Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time

TL;DR

This paper evaluates various hybrid fractional order fuzzy PID controllers for oscillatory processes with dead time, optimizing their parameters with genetic algorithms to improve set-point tracking and disturbance rejection.

Contribution

It introduces a family of hybrid fractional order fuzzy PID controllers tuned with genetic algorithms and compares their performance on different oscillatory processes.

Findings

Hybrid controllers outperform traditional ones in set-point tracking.

Optimal tuning reduces control signal variation.

Pareto analysis reveals trade-offs between tracking and disturbance rejection.

Abstract

Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes.