2 Perturbation and sensitivity functions

Proceedings ◽  
2020 ◽  
Vol 63 (1) ◽  
pp. 46
Author(s):  
Mircea Dulau ◽  
Stelian-Emilian Oltean

An important stage in robust control design is to define the desired performances of the closed loop control system using the models of the frequency sensitivity functions S. If the frequency sensitivity functions remain within the limits imposed by these models, the control performances are met. In terms of the sensitivity functions, the specifications include: shape of S over selected frequency ranges, peak magnitude of S, bandwidth frequency, and tracking error at selected frequencies. In this context, this paper presents a study of the effects of the specifications of the weighting functions on the performances of robust control systems.


2016 ◽  
Vol 16 (15) ◽  
pp. 15 ◽  
Author(s):  
Steven M. Thurman ◽  
Pinakin Gunvant Davey ◽  
Kaydee Lynn McCray ◽  
Violeta Paronian ◽  
Aaron R. Seitz

1996 ◽  
Vol 75 (1) ◽  
pp. 75-96 ◽  
Author(s):  
D. R. Irvine ◽  
R. Rajan ◽  
L. M. Aitkin

1. Interaural intensity differences (IIDs) provide the major cue to the azimuthal location of high-frequency narrowband sounds. In recent studies of the azimuthal sensitivity of high-frequency neurons in the primary auditory cortex (field AI) of the cat, a number of different types of azimuthal sensitivity have been described and the azimuthal sensitivity of many neurons was found to vary as a function of changes in stimulus intensity. The extent to which the shape and the intensity dependence of the azimuthal sensitivity of AI neurons reflects features of their IID sensitivity was investigated by obtaining data on IID sensitivity from a large sample of neurons with a characteristic frequency (CF) > 5.5 kHz in AI of anesthetized cats. IID sensitivity functions were classified in a manner that facilitated comparison with previously obtained data on azimuthal sensitivity, and the effects of changes in the base intensity at which IIDs were introduced were examined. 2. IID sensitivity functions for CF tonal stimuli were obtained at one or more intensities for a total of 294 neurons, in most cases by a method of generating IIDs that kept the average binaural intensity (ABI) of the stimuli at the two ears constant. In the standard ABI range at which a function was obtained for each unit, five types of IID sensitivity were distinguished. Contra-max neurons (50% of the sample) had maximum response (a peak or a plateau) at IIDs corresponding to contralateral azimuths, whereas ipsi-max neurons (17%) had the mirror-image form of sensitivity. Near-zero-max neurons (18%) had a clearly defined maximum response (peak) in the range of +/- 10 dB IID, whereas a small group of tough neurons (2%) had a restricted range of minimal responsiveness with near-maximal responses at IIDs on either side. A final 18% of AI neurons were classified as insensitive to IIDs. The proportions of neurons exhibiting the various types of sensitivity corresponded closely to the proportions found to exhibit corresponding types of azimuthal sensitivity in a previous study. 3. There was a strong correlation between a neuron's binaural interaction characteristics and the form of its IID sensitivity function. Thus, neurons excited by monaural stimulation of only one ear but with either inhibitory, facilitatory, or mixed facilitatory-inhibitory effects of stimulation of the other ear had predominantly contra-max IID sensitivity (if contralateral monaural stimulation was excitatory) or ipsi-max sensitivity (if ipsilateral monaural stimulation was excitatory). Neurons driven weakly or not at all by monaural stimulation but facilitated binaurally almost all exhibited near-zero-max IID sensitivity. The exception to this tight association between binaural input and IID sensitivity was provided by neurons excited by monaural stimulation of either ear (EE neurons). Although EE neurons have frequently been considered to be insensitive to IIDs, our data were in agreement with two recent reports indicating that they can exhibit various forms of IID sensitivity: only 23 of 75 EE neurons were classified as insensitive and the remainder exhibited diverse types of sensitivity. 4. IID sensitivity was examined at two or more intensities (3-5 in most cases) for 84 neurons. The form of the IID sensitivity function (defined in terms of both shape and position along the IID axis) was invariant with changes in ABI for only a small proportion of IID-sensitive neurons (approximately 15% if a strict criterion of invariance was employed), and for many of these neurons the spike counts associated with a given IID varied with ABI, particularly at near-threshold levels. When the patterns of variation in the form of IID sensitivity produced by changes in ABI were classified in a manner equivalent to that used previously to classify the effects of intensity on azimuthal sensitivity, there was a close correspondence between the effects of intensity on corresponding types of azimuthal and IID sensitivity


Author(s):  
J. C. Luxat

In a limiting critical break loss of coolant accident in a CANDU reactor significant degradation of heat transfer from the fuel can occur. As a result of the subsequent increase in fuel temperature it is possible that the pressure tube undergoes heat up at intermediate pressure during blowdown. This can result in ballooning deformation of the pressure tube into contact with its calandria tube. It is required that fuel channels not fail as a consequence of the thermal mechanical deformation of the pressure tube and calandria tube in such events. Dynamic sensitivity functions are derived as analytical partial differential equations derived from the equations used to model the time-dependent behavior of physical systems. The dynamic sensitivity functions can be used to propagate uncertainties using a time-dependent perturbation approach in which the variations in a set of output variables, with respect to perturbations of the input parameters, are evaluated about reference response trajectories of the input parameters and associated output variables. The dynamic sensitivity method is described in this paper and results are presented for the pressure tube heatup phase of a LOCA. These results show the importance of all key parameters with respect to specified safety evaluation criteria. The dynamic sensitivity method is applied in a probabilistic uncertainty analysis to evaluate the probability of a pressure tube experiencing creep strain deformation to contact its calandria tube during the early stages of a LOCA.


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