Switching Line Design for VSC of the Second Order Systems with Conventional and Elastic Constraints

This paper focuses on a new sliding mode control algorithm for the second order nonlinear, time-varying, uncertain dynamic systems subject to velocity and acceleration constraints. The proposed algorithm employs a time-varying switching line that passes through the origin of the error state space. The line is selected in such a way that the reaching phase is eliminated, insensitivity of the system to the external disturbance and parameter uncertainties is guaranteed from the very beginning of the proposed control action, and fast, monotonic error convergence to zero is achieved. Two different approaches to the selection of the optimal switching line are investigated. First, the optimisation problem is considered with the velocity and acceleration constraints expressed by inequalities. Since such conventional constraints are often impractical the second concept proposed in the paper is based on the elastic constraints