CONTROL OF NON-LINEAR SYSTEM USING BACKSTEPPING

Abstract

The defining attribute of a servomechanism is that the controlled output of a mechanism is automatically compared with the controlling input. The difference between the settings or positions of the output and the input is called the error signal, which acts to bring the output to its desired value.The paper work shows the application of backstepping technique to stabilize a nonlinear dynamical system. Any nonlinear dynamical system can be stabilized only by means of Lyapunov function approach. In this approach backstepping technique is invariably adopted. In case of normal backstepping technique stabilizing function is designed at every step of dynamics starting from the output towards input. The Backstepping approach provides a recursive method for stabilizing the origin of a system in strict-feedback form. The controller contains the terms of system state variables, reference input & its derivatives, and error. The basic aim of the controller is to settle down error and its derivatives to zero. The controller is designed through Lyapunov based function so as to render strong closed loop stability.In the theory of control systems, Lyapunov functions are scalar functions that may be used to prove the stability of equilibrium of a control system.