Generalized characteristic ratios assignment for commensurate fractional order systems with one zero

Area of Science:

• Control Systems Engineering
• Fractional Calculus Applications
• System Dynamics Analysis

Background:

• Fractional order systems offer enhanced modeling capabilities over traditional integer order systems.
• Determining characteristic equations and zero locations is crucial for stability and performance analysis.
• Existing methods may not adequately address systems with zeros, particularly in fractional domains.

Purpose of the Study:

• To introduce a new method for determining characteristic equations and zero locations in commensurate fractional order systems.
• To extend the concept of characteristic ratios to include systems with zeros.
• To design fractional order controllers with specific step response characteristics.

Main Methods:

• Extension of the characteristic ratio concept for zero-including fractional order systems.
• Definition of generalized characteristic ratios preserving time-scaling properties.
• Utilizing magnitude frequency response monotonicity for ratio assignment.
• Developing patterns for characteristic ratios to achieve non-overshooting and low-overshoot responses.

Main Results:

• A generalized characteristic ratio definition is proposed for fractional order systems with zeros.
• Methodology allows for the assignment of these ratios to achieve desired step response characteristics (non-overshooting or low-overshoot).
• Design of fractional order PI and lag/lead controllers demonstrated through numerical simulations.

Conclusions:

• The proposed method effectively determines characteristic equations and zero locations for fractional order systems.
• Generalized characteristic ratios provide a robust tool for designing controllers with specific performance criteria.
• The developed technique enhances the design of fractional order control systems, validated by simulation results.