Fail-safe numerical control

System provides duplicate set of control logic circuitry. Comparators insure that the same data is present in both circuits. If any discrepancy is found, the machine is automatically stopped, before damage can occur

Numerical Control Machine Data Manual

Numerical Control Machine Data Manual provides programmers with specific information for various types and sizes of numerical control machine tools and auxiliary equipment

Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations

In this work we study the problem of step size selection for numerical schemes, which guarantees that the numerical solution presents the same qualitative behavior as the original system of ordinary differential equations, by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain feedback stabilization methods are exploited and numerous illustrating applications are presented for systems with a globally asymptotically stable equilibrium point. The obtained results can be used for the control of the global discretization error as well.Comment: 33 pages, 9 figures. Submitted for possible publication to BIT Numerical Mathematic

Numerical Simulation of Nano Scanning in Intermittent-Contact Mode AFM under Q control

We investigate nano scanning in tapping mode atomic force microscopy (AFM) under quality (Q) control via numerical simulations performed in SIMULINK. We focus on the simulation of whole scan process rather than the simulation of cantilever dynamics and the force interactions between the probe tip and the surface alone, as in most of the earlier numerical studies. This enables us to quantify the scan performance under Q control for different scan settings. Using the numerical simulations, we first investigate the effect of elastic modulus of sample (relative to the substrate surface) and probe stiffness on the scan results. Our numerical simulations show that scanning in attractive regime using soft cantilevers with high Qeff results in a better image quality. We, then demonstrate the trade-off in setting the effective Q factor (Qeff) of the probe in Q control: low values of Qeff cause an increase in tapping forces while higher ones limit the maximum achievable scan speed due to the slow response of the cantilever to the rapid changes in surface profile. Finally, we show that it is possible to achieve higher scan speeds without causing an increase in the tapping forces using adaptive Q control (AQC), in which the Q factor of the probe is changed instantaneously depending on the magnitude of the error signal in oscillation amplitude. The scan performance of AQC is quantitatively compared to that of standard Q control using iso-error curves obtained from numerical simulations first and then the results are validated through scan experiments performed using a physical set-up

Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no interaction between the agents. We give a characterization of the minimal time both for microscopic and macroscopic descriptions of a crowd. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control region to feed the desired final configuration. The construction of the control is explicit, providing a numerical algorithm for computing it. We finally give some numerical simulations