Piotr Ostalczyk

Variable-fractional-order Dead-beat Control of an Electromagnetic Servo

In this article, a simple dead-beat control for an electromagnetic servo is proposed. An electromagnetic servo is identified as a third-order linear continuous-time plant. A method of a dead-beat control of its discrete equivalence is proposed. A variable-order, fractional-order backward difference is used in the control algorithm.

The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control

In this paper, the discrete differentiation order functions of the variable, fractional-order PD controller (VFOPD) are considered. In the proposed VFOPD controller, a variable, fractional-order backward difference is applied to perform closed-loop, system error, discrete-time differentiation. The controller orders functions which may be related to the controller input or output signal or an input and output signal. An example of the VFOPD controller is applied to the robot arm closed-loop control due to system changes in moment of inertia. The close-loop system step responses are presented.

Order Functions Selection in the Variable-, Fractional-Order PID Controller

In the paper a variable-, fractional-order PID (VFOPID) controller microprocessor realization problems are discussed. In such controllers the variable-, fractional-orders backward differences and sums (VFOBD/S) are used to perform closed-loop system error discrete-time differentiation and integration. In practice all digitally differentiated and integrated signals are noised so there is a necessity of a digital signal pre-filtering. This additionally loads the DSP system. A solution of this problem is proposed. Also the possibilities of the VFOPID controller DSP realizations are presented and compared with the computer simulation results.

Generalized Fractional-Order Discrete-Time Integrator

We investigate a generalization of discrete-time integrator. Proposed linear discrete-time integrator is characterised by the variable, fractional order of integration/summation. Graphical illustrations of an analysis of particular vector matrices are presented. In numerical examples, we show relations between the order functions and element responses.

Fractional-Order PID Controllers in a Mobile Robot Control

Abstract In this paper fractional PID controllers are applied to the control system of a mobile robot. The short memory principle related to problems in a numerical implementation of a fractional order differ-integration is analyzed and some solutions of this problem are presented.

Variable-, Fractional-Order Dead-Beat Control of a Robot Arm

In the paper a synthesis method of the variable-, fractional – order dead – beat controller is proposed. It is applied to control of a robot arm described as a simple integrating element. The system structure is presented. The transient characteristic of a closed – loop system with the proposed controller are measured and compared with computer simulations performed for classical controllers.

Variable-, fractional-order discrete PID controllers

The fractional calculus is the area of mathematics that handles derivatives and integrals of any arbitrary order (fractional or integer, real or complex order) [1,2,3,4]. Nowadays it is applied in almost all areas of science and engineering. Here one can mention its numerous and successful applications in dynamical systems modeling and control with increasing number of studies related to the theory and application of fractional-order controllers, specially ones. In such controllers μk <;0 and vk >; 0 denote the integration and differentiation order, respectively. Now research activities are focused on developing new analysis and closed-loop system synthesis methods for fractional-order controllers being an extension of classical control theory. In the fractional-order controller tuning there are two additional parameters μk <; 0 and vk >; 0. This impedes the controller tuning procedure but leads to new (unattainable in classical PID control [5]) closed-loop system transient responses. The closed-loop system with fractional controller must satisfy typical requirements among which one can mention the system robustness due to the plant model uncertainties.

Variable-, fractional-order Grünwald-Letnikov backward difference selected properties

There were investigated some particular properties of variable-, fractional-order backward differences (VFOBD). The most of proved properties are connected with coefficients of VFOBD. There are presented examples of the numerical results of VFOBD.

The second form of the variable-, fractional-order discrete-time integrator

The paper investigates the second form of a linear discrete-time integrator characterised by the variable-, fractional-order of integration. An equation of such dynamic element is given. A special vector-matrix description is proposed. Relations between the order functions and element responses are given in numerical examples.

The Fractional-Order Backward-Difference of a Product of Two Discrete-Variable Functions (Discrete Fractional Leibnitz Rule)

In this paper a discrete fractional case of the so called Leibnitz Rule is presented The fractional-order backward difference of a product of two discrete-variable functions is derived. It is a generalisation to the first-order bacward difference of a product. The formula may be useful in the fractional-order backward differences of selected functions evaluation.