Chaos control applied to adaptive mechanical systems

Abstract

This work studies the application of continuous chaos controllers to mechanical systems in two parts. In the first part, the controllers are applied in smart structures with shape memory alloys (SMA) elements. Actuation is provided by exploring the thermomechanical behaviour of SMA, which is limited by heat transfer constraints. The controlled orbits stability analysis is performed by the calculation of its Floquet exponents (FE). A novel method to extract a controlled orbit FE through its time series is proposed. The control method, based on the extended time-delayed feedback control (ETDF), is applied to an SMA pendulum system and an SMA two-bar truss. Two constitutive models are used to verify the SMA actuation and the influence of the thermal constraints. Results show that, even with the imposed actuation constraints, the controller can perform the stabilization of the targeted unstable periodic orbit (UPO). It is shown that the controlled orbit FE exponents present an exponential dependence with the heat transfer coefficient. In regards to bifurcation control, results show that actuation constraints define the range of parameters where the controller can maintain orbit stability. In the second part, controllers are used to perform exchange between coexisting attractors on an experimental impact oscillator. In this context, three control methods are used, the time-delayed feedback method, the intermittent control and a novel method named fractional time-delayed feedback control (FTDF). Results show that the FTDF can perform the exchange between attractors even in a scenario where TDF alone cannot.