Active vibration control at machinery feet

The unmitigated transmission of undesirable vibration can result in problems by way of causing human discomfort, machinery and equipment failure, and affecting the quality of a manufacturing process. When identifiable transmission paths are discernible, vibrations from the source can be isolated from the rest of the system and this prevents or minimises the problems. The approach proposed here for vibration isolation is active force cancellation at points close to the vibration source. It uses force feedback for multiple-input and multiple-output control at the mounting locations. This is particularly attractive for rigid mounting of machine on relative flexible base where machine alignment and motions are to be restricted. The force transfer function matrix is used as a disturbance rejection performance specification for the design of MIMO controllers. For machine soft-mounted via flexible isolators, a model for this matrix has been derived. Under certain conditions, a simple multiplicative uncertainty model is obtained that shows the amount of perturbation a flexible base has on the machine-isolator-rigid base transmissibility matrix. Such a model is very suitable for use with robust control design paradigm. A different model is derived for the machine on hard-mounts without the flexible isolators. With this model, the level of force transmitted from a machine to a final mounting structure using the measurements for the machine running on another mounting structure can be determined. The two mounting structures have dissimilar dynamic characteristics. Experiments have verified the usefulness of the expression. The model compares well with other methods in the literature. The disadvantage lies with the large amount of data that has to be collected. Active force cancellation is demonstrated on an experimental rig using an AC industrial motor hard-mounted onto a relative flexible structure. The force transfer function matrix, determined from measurements, is used to design H and Static Output Feedback controllers. Both types of controllers are stable and robust to modelling errors within the identified frequency range. They reduce the RMS of transmitted force by between 30?80% at all mounting locations for machine running at 1340 rpm. At the rated speed of 1440 rpm only the static gain controller is able to provide 30?55% reduction at all locations. The H controllers on the other hand could only give a small reduction at one mount location. This is due in part to the deficient of the model used in the design. Higher frequency dynamics has been ignored in the model. This can be resolved by the use of a higher order model that can result in a high order controller. A low order static gain controller, with some tuning, performs better. But it lacks the analytical framework for analysis and design.

An opportunity for system dynamics in manufacturing system modelling

The computer simulation of manufacturing systems is commonly carried out using discrete event simulation (DES). Indeed, there appears to be a lack of applications of continuous simulation methods, particularly system dynamics (SD), despite evidence that this technique is suitable for industrial modelling. This paper investigates whether this is due to a decline in the general popularity of SD, or whether modelling of manufacturing systems represents a missed opportunity for SD. On this basis, the paper first gives a review of the concept of SD and fully describes the modelling technique. Following on, a survey of the published applications of SD in the 1990s is made by developing and using a structured classification approach. From this review, observations are made about the application of the SD method and opportunities for future research are suggested.

Quality control of pharmaceutical ingredients:developing a caking test for industry

Objectives - Powdered and granulated particulate materials make up most of the ingredients of pharmaceuticals and are often at risk of undergoing unwanted agglomeration, or caking, during transport or storage. This is particularly acute when bulk powders are exposed to extreme swings in temperature and relative humidity, which is now common as drugs are produced and administered in increasingly hostile climates and are stored for longer periods of time prior to use. This study explores the possibility of using a uniaxial unconfined compression test to compare the strength of caked agglomerates exposed to different temperatures and relative humidities. This is part of a longer-term study to construct a protocol to predict the caking tendency of a new bulk material from individual particle properties. The main challenge is to develop techniques that provide repeatable results yet are presented simply enough to be useful to a wide range of industries. Methods - Powdered sucrose, a major pharmaceutical ingredient, was poured into a split die and exposed to high and low relative humidity cycles at room temperature. The typical ranges were 20–30% for the lower value and 70–80% for the higher value. The outer die casing was then removed and the resultant agglomerate was subjected to an unconfined compression test using a plunger fitted to a Zwick compression tester. The force against displacement was logged so that the dynamics of failure as well as the failure load of the sample could be recorded. The experimental matrix included varying the number of cycles, the amount between the maximum and minimum relative humidity, the height and diameters of the samples, the number of cycles and the particle size. Results - Trends showed that the tensile strength of the agglomerates increased with the number of cycles and also with the more extreme swings in relative humidity. This agrees with previous work on alternative methods of measuring the tensile strength of sugar agglomerates formed from humidity cycling (Leaper et al 2003). Conclusions - The results show that at the very least the uniaxial tester is a good comparative tester to examine the caking tendency of powdered materials, with a simple arrangement and operation that are compatible with the requirements of industry. However, further work is required to continue to optimize the height/ diameter ratio during tests.

