A moving switching plane for the sliding mode control of the third order system

A new sliding mode control algorithm for the third order uncertain, nonlinear and time-varying dynamic system subject to unknown disturbance and input constraint is proposed. The algorithm employs a time-varying switching plane. At the initial time, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves with a constant velocity to the origin of the space. The plane is selected in such a way that the integral of the absolute value of the system error over the whole period of the control action is minimised and the input constraint is satisfied. By this means, the reaching phase is eliminated, insensitivity of the system to the external disturbance is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.