Design of a nonlinear time-varying switching line for second order systems

In this paper a new sliding mode control algorithm for the second-order dynamic system subject to unknown disturbance is designed. The algorithm eliminates the reaching phase and it guarantees error convergence to zero in a finite time, without violating constraints on the state of the system. The algorithm employs a nonlinear and time-varying switching line. At the initial time t=t₀, the line naturally consists of these points in the error state space which represent all the admissible initial conditions of the system. Afterwards, the line moves smoothly to reach its predetermined shape. By this means insensitivity of the system to external disturbance is guaranteed from the very beginning of the proposed control action. Furthermore, fast, monotonic, and finite time error convergence is achieved