Application of Laguerre based adaptive predictive control to Shape Memory Alloy (SMA) actuators

This paper discusses the use of an existing adaptive predictive controller to control some Shape Memory Alloy (SMA) linear actuators. The model consists in a truncated linear combination of Laguerre filters identified online. The controller stability is studied in details. It is proven that the tracking error is asymptotically stable under some conditions on the modelling error. Moreover, the tracking error converge toward zero for step references, even if the identified model is inaccurate. Experimentalcresults obtained on two different kind of actuator validate the proposed control. They also show that it is robust with regard to input constraints.ANR MAFESM

Design of interpolative sigma delta modulators via a semi- infinite programming approach

This paper considers the design of interpolative sigma delta modulators (SDMs). The design problem is formulated as two different optimization problems. The first optimization problem is to determine the denominator coefficients. The objective of the optimization problem is to minimize the energy of the error function in the passband of the loop filter in which the error function reflects the noise output transfer function and the ripple of the input output transfer function. The constraint of the optimization problem refers to the specification of the error function defined in the frequency domain. The second optimization problem is to determine the numerator coefficients in which the cost function is to minimize the stopband ripple energy of the loop filter subject to the stability condition of the noise output and input output transfer functions. These two optimization problems are actually quadratic semi-infinite programming (SIP) problems. By employing our recently proposed dual parameterization method for solving the problems, global optimal solutions that satisfy the corresponding continuous constraint are guaranteed if the solutions exist. The advantages of this formulation are the guarantee of the stability of the noise output and input output transfer functions, applicability to design rational IIR filters without imposing specific filter structures such as Laguerre filter and Butterworth filter structures, and the avoidance of the iterative design of numerator and the denominator coefficients because the convergence of the iterative design is not guaranteed. Our simulation results show that this proposed design yields a significant improvement in the signal-to-noise ratio (SNR) compared to the existing designs

An approximate solution of the MHD Falkner-Skan flow by Hermite functions pseudospectral method

Based on a new approximation method, namely pseudospectral method, a solution for the three order nonlinear ordinary differential laminar boundary layer Falkner-Skan equation has been obtained on the semi-infinite domain. The proposed approach is equipped by the orthogonal Hermite functions that have perfect properties to achieve this goal. This method solves the problem on the semi-infinite domain without truncating it to a finite domain and transforming domain of the problem to a finite domain. In addition, this method reduces solution of the problem to solution of a system of algebraic equations. We also present the comparison of this work with numerical results and show that the present method is applicable.Comment: 15 pages, 4 figures; Published online in the journal of "Communications in Nonlinear Science and Numerical Simulation

A simple algorithm for stable order reduction of z-domain Laguerre models

International audienceDiscrete-time Laguerre series are a well known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model

Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples

Continuous-Time Identification of SISO Systems using Laguerre Functions

This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm

An Application of Volterra Series to IC Buffer Models

International audienceThis paper presents a Volterra-based method of behavioral modeling for the I/O buffers of digital ICs. While this technique brings a slight improvement in accuracy over previous ones, its main strength is a greater degree of generality. With a modeling approach less dependent on the nature of the devices and more easily extendable to include the effects of multiple inputs one may hope better meet the challenges of advancing technology. The proposed models can be obtained from device port transient responses only and can be easily implemented in any simulation environment, including SPICE-based circuit description software. Two illustrative examples conclude the paper

Convergence of Laguerre Impulse Response Approximation for Noninteger Order Systems

One of the most important issues in application of noninteger order systems concerns their implementation. One of the possible approaches is the approximation of convolution operation with the impulse response of noninteger system. In this paper, new results on the Laguerre Impulse Response Approximation method are presented. Among the others, a new proof of convergence of approximation is given, allowing less strict assumptions. Additionally, more general results are given including one regarding functions that are in the joint part of and spaces. The method was also illustrated with examples of use: analysis of “fractional order lag” system, application to noninteger order filters design, and parametric optimization of fractional controllers

Influence of the state of light on the optically induced interparticle interaction

A general expression for the energy of interparticle interaction induced by an arbitrary mode of light is determined using quantum electrodynamics, and it is shown that the Casimir-Polder potential is included within this quantum result. Equations are also derived for the corresponding coupling induced by multimode number states of light, and the dependence of the pair energy on the Poynting vector and polarization state is determined. Attention is then focused on the interactions between particles trapped in counterpropagating coherent beams, both with and without interference, and it is shown that the results afford insights into the multiparticle structures that can be optically fabricated with counterpropagating input. Brief consideration is also given to the effect of squeezing the optical coherent state. Extending previous studies of optical binding in Laguerre-Gaussian beams, results are given for the case of particles trapped at radially different locations within the beam structure. Finally, consideration is given to interparticle interactions induced by broadband light, and it is shown how the length of optically fabricated particle chains can be controlled by the use of wavelength filters