Sharif Digital Repository

This paper presents an adaptive controller to achieve consensus tracking for the fractional-order linear time invariant swarm systems in which the matrices describing the agent dynamics and the interactive dynamics between agents are unknown. This controller consists of two parts: an adaptive stabilizer and an adaptive tracker. The adaptive stabilizer guarantees the asymptotic swarm stability of the considered swarm system. Also, the adaptive tracker enforces the system agents to track a desired trajectory while achieving consensus. Numerical simulation results are presented to show the effectiveness of the proposed controller. Copyright  

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 this paper, an algebraic rule for tuning the integer realizations of fractional-order PI controllers is developed, with an integral square error performance index, which outperforms that of an optimal ordinary PI controller. To this end, the PIλ control structure is used in conjunction with a third-order integer approximating filter to provide a three parameter fixed-structure extension of the ordinary PI controller. Next, the extra degree of freedom in setting the order of integration λ is leveraged to introduce a steepest descent direction in the extended controller parameter space. It is then stated that shifting the parameters of an ordinary PI controller along the proposed descent... 

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  

A method recently proposed for tuning fractional order [proportional integral] (FO[PI]) controllers is investigated. This tuning method, when applied in control of first-order plus dead time (FOPDT) processes, can ensure the desired phase margin, the desired gain crossover frequency and the flatness of the phase Bode plot at such a frequency. The necessary and sufficient condition for the applicability of the aforementioned tuning method is derived. Also, it is shown that this condition can be used in obtaining the achievable performance region of the tuning method in the gain crossover frequency-phase margin plane  

This paper deals with a method recently proposed for tuning fractional order [proportional-derivative] (FO-[PD]) controllers. Using this tuning method, the tuned FO-[PD] controller can ensure the desired phase margin, the desired gain crossover frequency, and the flatness of the phase Bode plot at such a frequency. In the present paper, the achievable region of this tuning method in the gain crossover frequency-phase margin plane is obtained analytically. Also, the continuity of this region and uniqueness of the tuned parameters are investigated. Moreover, the achievable region of the aforementioned tuning method in the presence of time delay in the feedback loop is found  

This paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results  

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  

This paper studies undamped oscillations generated by marginally stable fractional order linear time invariant (LTI) systems. In this study, an analytical approach is proposed to be used for harmonic analysis of such oscillations in marginally stable commensurate order LTI systems. Also, it is shown that the Q-semi norm of the limit sets for a trajectory of these systems can be analytically determined based on the Q-semi norm of the initial condition, where Q is a specific matrix. Moreover, this result is extended to the wider class of rational order systems. Finally, some numerical examples are presented to demonstrate the use of the paper results  

In this paper, it is shown that by benefiting from a static feedback control signal it is possible to reduce the effect of fractionality of the electrical capacitors on the amplitude of the oscillations produced by a Van der Pol circuit. The averaging method is used in this paper for the behavior analysis of the approximated responses of the under study circuits. Numerical simulation results are presented to confirm the effectiveness of the proposed control technique  

This paper offers a systematic framework for the design of suboptimal integer-order controllers based on fractional-order structures. The proposed approach is built upon the integer-order approximations that are traditionally used to implement fractional-order controllers after they are designed. Accordingly, the fractional-order structures are exploited to derive a suitable parameterization for a fixed-structure integer-order controller. The parameters, which describe the structure of the fixed-order integer controller, are the same as those used to describe the original fractional structure. Optimal tuning is then performed in the parameter space of the fractional structure and the... 

Recently, exploiting the centroids of stability regions (admissible regions) to be used in tuning two-parameter controllers has been considered as an approach to obtain non-fragile two-parameter controllers. Such an approach can be extended for three-dimensional stability spaces (admissible spaces) by considering the center of mass of these spaces in tuning three-parameter controllers. In this paper, the mentioned approach is used to tune PID controllers for controlling integrator plus dead-time (IPDT) and first order plus dead-time (FOPDT) processes. It is shown that the tuning method resulted from this approach is very similar to the Ziegler-Nichols step response tuning method.... 

This Letter tries to find the area in parameter space of a non-salient Permanent-Magnet Synchronous Machine (PMSM) in which chaos can occur. This area is briefly named as chaotic area. The predicted chaotic area is obtained by checking some conditions which are necessary for existence of chaos in a dynamical system. In this Letter, it is assumed that this machine is in the generator mode, and its model is based on direct and quadrature axis of stator voltages and currents. The information of the predicted area is used in non-chaotic maximum power control of torque in the machine  

In this paper we offer a tuning method for the design of stabilizing PI controllers that utilizes the stability region centroid in the controller parameter space. To this end, analytical formulas are derived to describe the stability boundaries of a class of relative-degree-one linear time invariant second-order systems, the stability region of which has a closed convex shape. The so-called centroid stable point is then calculated analytically and the resultant set of algebraic formulas are utilized to tune the controller parameters. The freedom to choose the surface density function in the calculation of centroid stable point provides the designer with the possibility to incorporate optimal... 

The problem of tuning a two-parameter controller has been formulated as finding the centroid of the admissible region specified by the set of constraints that the controller should satisfy. The constraints can be as general as the closed-loop system stability or they may include several requirements on various stability, sensitivity, or performance measures. The design of stabilizing proportional-derivative (PD) controllers using the centroid of the stability region in the controller parameter space is considered as a case study. To this end, analytical formulas are derived to describe the stability boundaries of a class of integrating time delay systems, the stability region of which has a... 

In this paper, an algebraic tuning rule is presented for fractional PI controllers to control first order plus dead-time processes. By using the performance map (PM) method, this tuning rule is derived in order to set the gain margin of the control system close to 3 and the phase margin close to 60 degrees. The robustness and performance of this tuning rule are compared with some well-known PI tuning rules. Simulation results are brought to demonstrate the effectiveness and robustness of this tuning formula against process dynamic uncertainties in comparison with the other tuning methods  

This paper is devoted to analysis of undamped oscillations generated by fractional order linear time invariant (LTI) systems. At first, the trajectories of marginally stable commensurate order systems are investigated. It is verified that we can not use the time-independent phase flow concept for this kind of systems. Also, the differences with the integer order case are highlighted. Then, it is shown that we can determine the Q-norm of the limit sets of a trajectory for these systems based on the Q-norm of the initial condition. Some numerical examples are brought to confirm the achievements of the paper  

This paper presents a method to determine the denominator and numerator polynomials of a closed-loop transfer function in order to obtain desired transient and steady-state responses in terms of the overshoot, speed (time needed for the relative error to become less than a specific amount) and the steady-state error when the desired output is a ramp signal. Meanwhile, a controller is designed with the same characteristic equation for the closed-loop system to eliminate step and ramp disturbances  

This paper deals with realization of fractional-order impedance functions by passive electrical networks composed of a fractional capacitor and some RLC components. The necessary and sufficient conditions for the existence of such a realization are found in a general case. Also for impedance functions described by a class of fractional-order transfer functions, the realizability conditions are stated as some algebraic conditions on the parameters of the transfer function. Moreover, a procedure is proposed for implementation of such impedance functions by passive electrical networks composed of a fractional capacitor and some RLC components. Numerical examples are presented to show the...