Computational Methods in Engineering

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In the last few years, Run-to-Run (R2R) control techniques have been developed and used to control various processes in industries. These techniques combine response surface, statistical process control, and feedback control techniques. The R2R controller consists of a linear regression model that relates input variables to output variables using Exponentially Weighted Moving Average (EWMA). In this paper, we have developed a R2R controller model based on quality costs. The model consists of finding optimum weight of EWMA procedure in R2R controllers with respect to conformities and nonconformities costs. The validity and performance of the developed model were tested using a real case study in an optic industry application.

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For solving the dynamic equilibrium equation of structures, several second-order numerical methods have so far
been proposed. In these algorithms, conditional stability, period elongation, amplitude error, appearance of spurious frequencies
and dependency of the algorithms to the time steps are the crucial problems. Among the numerical methods, Newmark average
acceleration algorithm, regardless of existence of spurious frequencies, is very popular in the structural dynamics due to its
unconditionally stability status of the method. Recently, several first-order methods have been introduced for resolving the
accuracy and stability issues. However, in these methods stability, accuracy and error in inversion of the state matrix are known
as major issues. When the state matrix became singular or ill conditioned, numerical errors will occure in the computational
process. Many of the available first-order methods were to improve the stability and accuracy and also to remove the error of
inversion. Even though the introduced methods are conditionally stable, no investigation on errors, occuring during dynamic
loading, has been reported for them. The main purpose of this paper is to utilize a specific decomposition method based on
Singular Value Decomposition (SVD) for modifying PIM algorithm. Using the SVD inversion technique, the singularity problem
of the state matrix has been resolved. In this paper, the modified method is called PIMS. As well, by applying the developed
method for dynamic loading, the error of responses has been investigated. The results show that PIMS algorithm is stable and,
comparing with secoend order Newmark and other available first order methods, has more accuracy.