Sliding Control Of Nonlinear Systems Based On Iteration Technique

In the iteration technique for finite nonlinear systems, the nonlinear system is approached by a sequence of linear time-varying systems. Thus the control of nonlinear system could be studied via the linear time-varying (LTV) approximations. This gives a new solution for the control of nonlinear systems. This dissertation presents the sliding control method based on the iteration technique: a series of sliding controllers could be designed for the sequence of LTV approximations, these controllers will converge to the controller of the original nonlinear system. In this dissertation we use a simple sliding surface design method, which is developed from a necessary condition of system stability, for LTV systems.Many real systems are distributed and are given, by particular, by functional differential equations (FDE). Currently, the control problem of FDEs has not been widely studied. This dissertation extends the iteration technique to FDEs and proves the LTV approximations are global convergent to the original nonlinear system under local Lip-schitz conditions. Thus a sliding controller for FDE could be designed via the LTV approximations.The velocity control systems of hydraulic systems are governed by FDEs. As an example, this dissertation sets up the model of the THP10-630 hydraulic press and designs a sliding controller for the model by the iteration technique . Simulation results shows that when the effective bulk modulusβe and the reaction force f change, the controller is robust.The control of distributed parameter system given by partial differential equations (PDE) is far more difficult and complex then lumped systems given by ordinary differential equations. This dissertation extends the iteration technique to nonlinear PDEs. As an example, we use a sequence of LTV PDEs to approximate the nonlinear wave equation and prove the convergence through finite approximations of PDE. Then a slid- ing controller is designed based on the iteration technique. Simulation results show that the controller could stabilize the nonlinear wave equation.