of the cable and other accessories of the structure. These problems justified the research effort made in the last few decades in order to develop damping devices and methods to mitigate high-frequency cable vibr
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