ITAE optimal sliding mode control of cable suspended loads

In this paper a sliding mode control algorithm for cable suspended loads subject to acceleration and velocity constraints is presented. The algorithm guarantees the reaching phase elimination. Moreover, it ensures fast and monotonic system error convergence to zero without violating the acceleration and velocity constraints. The proposed method employs a time-varying switching line. At the initial time t=t₀ the line passes through the representative point of the system in the error state space. Afterwards, the line moves with a constant velocity and a constant angle of inclination to the origin of the space and having reached the origin it stops moving. By this means insensitivity of the system with respect to external disturbance and model uncertainty from the very beginning of the control action is ensured. Parameters of the line are selected in such a way that the integral of the time multiplied by the absolute error (ITAE) is minimized.