Simulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors

TL;DR

This paper employs a genetic algorithm-based approach to design optimal PID controllers that effectively suppress chaotic oscillations in complex multi-wing Lorenz-like systems, demonstrating robustness across various initial conditions.

Contribution

It introduces a global optimization framework using genetic algorithms for designing PID controllers tailored to multi-wing chaotic systems, a novel approach for such complex dynamics.

Findings

Successful suppression of chaos in four different multi-wing systems

Robust control performance across multiple initial conditions

Demonstration of the effectiveness of GA-based PID tuning

Abstract

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series for these multi-wing chaotic systems is much higher than that of the conventional double-wing chaotic attractors. A real-coded Genetic Algorithm (GA) based global optimization framework has been adopted in this paper as a common template for designing optimum Proportional-Integral-Derivative (PID) controllers in order to control the state trajectories of four different multi-wing chaotic systems among the Lorenz family viz. Lu system, Chen system, Rucklidge (or Shimizu Morioka) system and Sprott-1 system. Robustness of the control scheme for different initial conditions of the multi-wing chaotic systems has also been shown.