Certifying Safety for Nonlinear Time Delay Systems via Safety Functionals: A Discretization Based Approach

In this paper, we consider the safety of continuous time control systems with input delays. Safety functionals are constructed that define safety sets in the infinite-dimensional state space. Time-discretization is used in order to compute safety sets in finite dimensions and it is shown that these sets approach an infinite-dimensional safety set as the time step is decreased. A simple example of a nonlinear scalar system is used to demonstrate the convergence of the proposed methods. © 2021 American Automatic Control Council

State-dependent distributed-delay model of orthogonal cutting

In this paper we present a model of turning operations with state-dependent distributed time delay. We apply the theory of regenerative machine tool chat- ter and describe the dynamics of the tool-workpiece sys- tem during cutting by delay-diferential equations. We model the cutting-force as the resultant of a force sys- tem distributed along the rake face of the tool, which results in a short distributed delay in the governing equation superimposed on the large regenerative de- lay. According to the literature on stress distribution along the rake face, the length of the chip-tool inter- face, where the distributed cutting-force system is act- ing, is function of the chip thickness, which depends on the vibrations of the tool-workpiece system due to the regenerative efect. Therefore, the additional short de- lay is state-dependent. It is shown that involving state- dependent delay in the model does not afect linear sta- bility properties, but does afect the nonlinear dynamics of the cutting process. Namely, the sense of the Hopf bi- furcation along the stability boundaries may turn from sub- to supercritical at certain spindle speed regions

On the moment dynamics of stochastically delayed linear control systems

In this article, the dynamics and stability of a linear system with stochastic delay and additive noise are investigated. It is assumed that the delay value is sampled periodically from a stationary distribution. A semi‐discretization technique is used to time‐discretize the system and derive the mean and second‐moment dynamics. These dynamics are used to obtain the stationary moments and the corresponding necessary and sufficient stability conditions. The application of the proposed method is illustrated through the analysis of the Hayes equation with stochastic delay and additive noise. The method is also applied to the control design of a connected automated vehicle. These examples illuminate the effects of stochastic delays on the robustness of dynamical systems

Chatter Detection based on a Contact Sensor in Milling Operations

Chatter vibrations during machining operations are large-amplitude self-excited vibrations, which result in the loss of physical contact between the workpiece and the tool. This paper presents an electric contact sensor, which is used to detect the cutting and noncutting periods during the operation. The spectrum of the signal of the electric contact sensor is free from environmental noise and can be used to select the chatter frequencies as the boundary of stability is approached. The detection is automatic with the use of an analog phototransistor that helps the time-periodic sectioning of the measured signals. The presented approach makes chatter detection possible before harmful vibrations arise

Dynamic Characterization of Milling based on Interrupted Feed Motion

This study presents an experimental method for detecting and avoiding chatter vibrations that occur during general milling processes. The main idea is to capture the so-called dominant spectral properties from the transient vibrations of the milling process, which gives a good approximation for its dynamical behavior and provides a quantitative measure of stability. To induce transient vibration, the machining process is momentarily interrupted. Therefore, the method offers the possibility that the stability limit can be forecasted by extrapolation from stable and accurate measurement points without reaching harmful vibration on the machine tool. We present laboratory tests with momentary interrupted straight tool path to demonstrate the applicability of the proposed method