This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

This study employs wavelet transforms to address the issue of boundary effects. Additionally, it utilizes probit transform techniques, which are based on probit functions, to estimate the copula density function. This estimation is dependent on the empirical distribution function of the variables. The density is estimated within a transformed domain. Recent research indicates that the early implementations of this strategy may have been more efficient. Nevertheless, in this work, we implemented two novel methodologies utilizing probit transform and wavelet transform. We then proceeded to evaluate and contrast these methodologies using three specific criteria: root mean square error (RMSE), Akaike information criterion (AIC), and log

The Dirichlet process is an important fundamental object in nonparametric Bayesian modelling, applied to a wide range of problems in machine learning, statistics, and bioinformatics, among other fields. This flexible stochastic process models rich data structures with unknown or evolving number of clusters. It is a valuable tool for encoding the true complexity of real-world data in computer models. Our results show that the Dirichlet process improves, both in distribution density and in signal-to-noise ratio, with larger sample size; achieves slow decay rate to its base distribution; has improved convergence and stability; and thrives with a Gaussian base distribution, which is much better than the Gamma distribution. The performance depen

In this paper, a handwritten digit classification system is proposed based on the Discrete Wavelet Transform and Spike Neural Network. The system consists of three stages. The first stage is for preprocessing the data and the second stage is for feature extraction, which is based on Discrete Wavelet Transform (DWT). The third stage is for classification and is based on a Spiking Neural Network (SNN). To evaluate the system, two standard databases are used: the MADBase database and the MNIST database. The proposed system achieved a high classification accuracy rate with 99.1% for the MADBase database and 99.9% for the MNIST database

This paper is concerned with the design and implementation of an image compression method based on biorthogonal tap-9/7 discrete wavelet transform (DWT) and quadtree coding method. As a first step the color correlation is handled using YUV color representation instead of RGB. Then, the chromatic sub-bands are downsampled, and the data of each color band is transformed using wavelet transform. The produced wavelet sub-bands are quantized using hierarchal scalar quantization method. The detail quantized coefficient is coded using quadtree coding followed by Lempel-Ziv-Welch (LZW) encoding. While the approximation coefficients are coded using delta coding followed by LZW encoding. The test results indicated that the compression results are com

        In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E₁ , E₂ , E₃)  of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.