Sharif Digital Repository

This paper presents a new analytical method to design fractional-order proportional- integral-derivative (PID) controllers. The control parameters are calculated so that the closedloop system approximates a desired transfer function with transient response requirements. This function is determined based on the characteristic ratio assignment method. The control parameters are calculated by matching the first three moments of the closed-loop transfer function with the corresponding values of the desired system. Furthermore, to ensure closed-loop stability the proposed method is improved by using the shifted moments around the crossover frequency. Illustrative examples are given to show the... 

This study presents a set of rules for optimal tuning of a class of integer-order controllers, known as implementable fractional-order PID controllers, so that they can be employed to control First Order Plus Dead Time (FOPDT) processes. To this end, "tuning based on the implementable form of the controller"is an approach that has been applied instead of the common approach of "tuning based on the ideal form of the controller". Consequently, no contradiction is found between the behavior of the tuned controller and that of the implemented controller. Also, algebraic relations between the values of cost functions, which are defined based on Integral Square Error (ISE) and Integral Square Time... 

A fractional order PID controller is designed to stabilize fractional delay systems with commensurate orders and multiple commensurate delays, where the time delays in the system may belong to several distinct intervals. Moreover, the controller parameters should belong to given intervals. In order to stabilize the system, the D-subdivision method is employed to choose the stabilizing set of the controller parameters from their available values. Furthermore, the nearest values of the obtained stabilizing set to their mean values are selected as the controller parameters so that a non-fragile controller is concluded. Two numerical examples evaluate the proposed control design method  

In this paper, the fractionalized differentiating method is implemented to reduce commensurate fractional order models complexity. The prominent properties of this method are its simplicity and guarantee of preserving the stability of a specific class of fractional order models in their reduced counterparts. The presented reduction method is employed in simplifying complicated fractional order controllers to a fractional order PID (FOPID) controller and proposing tuning rules for its parameters adjustment. Finally, the efficiency of the FOPID tuning rule obtained based on the proposed reduction method is shown in the temperature control of a cutting process  

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... 

Application of fractional order PID (FOPID) controller to an automatic voltage regulator (AVR) is presented and studied in this paper. An FOPID is a PID whose derivative and integral orders are fractional numbers rather than integers. Design stage of such a controller consists of determining five parameters. This paper employs particle swarm optimization (PSO) algorithm to carry out the aforementioned design procedure. PSO is an advanced search procedure that has proved to have very high efficiency. A novel cost function is defined to facilitate the control strategy over both the time-domain and the frequency-domain specifications. Comparisons are made with a PID controller and it is shown...