Abstract
This paper contributes to the problem of tracking control for nonlinearly vibrating structure supporting a vibrational mass-carrying string with unknown string tension. The control scheme is constructed based on optimally designed reaching law considering actuator force limit, parametric uncertainties and Lyapunov stability conditions. The reaching law is designed through real-time detection of stability margins and analyzing actuator capabilities such that system dynamics are either driven into reaching or attraction phase in finite time. The control algorithm boasts robustness against parametric uncertainty by narrowing stability bounds and features an online string tension estimation engine based on data analysis obtained from acceleration and proximity sensors measurements. In order to provide smooth tracking, string vibration suppression is achieved by incorporating corresponding dynamical terms in construction of control algorithm. The closed-loop system is simulated alongside conventional discrete sliding mode technique, the results of which are compared and analyzed to pinpoint viable advantages.
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