N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.

An experimental methodology for the concurrent characterization of multiple parameters influencing nanoscale friction

A structured transdisciplinary method for the experimental determination of friction in the nanometric domain is proposed in this paper.The dependence of nanoscale friction on multiple process parameters on these scales,which comprise normal forces,sliding velocities,and temperature,was studied via the lateral force microscopy approach.The procedure used to characterize the stiffness of the probes used,and especially the influence of adhesion on the obtained results,is thoroughly described.The analyzed thin films were obtained by using either atomic layer or pulsed laser deposition.The developed methodology,based on elaborated design of experiments algorithms,was successfully implemented to concurrently characterize the dependence of nanoscale friction in the multidimensional space defined by the considered process parameters.This enables the establishment of a novel methodology that extends the current state-of-the-art of nanotribological studies,as it allows not only the gathering of experimental data,but also the ability to do so systematically and concurrently for several influencing variables at once.This,in turn,creates the basis for determining generalizing correlations of the value of nanoscale friction in any multidimensional experimental space.These developments create the preconditions to eventually extend the available macro-and mesoscale friction models to a true multiscale model that will considerably improve the design,modelling and production of MEMS devices,as well as all precision positioning systems aimed at micro-and nanometric accuracy and precision.

Optimization on class of operator equations in the probabilistic case setting

In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Freldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.