Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Area of Science:

• Control Systems Engineering
• Applied Mathematics

Background:

• Traditional Proportional-Integral-Derivative (PID) controllers face limitations in complex systems.
• Fractional-order calculus offers enhanced flexibility for controller design.

Purpose of the Study:

• To implement and tune a variable-order fractional PID controller.
• To evaluate its performance on a third-order plant with delay using the Grünwald-Letnikov definition.

Main Methods:

• Development of a variable-order fractional PID controller.
• Tuning algorithms based on the Grünwald-Letnikov difference definition.
• Simulation of a third-order plant with time delay.

Main Results:

• Unit step response analysis presented graphically and in tables.
• Performance evaluation using Summation of Squared Error (SSE), Summation of Squared Time Weighted Error (SSTE), and Summation of Squared Time-squared Weighted Error (SST2E).
• Assessment of overshoot and rise time for system outputs.

Conclusions:

• The implemented fractional PID controller shows promising results for the tested system.
• Variable-order fractional PID controllers offer a viable alternative for complex control problems.