MS19.1: Systems with Time Delay

In the study, we analyse the experimental implementation of the act-and-wait control concept used for the purpose of digital position control. The initial model and simulation demonstrates the relevance of the control concept, which results are validated by experiments on a linear actuator. To get a better explanation of the measurement results, the model of the controlled system is improved. The effects of back electromotive force and the inductance is included into the motor model. The effect of the damping from dry friction is considered. Moreover, the limiting factors of the electric circuit are included on the voltage and current, which serves as a nonlinear saturation effect on the control. The significance of the different effect are analysed and compared to the measurement results.

We propose two approaches to approximating the Lyapunov exponents of renewal equations (delay equations of Volterra type). One is based on the pseudospectral reduction to ordinary differential equations and the application of the discrete QR method; the other consists in lifting the discrete QR method to infinite dimension and applying it to the renewal equation reformulated in a suitable Hilbert space.

The stabilization problem for a nonlinear Ordinary Differential Equation (ODE) coupled with a system of hyperbolic Partial Differential Equations (PDEs) in the actuating path is investigated. Herein, a general prediction-based control law is proposed. It is mathematically proved that the proposed control law can stabilize the system. Compared to the previous related studies, firstly, this approach is applicable for nonlinear systems and, secondly, distributed states along the spatial domain do not need to be measured and only boundary state measurement suffices for the feedback law.

The effects of the time-delayed vibration absorbers (TDVAs) on the dynamic characteristics of a nonlinear metastructure are explored. First, the effect of using a single TDVA on the metastructure for vibration suppression is studied. The results show that the introduction of time-delayed feedback control is beneficial to improve the vibration suppression of the metastructure in the anti-resonance range. Then, the relationship between the dynamic response of the metastructure and the control parameters of the multiple TDVAs which are evenly distributed is explored. The relationship between the effective vibration suppression frequency band and the control parameters is given. From the results in this study, it is found that the introduction of equivalent damping by time-delayed control can achieve a significant broadening of the effective vibration suppression frequency band. The band gap can be expanded to more than twice its original width.