Discrete-time sliding mode controllers with disturbance estimation

The paper deals with the problem of output stabilisation of a linear system in the presence of an unknown external disturbance by using continuous-time and discrete-time dynamic Variable Structure controllers. The considered linear system is the cascade of r integrators. The main feature of the proposed controllers is the presence of a nonlinear integral action which acts as "estimator of the total external disturbance" present at the input of the system. This estimator provides a feed-forward control action which allows to keep small the amplitude of the discontinuous control term and therefore it proves to be effective in chattering reduction. The stability of the controlled system in the presence of an external disturbance with bounded derivative is proved. After a transient, a discrete sliding mode with low chattering arises in the system. Simulation results end the paper