Multivariable H control for an active magnetic bearing flywheel system
Steyn, Stephanus Jacobus Marais
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Objectives: The aims of this pilot study were to quantify respiratory and potential dermal exposure of nail technicians to acetone, formaldehyde, ethyl methacrylate, methyl methacrylate, toluene and xylene. Fifteen female nail technicians, working in different salons participated in this study. Products used for nail treatments differed between salons. Most salons used acrylate based nail products whereas others used UV–gel products exclusively. Methods: The participants were divided into two groups, those who used acrylate– and those who used UV–gel products exclusively. Eight hour personal respiration exposure to acetone, formaldehyde, ethyl methacrylate, methyl methacrylate, toluene and xylene were determined. The concentration of airborne volatile organic compounds in the salons was also determined with the use of a direct reading instrument (EntryRAE). Potential dermal exposure to the above mentioned solvents (excluding formaldehyde) was determined with the use of charcoal pads (surrogate skin method). During respiratory and dermal sampling, observations were made regarding work practices and control measures used in the salons. Results: It was found that the eight hour time weighed average exposure is well below the recommended occupational exposure limits of the individual chemicals and showed no additive effect. The highest mean respiratory exposures in both groups were acetone (27.22 mg/m3 and 28.36 mg/m3). EntryRAE results showed peak periods of exposure to volatile organic compounds during the day (322.16 ppm) that were much higher than the average eight hour exposure (0.21 ppm). The two groups’ exposure levels were compared to determine if there is a significant difference between the exposures levels but no statistically significant difference was found. The dermal exposures on hand and neck to acetone, ethyl methacrylate and methyl methacrylate showed strong significant correlations to the concordant chemical’s respiratory exposures. Correlations between air and dermal exposure was calculated once more after adjusting dermal exposure but the findings indicated only one statistically significant correlation of 0.42 in the case of ethyl methacrylate. Conclusion: Nail technicians are not at immediate health risk as the exposure in nail salons are well below recommended occupational exposure limits. However the unknown effects of chronic low level exposure to solvents and the large number of previous studies that reported increased health risks in nail technicians must also be considered. The use of methyl methacrylate in nail products sold in South Africa is also worrying as methyl methacrylate is banned by the FDA in the US due to its skin sensitisation potential that may lead to allergic contact dermatitis. The methods used to determine potential dermal exposure as well as adjusted dermal exposure remains problematic. This is due to the high percentage of adjusted dermal exposure values that had to be estimated and the fact that the activated charcoal pads have a higher absorption potential than human skin. Both methods must be improved to increase accuracy of results. Observations and EntryRAE results demonstrated the irregular nature of a nail technician’s work shift as well tasks performed from day to day. This complicates gathering data that is representative of a nail technicians eight hour exposure. Therefore to further improve accuracy of results, sampling should in future be task specific. Conventional ball–bearings in rotational applications can potentially be replaced by active magnetic bearings (AMBs). AMBs levitate the rotor via contact–free, actively controlled, electromagnetic forces. At the North–West University, AMBs are applied to a flywheel unin–terrupted power supply (Fly–UPS) system. Regrettably, AMBs are inherently open–loop un–stable because of the inverse displacement–force relationship, and for this reason requires closed–loop feedback control. Thus, the feasibility of multivariable H control for a Fly–UPS system is investigated. At present, the Fly–UPS system is being controlled by a number of decentralized single–input single–output (SISO), PD controllers. Ultimately, the combination of a multivariable plant, inherent instability, model uncertainties, cross–coupled stiffness, high rotational speed as well as external disturbances, calls for the development of a multivariable robust H controller. The aim of H control is to compute a controller such that the modelling uncertainties, noise and disturbances are minimized according to predefined performance and robustness re–quirements. A state–space model of both the radial AMBs and the axial AMB of the Fly–UPS system is developed and modelled according to the parameters of the physical rotor system. The sen–sors, power amplifiers and anti–aliasing filters are modelled and cascaded onto the rotor model. Finally, the system response is evaluated whereby the developed multivariable model is verified and validated. In the context of robust H control, it is vital in specifying the uncertainty bound (difference weighting function) between the mathematical model and physical system in order to ascer–tain stability robustness. Thus, the additive uncertainties between the nominal simulation model and the physical model at varied rotational speeds are characterised. Furthermore, the mixed sensitivity H control synthesis strategy is described. Different weighting schemes are explained and the six block problem weighting scheme is used for H controller synthesis. A multivariable controller is synthesised with weighting functions relevant to the AMB Fly–UPS system and the controller is reduced to a 19th order controller for implementation.
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