Robust Control Of Liu Chaotic System With Parametric Uncertainty

The ship itself is a nonlinear complex dynamic system with large inertia.Changes in mass of the ship,moment of inertia and the center of gravity caused by changes in speed and loading of the ship lead to changes of corresponding fluid hydrodynamic derivatives,which are the reason why chaotic phenomenon might be happened in ship motion.The newly-proposed Liu chaotic system is a three-dimensional autonomous system which has quadratic nonlinear term.It is of great significance to design a simple and effective robust controller and to do research on the chaotic system control.This paper surveys the general theory of chaos appeared in nonlinear systems and analyzes dynamical properties of a new chaotic system—Liu chaotic system,such as phase diagram,Lyapunov exponents,power spectrum.The influence of system parameter on the chaotic system is also discussed.In this paper the robust control method of the Liu chaotic system with uncertainty parametric is analyzed.The Liu chaotic system is linearized in the vicinity of the equilibrium point.The system is reduced to second order deep strictly proper model through Bode graph reduction method.The robust controller is designed using the PID parameters solving method based on closed-loop gain shaping.At last,a class of nonlinear Abkowitz ship motion mathematical model is constructed,and the possibility of the model having Liu chaotic phenomena is discussed.The programs for chaos research are developed in MATLAB.The closed-loop gain shaping algorithm is applied in control simulation,which can be applied to both the systems with certain parameters and uncertain parameters.The results of both simulations show that the controller has good robustness to the model.The programs developed in this paper are beneficial to the rapid identification of chaotic model.The robust control method in this paper is effective and it is in common use for continuous chaotic systems.The chaotic research for ship motion mathematical model lays a foundation for further study.