An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions.

Area of Science:

• Control Systems Engineering
• Applied Mathematics

Background:

• Fractional order systems offer advanced modeling and control capabilities across diverse fields.
• Implementing these systems in real-world applications is challenging due to computational complexity of numerical approximations.
• Existing methods often result in high-order approximations that negate the inherent simplicity of fractional order models.

Purpose of the Study:

• To develop a computationally stable and efficient low-order method for approximating general fractional order systems.
• To represent fractional order systems as discrete-time rational transfer functions suitable for practical implementation.
• To provide a direct comparison with existing discretization techniques.

Main Methods:

• A novel direct approximation method is proposed for fractional order systems.
• The method focuses on generating low-order, discrete-time rational transfer functions.
• Performance is evaluated against established direct discretization techniques.

Main Results:

• The proposed method achieves a low-order approximation of fractional order systems.
• The approach demonstrates computational stability and efficiency.
• Comparative analysis confirms the added value of this method over current state-of-the-art techniques.

Conclusions:

• The developed method offers a practical solution for implementing fractional order systems.
• It bridges the gap between theoretical fractional order models and real-world engineering applications.
• This work advances the state-of-the-art in fractional order system approximation and control.