Improved Model Reduction and Tuning of Fractional Order PI{\lambda}D{\mu} Controllers for Analytical Rule Extraction with Genetic Programming

TL;DR

This paper introduces a genetic algorithm-based approach for model reduction and optimal tuning of fractional order PI{ extlambda}D{ extmu} controllers, resulting in analytical tuning rules that outperform traditional methods and are easier to implement.

Contribution

It presents a novel Nyquist-based model reduction technique combined with genetic programming to derive simple, effective analytical tuning rules for fractional order controllers, improving control performance and robustness.

Findings

Nyquist-based reduction outperforms H2 norm methods

GP-derived tuning rules match or exceed GA performance

Rules are computationally efficient and robust

Abstract

Genetic Algorithm (GA) has been used in this paper for a new approach of sub-optimal model reduction in the Nyquist plane and optimal time domain tuning of PID and fractional order (FO) PI{\lambda}D{\mu} controllers. Simulation studies show that the Nyquist based new model reduction technique outperforms the conventional H2 norm based reduced parameter modeling technique. With the tuned controller parameters and reduced order model parameter data-set, optimum tuning rules have been developed with a test-bench of higher order processes via Genetic Programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by weighted sum of error index and controller effort. From the reported Pareto optimal front of GP based optimal rule extraction technique a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP based tuning rules has been compared with original GA based control performance for the PID and PI{\lambda}D{\mu} controllers, handling four different class of representative higher order processes. These rules are very useful for process control engineers as they inherit the power of the GA based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three dimensional plots of the required variation in PID/FOPID controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP based tuning rules has also been shown with credible simulation examples.