Vibrations in Single-Degrees-of-Freedom Sampled-Data Linear Mechanical Systems

This paper aims to present that the effect of sampling can result in multi-frequency vibration even in the case of a single-degree-of-freedom linear mechanical model. Even though the sampled-data systems have an infinite number of characteristic exponents due to sampling, the vibrations of these systems can still be characterized by an effective system model with a single dominant frequency. However, as this paper shows, additional harmonics become relevant, resulting in multi-frequency vibrations depending on the magnitude of applied control parameters. The vibrations presented by the time histories of vibration and their spectra resulted in numerical simulation of the sampled-data system

Alternative Method to Determine the Characteristic Polynomial Applying Three-by-Three Matrices

The main aim of this paper is the presentation of the connection between the elements of the classical matrix arithmetic in case of three-by-three arbitrary real matrices. The given formulae can be used as well in case of the topic of stability analysis connected to the characteristic polynomial. The theorems and formulae presented in this article can be used in linear algebra courses or e.g. in three Degrees-of-Freedom mechanical problems, in machine tool bases designing, or in analyzes of earthquake effect on different type of structures

On the Stability of Digital Position Control with Viscous Damping and Coulomb Friction

In this paper, we investigate the combined effect of viscous damping and Coulomb friction on sampled-data mechanical systems. In these systems, instability can occur due the sampling of the applied discrete-time controller which is compensated by the two different physical dissipation effects. In order to investigate the interplay between these, we focus on how the stable domain of operation is extended by the dry friction compared to viscous damping. We also show that dry friction causes concave envelope vibrations in this extended region. The analytical results, presented in the form of stability charts, are verified by a detailed set of simulations at different representative control parameter values

Friction Effects on Stability of a Digitally Controlled Pendulum

This paper investigates the stability of a digitally controlled pendulum with Coulomb friction as primary source of dissipation. We focus on the stabilizing effect of friction against vibrations due to the otherwise unstable parameter settings, and we show how the stable domain of operation is expanded compared to the undamped case. Continuous time and discrete switched models are simulated to get information about the stabilization effect of friction. A special concave vibration envelope is identified, validated by experiments and shown as a characteristic form of vibrations for digitally controlled systems with dry friction

Experimental investigation of micro-chaos

Micro-chaos is a phenomenon when small amplitude chaotic oscillations are inflicted by digital effects (sampling, roundoff and processing delay). In previous works, various digitally controlled unstable linear mechanical systems were analysed; the corresponding micro-chaos maps were derived and the coexistence of several disconnected chaotic attractors was proven. The distance of the farthest attractor from the desired state can be quite large, while the size of these attractors is usually negligible from practical point of view. This is why the phenomenon could be the source of remarkable control error. In this paper, the micro-chaos map of the PD-controlled inverted pendulum – with rounding applied to the calculated control effort, and considering dry friction – is examined by modified Simple Cell Mapping methods and the possibility of constructing an experimental device showing the phenomenon of micro-chaos is analysed. A device having variable control force resolution is presented, and experiments are carried out to verify the theoretical and numerical results

Haptic Rendering and Human Stabilization in Presence of Structural Flexibility

Unstable behaviour is a significant problem in many haptic applications. The sampled-data nature and time delays induce complex dynamic behaviours in such systems. Structural flexibility may further reduce the stable domain of operation. This is illustrated via the systematic modeling and analysis of an impedance type haptic device with typical design elements such as closed-loop mechanisms and cable/capstan drives. The role of the operator in the dynamics of these systems is also demonstrated. The present work provide stability analysis, experimental validation and derive conditions for the range of parameters in which the operator can significantly contribute to the stabilization of the system

Mintavételes nemlineáris rendszerek stabilitásvizsgálata: Stability analysis of sampled-data nonlinear systems

Nowadays, positioning tasks are implemented with computers, which are basically resulted in sampled-data systems. Stability is the most important aspect in designing of closed-loop control systems. Models for establishing stability criteria often approximate or neglect some physical phenomena – dry friction for example. The purpose of this paper is to study the effects of sampling and dry friction in closed-loop control using analytic methods, simulation and experiments. Kivonat A pozícionálási feladatok napjainkban számítógépek segítségével kerülnek megvalósításra, mintavételes rendszereket eredményezve. A szabályozók fő tervezési szempontja a stabilitás, melynek vizsgálatához felállított modellek bizonyos jelenségeket (például a száraz súrlódást) gyakran elhanyagolnak. Ezen cikk célja a mintavételezés és a száraz súrlódás hatásainak vizsgálata analitikus, szimulációs és kísérleti módszerek segítségével egy egyenáramú villamos motor példáján keresztül

Limitations Caused by Sampling and Quantization in Position Control of a Single Axis Robot

This paper presents the theoretical and experimental investigation of the dynamics of a single degree-of-freedom robotic arm subjected to digital position control. The experimental setup consists of an industrial robot axis, a microcontroller based low-level control unit, and a highlevel Matlab/Simulink position controller. The stable domain of operation is calculated in the parameter space of the sampling time and the gains of the applied proportional-derivative (PD) controller. The calculated stability charts are verified by experiments, and the paper reports the limitations on system stability caused by the digital effects and the applied control setup

Macrophages engulf apoptotic and primary necrotic thymocytes through similar phosphatidylserine-dependent mechanisms

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