Continuous and smooth sliding mode control

Continuous asymptotic and smooth ideal sliding mode control algorithms that have finite reaching time to the sliding surface are developed. The continuous and smooth sliding mode controllers are developed using Lyapunov function techniques. The conditions for finite time convergence and smoothness of the smooth controller are developed. Then the smooth controller is compared with a continuous approximation of the discontinuous sliding mode controller to demonstrate the enhanced robustness of the newly developed controller to noise, disturbances and uncertainties.; Once the smooth sliding mode controller is developed, a method to enhance the robustness of the controller to bounded disturbances and uncertainties using a sliding mode estimator is investigated. The resulting control maintains the finite reaching time and the required degree of smoothness for the smooth sliding mode controller.; A Lyapunov-based continuous sliding mode controller using an integral sliding surface to eliminate the bounded disturbance and uncertainty effects without the use of an estimator is then developed. This results in an asymptotic sliding mode controller that is continuous. The results of the three developed sliding mode controllers are then applied to a case study that considers a simplified ballistic missile interceptor.