Generalized mean field approximation for parallel dynamics of the Ising model

The dynamics of the non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The proposed method shows significant improvement in predicting local system properties compared to other mean field approximation techniques, particularly in systems with symmetric interactions. Results are also evaluated against those obtained from Monte Carlo simulations. The method is also employed to obtain parameter values for the kinetic inverse Ising modeling problem, where couplings and local field values of a fully connected spin system are inferred from data. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Monitoring of transcriptional dynamics of HIF and NFκB activities

Genetic experiments over the last few decades have identified many regulatory proteins critical for DNA transcription. The dynamics of their transcriptional activities shape the differential expression of the genes they control. Here we describe a simple method, based on the secreted luciferase, to measure the activities of two transcription factors NF?B and HIF. This technique can effectively monitor dynamics of transcriptional events in a population of cells and be up-scaled for high-throughput screening and promoter analysis, making it ideal for data-demanding applications such as mathematical modelling.

Polarisation dynamics of vector soliton molecules in mode locked fibre laser

Two fundamental laser physics phenomena - dissipative soliton and polarisation of light are recently merged to the concept of vector dissipative soliton (VDS), viz. train of short pulses with specific state of polarisation (SOP) and shape defined by an interplay between anisotropy, gain/loss, dispersion, and nonlinearity. Emergence of VDSs is both of the fundamental scientific interest and is also a promising technique for control of dynamic SOPs important for numerous applications from nano-optics to high capacity fibre optic communications. Using specially designed and developed fast polarimeter, we present here the first experimental results on SOP evolution of vector soliton molecules with periodic polarisation switching between two and three SOPs and superposition of polarisation switching with SOP precessing. The underlying physics presents an interplay between linear and circular birefringence of a laser cavity along with light induced anisotropy caused by polarisation hole burning.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

Neural Control of Chaos and Aplications

Signal processing is an important topic in technological research today. In the areas of nonlinear dynamics search, the endeavor to control or order chaos is an issue that has received increasing attention over the last few years. Increasing interest in neural networks composed of simple processing elements (neurons) has led to widespread use of such networks to control dynamic systems learning. This paper presents backpropagation-based neural network architecture that can be used as a controller to stabilize unsteady periodic orbits. It also presents a neural network-based method for transferring the dynamics among attractors, leading to more efficient system control. The procedure can be applied to every point of the basin, no matter how far away from the attractor they are. Finally, this paper shows how two mixed chaotic signals can be controlled using a backpropagation neural network as a filter to separate and control both signals at the same time. The neural network provides more effective control, overcoming the problems that arise with control feedback methods. Control is more effective because it can be applied to the system at any point, even if it is moving away from the target state, which prevents waiting times. Also control can be applied even if there is little information about the system and remains stable longer even in the presence of random dynamic noise.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical Manipulators

Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40

Comparison between conventional and stochastic pinning control

Theoretical developments on pinning control of complex dynamical networks have mainly focused on the deterministic versions of the model dynamics. However, the dynamical behavior of most real networks is often affected by stochastic noise components. In this paper the pinning control of a stochastic version of the coupled map lattice network with spatiotemporal characteristics is studied. The control of these complex dynamical networks have functional uncertainty which should be considered when calculating stabilizing control signals. Two feedback control methods are considered: the conventional feedback control and modified stochastic feedback control. It is shown that the typically-used conventional control method suffers from the ignorance of model uncertainty leading to a reduction and potentially a collapse in the control efficiency. Numerical verification of the main result is provided for a chaotic coupled map lattice network. © 2011 IEEE.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.