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Characteristic ratio assignment in fractional order systems.

Mohammad Tabatabaei¹, Mohammad Haeri

¹Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran. tabatabaei2008@yahoo.com

ISA Transactions

|July 13, 2010

Summary

This study introduces characteristic ratios for fractional order systems, providing a stability condition and a method for characteristic ratio assignment (CRA). The CRA approach enables the design of non-overshooting, fast fractional order controllers.

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Area of Science:

Control Systems Engineering
Fractional Calculus
System Stability Analysis

Background:

Fractional order systems offer enhanced modeling capabilities over traditional integer-order systems.
Stability analysis and controller design for fractional order systems remain active research areas.
Characteristic ratios are key parameters influencing the transient response of dynamical systems.

Purpose of the Study:

To define characteristic ratios and generalized time constant for all-pole commensurate fractional order systems.
To derive a sufficient condition for the stability of these systems.
To introduce an analytical method for characteristic ratio assignment (CRA) for non-overshooting, fast responses and design fractional order controllers.

Main Methods:

Definition of characteristic ratios and generalized time constant for fractional order systems.
Derivation of stability conditions based on characteristic ratios.
Development of an analytical characteristic ratio assignment (CRA) technique.
Design of fractional order controllers using the proposed CRA method.

Main Results:

Characteristic ratios and generalized time constant are defined for all-pole commensurate fractional order systems.
A sufficient condition for system stability in terms of characteristic ratios is established.
An analytical CRA method is presented, enabling non-overshooting fast closed-loop step responses.
Computer simulations validate the performance of CRA-based fractional order controllers.

Conclusions:

The defined characteristic ratios provide insights into the stability and transient behavior of fractional order systems.
The proposed CRA method offers an effective approach for designing high-performance fractional order controllers.
The study demonstrates the practical applicability of CRA in fractional order control system design.