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Discrete global-sliding mode (SM) control of switching DC-DC converters is presented in this paper. The existence and stability conditions of quasi global-sliding mode are proposed. The design method for the discrete global SM controller is studied and applied to Buck converter with global-sliding mode control. Computer simulation and experimental results verify the validity of the theoretical analysis.

The output tracking for a general family of nonlinear systems presents formidable technical challenges. In this paper, we present a novel scheme for tracking control of a class of affine nonlinear systems with multi-inputs. This effective procedure is based on a new sliding mode design for tracking control of such nonlinear systems. The construction of an optimal sliding mode is a difficult problem and no systematic and efficient method is currently available. Here, we develop an innovative approach that utilizes a chaotic optimizing algorithm, which is then successfully applied to obtain the optimal sliding manifold. The existing efficient reaching law approach is then utilized to synthesize the sliding mode control law. The sliding mode control scheme proposed here is particularly appropriate for robust tracking of the chaotic motion trajectory.

For a hypersonic flight vehicle with highly coupling nonlinear, a sliding mode controller based on reaching law is designed for its longitudinal motion model. Two proposals of reaching law are designed. One of which is a variable exponential reaching law, the other one is compound reaching law which consists of a conventional exponential reaching law and a power rate reaching law. The reaching law controller can speed up the system states arriving at the sliding mode condition, at the same time, it can guarantee better robustness. Simulation analysis is conducted for trimmed cruise condition of 110,000 ft and Mach 15, in which the responses of the vehicle to a step change of altitude and velocity respectively are analyzed. Simulation results show that the controller based on variable exponential reaching law enables the system to faster tracking speed than the conventional reaching law. Moreover the compound reaching law controller has shorter tracking time and strong robustness against parameters uncertainties.