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

摘要

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