Robust Control For Nonlinear Systems And Its Application To The Lift Feedback Fin Stabilizer

In general,all practical systems are nonlinear in which there exists many different uncertainties in controlled plants inevitably. It is necessary to design robust controllers based on the normal plants so that the controlled systems have satisfactory properties by considering the existence of uncertainties.Based on Lyapunov stability theory,geometry theory for nonlinear systems,dissipative theory and etc,the robust HK control for uncertain nonlinear systems and the reliable H control problem of uncertain nonlinear systems are studied,and the control laws are proposed correspondingly for several typical nonlinear systems in this paper.The robust controller design methods are presented and the proposed method is applied to design the control system of lift feedback fin stabilizer by considering the linear model,nonlinear model and coupled nonlinear model of ship motions.At first,the robust H control for uncertain nonlinear systems with norm bounded uncertainties is studied,based on a positive definite solution of Hamilton-Jacobi-Issacs inequality(HJI),a sufficient condition is given such that the closed loop system is asymptotically stable and its L2-gain is less than or equal to a prescribed value.Using this condition state feedback control law and an output feedback control law which ensured robust Hx performance of the closed-loop system are derived.Due to the difficulty to solve HJI,a method is proposed which do not require solving it by using an appropriate Lyapunov function.Secondly,the reliable Hx control problem of uncertain nonlinear systems with strictly redundant control elements is studied in detail.Based on HJI.the reliable state feedback controller and output feedback controller are presented.By considering a class of nonlinear time-varying uncertain systems with time-delay and unknown nonlinear disturbances,the linear memoryless dynamic output feedback controller based on a state observer is designed such that,for alladmissible uncerntainties as well as actuator failures occurring among a prescribed subset of actuators,the closed-loop system is quadratically stable with an Ha norm bound constraint.Thirdly,base on Lyapunov methods,a new robust controller for uncertain nonlinear systems without matching condition which can compensate the matching uncertainty and the mismatched uncertainty respectively is proposed,it is simple and smooth,that is to say,it is very easy to implement. By the simulation results,it is verified to have excellent performance.A class of uncertain nonlinear systems which can be transformed into strict feedback nonlinear systems is investigated based on feedback linearization approach of differential geometry.An adaptive robust controller with L2 -gain is proposed by using backstepping technique.The numerical method is given and it is proved to be practical by simulation results.lt is a more practical method to solve HJI for a special nonlinear system because the problem to solve HJI is very difficult in general case,and only get the approximate solution when it can be solved.An effective method to solve HJI is presented for a class of nonlinear system which is ordinary.At last,the simulating problem of random sea wave is discussed in terms of the sea wave spectrum.Based on DGKF method and LMI method of H control,the robust Hx controllers are designed to the linear model of ship roll motion by which the bounded control is taken into account.Furthermore,the robust adaptive control method with L2 -gain is applied to the nonlinear model of ship roll motion which can counteract sea wave disturbance effectively.The 1-DOF nonlinear model is obtained by applying singular perturbation theory to the Multi-DOF coupled model of ship motions which have different time scales.The robust sliding mode controller is designed for the system which can not only meets the demands of the composite controller and but also have robustness.