The Sliding Mode Control Of Nonlinear Systems

The analysis and synthesis of nonlinear systems has always been limited on a single point or in a narrow local area, before the differential geometric theory is introduced into the nonlinear system control. The decoupling and precise linearization control strategy based on the new theory changes the situation and makes it possible to be realized globally. However, the differential geometric method relies on the precise mathematic model of the system, while the practical system could not exclude the influence of time-delays, parameter perturbation or external disturbances, which to some extent limited its application.The paper is concerned with novel deign methods for sliding mode control of nonlinear systems. The presented techniques employ the sliding mode control approach and the differential geometric method to promote the closed-loop of the system to be more robust to the perturbation and external disturbances. Moreover, the nonlinear coordinate transformation is utilized to solve the problem of constructing the nonlinear sliding surfaces. The design solutions weaken the restrictive conditions about the mathematic model and the uncertainties of the system in the other correlative literatures. In addition, dynamic control parameters are employed not only to reduce the chattering phenomenon, but also to neutralize the influence of the parameter perturbation before the system's trajectories reach the sliding surface.Nonlinear time-delay systems control is a challenging, real life control problem, but which has not been extensively studied by now. The reason probably arises from its double complexity. To meet the requirement of the application, the precise linearization theory and the sliding mode control are applied to the multi-input-multi-output nonlinear time-delay system, respectively. The sufficient decoupling conditions of the system are discussed, based on which, the feedback decoupling controller and theoutput sliding mode controller are designed respectively. Moreover, the robust properties of the closed-loop system are compared under these tow control strategies.In recent years, the sustained attention has been given to the robust control of uncertain nonlinear systems. As the essential of the robust control strategy is sacrificing certain performance index of the system to promote its robust property, the control methods always limit bandwidth of the closed-loop system, and as a result, weaken the system's capability of tracking and disturbance proof. Sliding mode control is a substitute method to make the system being robust, but it is rather difficult to construct the nonlinear switching surfaces, which limits the application of the sliding mode control in nonlinear systems. The presented solutions employ the nonlinear coordinate transformation technique to construct sliding surfaces, and as a result, simplify the design of system. The designed controller exerts the invariance of the sliding mode to system perturbation and external disturbances, and the dynamic performance of the sliding mode could be designed with the linear system theory.With the excellent control performance of minimum phase nonlinear systems, they have been studied extensively in recent years. Considering the minimum-phase nonlinear system could be stabilized by feedback control, the derivatives of the output variables are utilized to design the switching functions, under the sliding mode control, the system reach the sliding surface and be linearized on it. Consequently, pole zero assignment, optimum control and the structure assignment of the optimum character could be realized with the state feedback. However, the zero dynamics of many practical nonlinear systems are unstable, the non-minimum nature of the plant restricts application of the feedback linearization and sliding mode control. The presented techniques first approximately linearized the internal mode of the system about the equilibrium point and introduce the virtual control into the design of the sliding mode control, when the sliding surfaces are reached, the zero dynamic could be stabilized and the dynamic performance of the system could be guaranteed in the local area of the equilibrium point as well.The design conclusions of the paper are applied to the control of autonomousunderwater vehicles worked in low speed. As the underwater vehicles are typical systems with strong coupling and strong nonlinearity, the control design is extremely difficult. The results for the first time change the situation that underwater systems could only be decoupled and linearized on single point, thus this complex nonlinear control system could be transformed into several single-input-single-output subsystems. The input control guarantees the asymptotical stability of the state variable error, and promotes the dynamic performance of the sliding mode control.