Sun-Yuan Tsay

A note on time-domain simulation of feedback fractional-order systems

The study of feedback fractional-order systems has been receiving considerable attention due to the facts that many physical systems are well characterized by fractional-order models, and that fractional-order controllers are used in feedback systems with the intention of breaking through the performance limitation of integer-order controllers. Owing to the lack of effective analytic methods for the time-domain analysis and simulation of linear feedback fractional-order systems, we suggest in this paper two reliable and accurate numerical methods for inverting fractional-order Laplace transforms. One is based on computing Bromwichs integral with a numerical integration scheme capable of accuracy control, and the other is based on expanding the time response function in a B-spline series. In order to demonstrate the superiority in solution accuracy and computational complexity of these two numerical methods over the Grunwald-Letniknov approximation method and Podlubnys analytic formulas, which are in a form of double infinite series, the time-domain simulations of the feedback control of a fractional-order process with a PD/sup /spl mu//-controller and a fractional-order band-limited lead compensator are worked out. The simulation results indicate that a convergence problem indeed occurs in using Podlubnys infinite series expressions, and that the problem could not be overcome by a series acceleration scheme.

Design of optimal fractional-order PID controllers

In this paper we are concerned with the design of a Fractional-order PID controller which involves noninteger-order integrator and differentiator. The three controller gains and two real orders of the fractional-order PID controller are determined to minimize an integral square error (ISE)performance index while satisfying the specified gain and phase margins. We formulate the design problem as a constrained parametric optimization and apply a differential evolution algorithm to search globally the optimal controller parameters. Due to the problem lack of analytic time-domain analysis methods for fractional-order systems, and effective numerical method is utilized to compute the ISE performance index as well as to check the stability in the frequency domain. Design examples are given to compare the performance of the optimal fractional-order PID controller with the optimal integer-order PID controller in controlling integer-order as well as fractional-order processes.

Analytical solutions for freezing a saturated liquid inside or outside cylinders

Abstract By the use of an analytical iteration technique successive solutions for the instantaneous frozen layer thickness and temperature profile for the freezing of a saturated liquid inside cylindrical containers with constant heat transfer coefficient are generated. Comparison of the results with experimental data and numerical solutions shows satisfactory coincidence. Successive solutions for freezing of a saturated liquid outside cylinders are also derived and compared with numerical solutions.

Extended Leveque solution for laminar heat transfer to power-law fluids in pipes with wall slip

The effect of wall slip on the laminar heat transfer to power-law fluids in pipes with constant wall temperature and constant wall heat flux is investigated for the case of a short axial distance. The transformed temperature is expanded in a Leveque series in terms of the powers of s−12, where s is the Laplace transformation variable with respect to the axial distance. For a constant wall temperature, the zero-order solution is the Leveque solution, whereas, for a constant wall heat flux, the first-order solution is the Leveque solution. Numerical solutions are obtained to show the convergence as well as the effect of wall slip on the Nusselt number vs the Graetz number. A significant increase in the Nusselt number is shown with an increase in the wall slip velocity. The effect of the Brinkman number is less important for high Graetz numbers.

APPLICATION OF GELATIN FOR ENCAPSULATING ASPIRIN INTO ETHYL CELLULOSE MICROCAPSULE IN AN O/W EMULSION

The application of gelatin protective colloid for microencapsulating aspirin in ethylcellulose was demonstrated using an oil-in-water emulsification/solvent evaporation technique. The gelatin concentration, alcohol co-solvent amount, and ethylcellulose viscosity were investigated by analyzing the recovered weight, particle size distribution, drug loading efficiency, aspirin release rate, surface characteristics, and release kinetics. Results showed that recovery increased with greater concentrations of gelatin (up to 1%). Adding co-solvent (ethanol) also changed the microcapsule particle size distribution. Higher recovery and release rates were obtained when the ethanol content in polymer solvent was at 25% and the viscosity of ethylcellulose was low (45cps). The release rate followed Higuchi matrix release kinetics, suggesting a monolithic system with aspirin uniformly distributed over the microcapsule.

Laminar forced convection in wedge flow with separation

Abstract A perturbation method is used to study the steady and unsteady laminar boundary layer heat transfer from a wedge with separation for a step‐discontinuity in the surface temperature. The analytic solutions obtained can be used to calculate the steady and unsteady heat transfer rate with arbitrary surface temperature. The effects of the Prandtl number on the temperature distribution and the heat transfer rate are discussed in detail. The solution is valid for large or moderate Prandtl number.

Computation of quadratic cost functionals for linear systems with multiple time delays

In this paper, we present a semianalytical method for evaluating quadratic cost functionals for linear time-invariant systems with multiple time delays. The main computational tasks involved in the method are the solution of a symbolic Diophantine equation by the Euclid algorithm and the factorization of a finite-degree polynomial. To illustrate the numerical implementation of the proposed method, an example is provided.

USE OF B-SPLINES TO OBTAIN ACCURATE TRANSIENT RESPONSES FOR FEEDBACK CONTROL SYSTEMS WITH TIME DELAYS∗

Abstract This paper is concerned with representing the transient time response of a closed-loop control system having pure and/or distributed time delays in terms of B-spline series. More precisely, it regards to the inversion of Laplace transforms of irrational type with the B-spline series expansion approach. The B-spline series for a time function/(f) with r ≥ 0 contains first several terms in boundary splines and the remaining terms in interior B-splines. It is shown that by matching the initial conditions of the response exactly, the coefficients associated with the interior B-splines can be accurately obtained by a computationally efficient FFT-based algorithm.

Variance and Covariance Computations for 2-D ARMA Processes

AbstractAn algorithm is presented to compute the variance of the output of a two-dimensional (2-D) stable auto-regressive moving-average (ARMA) process driven by a white noise bi-sequence with unity variance. Actually, the algorithm is dedicated to the evaluation of a complex integral of the form