A Terminal Sliding Mode Variable Structure Control Of Uncertain Systems

As one kind of control system design approaches, variable structure control with sliding mode is a powerful method for robust control, which is suitable to linear systems, nonlinear systems, time-varying systems and uncertain systems. The sliding mode controller, which is designed by selecting sliding mode surface, can drive the system states to reach the sliding hypersurface. Under certain matching conditions, the movement of system on the sliding hypersurface, i.e. the sliding mode, is completely insensitive to parametric uncertainty and external disturbance, which exhibits more superior characteristics than ordinary conventional robust control. Owing to this special feature, sliding mode control is attractive in solving the robust control problems for uncertain systems.After knowing well the development of variable structure control with sliding mode, variable structure control with terminal sliding mode for matched or unmatched uncertain systems is deeply studied. Main results are as follows.Fast terminal sliding control for uncertain multivariable linear systems is studied. As a novel nonlinear sliding mode surface, compared with linear sliding mode, the terminal sliding mode possesses faster convergence speed and higher steady-state precision. Unlike linear sliding mode being easily applied to the design of multivariable linear systems, terminal sliding mode is suitable to second-order system, which can not be easily extended to multivariable linear systems. For a class of uncertain multivariable linear systems, by using global fast terminal sliding mode, exponential fast terminal sliding mode and logarithmic fast terminal sliding mode, the robust control laws are derived respectively. The content contains structure of nonlinear terminal sliding hypersurface, selection of its parameter matrix, and algorithm of variable structure control law. It is proved that the system state variables can be driven to reach the sliding hypersurface in finite time, then retain on the sliding hypersurface and converge to the equilibrium point with higher speed than ordinary fast terminal sliding mode in finite time according to the motion law of the corresponding fast terminal sliding mode law.Nonsingular terminal sliding mode control for second-order uncertain system is studied. It is extended to the second-order uncertain system with parameter perturbation in control channel, and the corresponding sliding mode control law is gained. A model tracing variable structure control methodology based on nonsingular terminal mode for second-order uncertain systems is proposed. Using this method, BTT roll channel autopilot is designed. This method overcomes singular problem in ordinary terminal sliding mode control, and guarantees system tracking errors converge to equilibrium point in finite time. Simulation results prove the roll channel autopilot of BTT missile has fine instruction following performance and strong robustness.An integral nonsingular terminal sliding mode control for uncertain multivariable linear systems is studied. A new state transformation matrix is presented. By using this transformation, uncertain multivariable linear system is decomposed into two subsystems:an unmatched stable internal subsystem and a matched input-output subsystem. Then, integral nonsingular terminal sliding mode control law is applied to the input-output subsystem so that this subsystem states converge to the equilibrium points in finite time. Meanwhile, the states of the internal stability subsystem converge to the neighborhood of the equilibrium points and guarantee global uniform ultimate bounded stability. Integral sliding mode reduces the chattering phenomenon and steady-state error.A dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is studied.In order to eliminate the inherent chattering problem in sliding mode control, and avoid the singularity in conventional terminal sliding mode control, a dynamic nonsingular terminal sliding mode control for uncertain linear multivariable systems is proposed. Just as the integral nonsingular terminal sliding mode control mentioned above, uncertain multivariable linear system is decomposed into two subsystems through a special transformation:an unmatched stable internal subsystem and a matched input-output subsystem. A nonsingular terminal sliding mode manifold is used for the input-output subsystem to design the control law. The states of this subsystem converge to the equilibrium points. Meanwhile, the states of the internal subsystem converge to the neighborhood of the equilibrium points. This realizes the global uniform ultimate bounded stability. Dynamic sliding mode can be used to eliminate the sliding mode chattering, and smooth control input.