Attraction Region of Planar Linear Systems with One Unstable Pole and Saturated Feedback

Abstract.: The bifurcation of the attraction region for planar systems with one stable and one unstable pole under a saturated linear state feedback is considered. The attraction region can have either an unbounded hyperbolic shape or be bounded by a limit cycle. An analytical condition, under which either of these boundary shapes occurs, is given with a formal proof. This condition is based on the relationship between the stable and unstable manifolds associated with secondary saddle equilibrium points, whose presence is caused by the saturation on the inpu

Improving tokamak vertical position control in the presence of power supply voltage saturation

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the so-called instability of the current vertical position. Linearized models all share the feature of a single unstable eigenmode, attributable to this vertical instability of the plasma equilibrium movement, and a large number of stable or marginally stable eigenmodes, attributable to zero or positive resistance in all other model circuit equations. Due to the size and therefore cost of the ITER tokamak, there will naturally be smaller margins in the poloidal field coil power supplies, implying that the feedback control will experience actuator saturation during large transients due to a variety of plasma disturbances. Current saturation is relatively benign, due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling the approach to saturation which leads to the loss of one degree of freedom in the feedback control for each saturated coil. On the other hand, voltage saturation is produced. by the feedback controller itself, with no intrinsic delay. This paper presents a feedback controller design approach which explicitly takes saturation of the power supply voltage into account when producing the power supply demand signals. We consider the vertically stabilizing part of the ITER controller (fast controller) with one power supply and therefore a single saturated input. We. consider an existing ITER controller and enlarge its region of attraction to the full null controllable region by adding a continuous nonlinearity into the control. In a system with a single unstable eigenmode and a single stable eigenmode we have already provided a proof of the asymptotical stability of the closed loop system, and we have examined the performance of this new continuous nonlinear controller. We have subsequently extended this analysis to a system with a single eigenmode and multiple stable eigenmodes. The method requires state feedback control, and therefore a reconstruction of the states is indispensable. We discuss the feasibility of extracting these states from the available diagnostic information as well as other implementation details. As a complement to our ITER simulations we confirm the enlargement of the region of attraction by the new controller by a JET simulation

Clues for a standardised thermal-optical protocol for the assessment of organic and elemental carbon within ambient air particulate matter

Along with some research networking programmes, the European Directive 2008/50/CE requires chemical speciation of fine aerosol (PM_2.5), including elemental (EC) and organic carbon (OC), at a few rural sites in European countries. Meanwhile, the thermal-optical technique is considered by the European and US networking agencies and normalisation bodies as a reference method to quantify EC–OC collected on filters. Although commonly used for many years, this technique still suffers from a lack of information on the comparability of the different analytical protocols (temperature protocols, type of optical correction) currently applied in the laboratories. To better evaluate the EC–OC data set quality and related uncertainties, the French National Reference Laboratory for Ambient Air Quality Monitoring (LCSQA) organised an EC–OC comparison exercise for French laboratories using different thermal-optical methods (five laboratories only). While there is good agreement on total carbon (TC) measurements among all participants, some differences can be observed on the EC / TC ratio, even among laboratories using the same thermal protocol. These results led to further tests on the influence of the optical correction: results obtained from different European laboratories confirmed that there were higher differences between OC_TOT and OC_TOR measured with NIOSH 5040 in comparison to EUSAAR-2. Also, striking differences between EC_TOT / EC_TOR ratios can be observed when comparing results obtained for rural and urban samples, with EC_TOT being 50% lower than EC_TOR at rural sites whereas it is only 20% lower at urban sites. The PM chemical composition could explain these differences but the way it influences the EC–OC measurement is not clear and needs further investigation. Meanwhile, some additional tests seem to indicate an influence of oven soiling on the EC–OC measurement data quality. This highlights the necessity to follow the laser signal decrease with time and its impact on measurements. Nevertheless, this should be confirmed by further experiments, involving more samples and various instruments, to enable statistical processing. All these results provide insights to determine the quality of EC–OC analytical methods and may contribute to the work toward establishing method standardisation