Robust Backstepping Control Method Using Sliding Modes With Its Application To The Fin Stabilizer

The uncertainties exist everywhere in either the nature or the society. But the existence of the uncertainty is not permitted in the engineering. There is great difference between the actual systems and the mathematic models because of the uncertainties. So the engineering problem can not be solved satisfyingly if it is designed only based on the nominal system. All the above make the robustness of the nonlinear system a necessary problem to be researched. It's essential to make designed controller have excellent robustness to all kinds of uncertainties.In this paper the design of robust controllers for a broad class of nonlinear system is given, and two control algorithms are also discussed for a group of cascaded seconded order systems. The approach can overcome the uncertainties and has good robustness. The class of nonlinear systems considered is referred to as a semi-strict feedback system and includes parametric uncertainties, input gain uncertainties and the unknown but bounded nonlinear function and disturbance.The key components of the control design are the use of the backstepping design procedure, sliding mode control. The backstepping method is used to recursively design virtual controllers for each step in the procedure. Each virtual controller and the resulting actual controller are designed using sliding mode control to compensate for model uncertainty. The control method can be used in a broader class of nonlinear systems, and the tracking error is determined by the control parameters. The virtual controllers can compensate the error transformed from the previous subsystems.Based on the above the dynamical robust backstepping method is presented. The main feature of this approach is it alleviates the need to take derivatives of the virtual control at each step of the design. This has two positive effects. The first is that a reduction in the complexity in the controller design. The second is a drastically smaller amount of uncertainty results in the transformed dynamical systems. Therefore the controller at each step will require less gain to stabilize thesubsystem.Then the method of energy in part is given with which we can get the model of random wave, and predict the roll motion of unstabilized ship and stabilized ship using the wave model. The simulation of a ship stabilizer system is also made. The comparison of the simulation with real ship indicates that the method can be used in the calculation and prediction of roll motion of a stabilized ship in random wave.Finally the nonlinear model of ship is given. A robust controller is designed based on the sliding mode backstepping method presented in this paper to test the effectiveness of these approaches. The simulation achieves desired results and the controllers meet the requirement and have excellent robustness.