Backstepping Control Of Some Typical Nonlinear Systems

The Backstepping design technique, which aiming at the uncertainty system, is a kind of systematic synthetic technique to controller; it is a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The Backstepping design technique starts from the differential equation in its smallest order of the system, it introduces the concept of virtual control and designs the satisfied virtual control step by step, and the real control can be got in the end.Chaotic synchronization and suspension systems are two kinds of typical nonlinear systems, the controller designs of these two kinds of systems are representative. Based on the backstepping method the controllers are designed for the forenamed systems in the paper.Recently, as a result of the continuously development of the research of chaotic system, the application of chaotic synchronization theory has been got deeply into the field of Secure communication which has became a hot topic. With regard to the issue of chaotic synchronization, in this paper, firstly, Coullet and Rossler chaos systems are separately treated as the master and slaver systems, and then, two controller, a continuous-time chaotic synchronization controller and a sampled-data one, which both can keep all the states of the two systems synchronize separately are designed via the backstepping method. Secondly, based on the adaptive backstepping method, a continuous-time generalized synchronization controller and a sampled-data one are also proposed for multi-scroll chaotic systems with unknown parameters.The suspension is one of important automotive assembly, which has prodigious influence on performance of ride quality and handing stability. So it is crucial to design excellent suspension system for automotive quality. In this paper, adaptive backstepping method is used in the design of controllers for the active suspension system and the semi-active suspension system, as a result, these suspension systems can better adapt to the change of system parameters caused by the working environment.The results of numerical simulations verify the effectiveness of the controllers designed for the chaotic systems and the suspension systems.