Krzysztof Oprzędkiewicz

Application of fractional order transfer functions to modeling of high — Order systems

The paper presents an application of elementary fractional order transfer funtions to efective modeling of high order control plants. An example of modeling experimental heat plant is also given.

An Estimation of Accuracy of Oustaloup Approximation

In the paper a new accuracy estimation method for Oustaloup approximation is presented. Oustaloup approximation is a fundamental tool to describe fractional-order systems with the use of integer-order, proper transfer function. The accuracy of approximation can be estimated via comparison of impulse responses for plant and Oustaloup approximation. The impulse response of the plant was calculated with the use of an accurate analytical formula and it can be interpreted as a standard. Approach presented in the paper can be applied to effective tuning of Oustaloup approximant for given application (for example in FO PID controller). The use of proposed method does not require us to know time response of a modeled controller. The proposed methodology can be easily generalized to another known approximations. Results of simulations show that the good performance of approximation is reached for low order and narrow angular frequency range.

Parameter identification for non integer order, state space models of heat plant

In the paper the parameter idetification problem for new, non integer order, state space models of heat transfer process is presented. The solution of all proposed state equations bases directly onto definitions of suitable non integer order differences. The parameters estimation is done with the use of MSE (Mean Square Error) cost function. The order of all proposed state-space models is also estimated. Results of experiments show, that all proposed non integer order models are more accurate in the sense of MSE cost function than known integer order model.

Tuning of the Half-Order Robust PID Controller Dedicated to Oriented PV System

In the paper tuning rules for half - order PID controller dedicated to control an oriented PV system were presented. The plant is described with the use of interval transfer function. Results were by simulations depicted.

Fractional-Order P2D β Controller for Uncertain Parameter DC Motor

In this paper an uncertain-parameter DC motor controlled with the use of non integer order P2D β controller with uncertain-parameters is considered. For this system an analysis of BIBO (Bounded Input Bounded Output) stability with respect to uncertainty of plant’s parameters was done. Results were with an example depicted.

An Estimation of Accuracy of Charef Approximation

In the paper a new accuracy estimation method for Charef approximation was presented. Charef approximation allows us to describe fractional-order systems with the use of integer-order, proper transfer function. The accuracy of approximation can be estimated with the use of comparison step responses of plant and Charef approximation. The step response of the plant was calculated with the use of an accurate analytical formula and it can be interpreted as a standard. Approach presented in the paper can be applied to effective tuning of Charef approximant for given plant. The use of proposed method does not require to know a step response of the modeled plant. The proposed methodology can be easily generalized to another known approximations. Results are by simulations illustrated.

A Non Integer Order Model of Frequency Speed Control in AC Motor

In the paper new non integer order models for speed control in AC motor are proposed. The models have the form of hybrid transfer functions containing both integer order and non integer order parts. Parameters of models were assigned with the use of least square method. The proposed models were compared to integer order transfer function model with delay identified with the use of MATLAB. Results of experiments show that the proposed hybrid models containing fractional order part and integer order part are comparable in the sense of square cost function to reference integer order model and simultaneously they can be simpler to identify and their computational complexity is smaller than reference integer order model.

Modeling of Elementary Fractional Order Plants at PLC SIEMENS Platform

In the paper the problem of modeling elementary fractional order plants at PLC platform is presented. Models of considered plants were implemented at SIEMENS SIMATIC S7 300 platform with the use of STEP7 SCL language. Finally, comparison of simulation results and mathematical model is provided to demonstrate effectiveness of the proposed method.

A Sample Time Optimization Problem in a Digital Control System

In the paper a phenomenon of the existence of a sample time minimizing the settling time in a digital control system is described. As a control plant an experimental heat object was used. The control system was built with the use of a soft PLC system SIEMENS SIMATIC. As the control algorithm a finite dimensional dynamic compensator was applied. During tests of the control system it was observed that there exists a value of the sample time which minimizes the settling time in the system. This phenomenon is tried to explain.

A Tuning of a Fractional Order PID Controller with the Use of Particle Swarm Optimization Method

The paper is devoted to present a new tuning method for Fractional Order PID controller dedicated to temperature control. The proposed method uses Particle Swarm Optimization algorithm. The control plant is described by transfer function with delay. Results of experiments show that the proposed approach assures the good control performance in the sense of known integral cost functions.