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This paper considers the problem of stabilizing a first-order plants with known time delay using a fractional-order proportional–integral controller [Formula: see text]. Using a generalization of the Hermite–Biehler theorem applicable to quasi-polynomials, a complete analytical characterization of all stabilizing gain values ([Formula: see text]) is provided. The widespread industrial use of fractional PI controllers justifies a timely interest in [Formula: see text] tuning techniques.

This paper presents a new design procedure to tune the fractional order PIλDμ controller that stabilizes a first order plant with time delay. The procedure is based on a suitable version of the Hermite–Biehler Theorem and the Pontryagin Theorem. A Theorem and a Lemma are developed to compute the global stability region of the PIλDμ controller in the (kp,ki,kd) space. Hence, this Theorem and Lemma allow us to develop an algorithm for solving the PIλDμ stabilization problem of the closed loop plant. The proposed approach has been verified by numerical simulation that confirms the effectiveness of the procedure.

The problem of stabilizing a second-order delay system using classical proportional-integral-derivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasipolynomials, is used to seek the set of complete stabilizing PID parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be either a trapezoid or a triangle.

Weld defects detection using X-ray images is an effective method of nondestructive testing. Conventionally, this work is based on qualified human experts, although it requires their personal intervention for the extraction and classification of heterogeneity. Many approaches have been done using machine learning (ML) and image processing tools to solve those tasks. Although the detection and classification have been enhanced with regard to the problems of low contrast and poor quality, their result is still unsatisfying. Unlike the previous research based on ML, this paper proposes a novel classification method based on deep learning network. In this work, an original approach based on the use of the pretrained network AlexNet architecture aims at the classification of the shortcomings of welds and the increase of the correct recognition in our dataset. Transfer learning is used as methodology with the pretrained AlexNet model. For deep learning applications, a large amount of X-ray images is required, but there are few datasets of pipeline welding defects. For this, we have enhanced our dataset focusing on two types of defects and augmented using data augmentation (random image transformations over data such as translation and reflection). Finally, a fine-tuning technique is applied to classify the welding images and is compared to the deep convolutional activation features (DCFA) and several pretrained DCNN models, namely, VGG-16, VGG-19, ResNet50, ResNet101, and GoogLeNet. The main objective of this work is to explore the capacity of AlexNet and different pretrained architecture with transfer learning for the classification of X-ray images. The accuracy achieved with our model is thoroughly presented. The experimental results obtained on the weld dataset with our proposed model are validated using GDXray database. The results obtained also in the validation test set are compared to the others offered by DCNN models, which show a best performance in less time. This can be seen as evidence of the strength of our proposed classification model.

Abstract:In this paper, the problem of stabilizing an unstable second order delay system using classical proportional-integralderivative (PID) controller is considered. An extension of the Hermite-Biehler theorem, which is applicable to quasi-polynomials, is used to seek the set of complete stabilizing proportional-integral/proportional-integral-derivative (PI/PID) parameters. The range of admissible proportional gains is determined in closed form. For each proportional gain, the stabilizing set in the space of the integral and derivative gains is shown to be a triangle.

COVID-19 comes from a large family of viruses identi ed in 1965; to date, seven groups have been recorded which have been found to affect humans. In the healthcare industry, there is much evidence that Al or machine learning algorithms can provide effective models that solve problems in order to predict con rmed cases, recovered cases, and deaths. Many researchers and scientists in the eld of machine learning are also involved in solving this dilemma, seeking to understand the patterns and characteristics of virus attacks, so scientists may make the right decisions and take speci c actions. Furthermore, many models have been considered to predict the Coronavirus outbreak, such as the retro prediction model, pandemic Kaplan's model, and the neural forecasting model. Other research has used the time series-dependent face book prophet model for COVID-19 prediction in India's various countries. Thus, we proposed a prediction and analysis model to predict COVID-19 in Saudi Arabia. The time series dependent face book prophet model is used to t the data and provide future predictions. This study aimed to determine the pandemic prediction of COVID-19 in Saudi Arabia, using the Time Series Analysis to observe and predict the coronavirus pandemic's spread daily or weekly. We found that the proposed model has a low ability to forecast the recovered cases of the COVID-19 dataset. In contrast, the proposed model of death cases has a high ability to forecast the COVID-19 dataset. Finally, obtaining more data could empower the model for further validation.

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