Sharif Digital Repository

In this paper, two integral based methods are proposed to estimate the order and the parameters of simple fractional order models from the noisy step response data. Numerical simulation results show the efficiency of the proposed methods in the presence of the measurement noise  

Fractional order models have been widely used in modeling and identification of thermal systems. General model in this category is considered as the model of thermal systems in this paper, and a fractional order controller is proposed for controlling such systems. The proposed controller is a generalization for the traditional PI controllers. The parameters of this controller can be obtained by using a recently introduced tuning method which can simultaneously ensure the following three requirements: desired phase margin, desired gain crossover frequency, and flatness of the phase Bode plot at this frequency. In this paper, it is found whether simultaneously achieving the mentioned... 

This paper deals with integral based methods to estimate the order and parameters of simple fractional order models from the extracted noisy step response data of a process. This data can be obtained from both open-loop and closed-loop tests. Numerical simulation results are presented to verify the robustness of these proposed methods in the presence of the measurement noise  

Fractional order models have been widely used in modeling and identification of thermal systems. General model in this category is considered as the model of thermal systems in this paper, and a fractional order controller is proposed for controlling such systems. The proposed controller is a generalization for the traditional PI controllers. The parameters of this controller can be obtained by using a recently introduced tuning method which can simultaneously ensure the following three requirements: desired phase margin, desired gain crossover frequency, and flatness of the phase Bode plot at this frequency. In this paper, it is found whether simultaneously achieving the mentioned... 

In practice, some differences are usually observed between computer simulation and experimental results of a chaotic circuit. In this paper, it is tried to obtain computer simulation results having more correlation with those obtained in practice by using more realistic models for chaotic circuits. This goal is achieved by considering the fractionality nature of electrical capacitors in the model of a chaotic circuit  

In this paper, a new method is proposed to determine parameters of some types of fractional order models to represent a system dynamics using its step response. The model structure is assumed to have rational commensurateorder as α = M/N . By this assumption infinite terms of the model step response is converted into finite terms limited to N. The proposed method is practically applicable on all fractional order model structures due to the order approximation imposed by the limited precisions in available computational tools  

The steer by wire system for vehicles has attracted much attention in recent years. Steer by wire systems provide many benefits in terms of functionality and at the same time present significant challenges too. It is essential to investigate the stability of steer by wire systems using a more sophisticated model rather than common approximated models. Fractional order modeling offers a good modeling framework for complex dynamical systems involving flexible structures such as multi-mass drives. In this paper a nonlinear fractional order model for steer by wire systems is presented  

This paper deals with proportional stabilization and closed-loop step response identification of the fractional order counterparts of the unstable first order plus dead time (FOPDT) processes. At first, the necessary and sufficient condition for stabilizability of such processes by proportional controllers is found. Then, by assuming that a process of this kind has been stabilized by a proportional controller and the step response data of the closed-loop system is available, an algorithm is proposed for estimating the order and the parameters of an unstable fractional order model by using the mentioned data  

This paper contains analysis and simulation of recent dynamic models, describing human emotion. The pharmacological discussions lead to a new model of drug taking, which also have a better performance for description of psychological and psychiatric phenomena. Studying the effects of the order of fractional model, obtains an advantage of the fractional order model over the integer order one  

Using elastic couplings in servo motor drives may lead to torsional oscillations which are usually extinguished by reducing the bandwidth of the control system as a countermeasure. A high performance servo drive however needs fast dynamic characteristics. The conventional controllers, such as PI controllers, may not be able to improve the dynamic response while keeping the system stable. Fractional order modeling offers a good framework for flexible structures such as two mass servo drives. In this paper, the dynamic response and stability of two-mass servo drive is improved using a fractional order controller. The fractional order controller allows increasing the phase margin of the system... 

Fractional order PI and PID controllers are the most common fractional order controllers used in practice. In this paper, a simple analytical method is proposed for tuning the parameters of these controllers. The proposed method is useful in designing fractional order PI and PID controllers for control of complicated fractional order systems. To achieve the goal, at first a reduction technique is presented for approximating complicated fractional order models. Then, based on the obtained reduced models some analytical rules are suggested to determine the parameters of fractional order PI and PID controllers. Finally, numerical results are given to show the efficiency of the proposed tuning... 

In this paper, firstly a four-parameter fractional order model structure is introduced to approximate processes having S-shaped step responses. Three different strategies are presented in order to determine the parameters of the proposed model. In a special case where the proposed model is not satisfactory, another fractional order model structure with five free parameters is introduced to improve the model approximation. Also in this case, a procedure is provided to estimate the parameters of the introduced five-parameter model. Then, some common classical integer order control design approaches are modified or extended to their fractional order counterparts in order to incorporate the... 

Existence of uncertainties in the model of real-world plants can trouble the control system designer in achievement of control objectives in control of such plants. In modeling of these plants by benefiting from fractional order models, one of the most commonplace types of uncertainties is the order uncertainty. This paper deals with presenting a method for tuning fractional order PI (FOPI) controllers to be used in control of plants, modeled by fractional order transfer functions consisting of a fractional order pole in addition to a time delay, such that the control system is robust against order variations. By the proposed tuning method, values of phase margin and gain crossover frequency... 

The vibration characteristics, including fundamental frequencies and loss factors, of a sandwich conical shell with constrained viscoelastic layer is presented. The mechanical properties of viscoelastic core is modeled using Zener fractional order model. The equations of motion are derived employing Donnell representation of classical shell theory and solved using Raighly-Ritz method. The results are compared with other investigations and the effects of geometric parameters including the length to radius, radius to thickness and core to facing thickness on fundamental frequencies and loss factors are studied. © 2019 Elsevier Ltd  

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz... 

Natural frequency and damping behavior of three-layer cylindrical shells with a viscoelastic core layer and functionally graded face layers are studied in this article. Using functionally graded face layers can reduce the stress discontinuity in the face–core interface that causes a catastrophic failure in sandwich structures. The viscoelastic layer is expressed using a fractional-order model, and the functionally graded layers are defined by a power law function. Assuming the classical shell theory for functionally graded layers and the first-order shear deformation theory for the viscoelastic core, equations of motion are derived using Lagrange’s equation and then solved via Rayleigh–Ritz...