Sliding mode control for three time scale system with matched disturbances

When dealing with large scale systems, the dimension and ill-conditioning of the state matrix motivates the use of singular perturbation theory. This paper presents the design of sliding mode control for three-time-scale system reduced in their slow, fast and very fast sub-models using singular perturbation approach in presence of external disturbances. Sliding mode control (SMC), a powerful tool dealing with uncertainty and disturbances, has been utilized for decades. Firstly, the decomposition of the system is carried out into three subsystems namely `slow´, `fast 1´ and `fast 2´. Secondly, individual SMC laws are designed satisfying asymptotic stability condition. Finally the composite SMC law is proposed for full order system. Numerical examples are given to demonstrate the robustness of the proposed control scheme. Through the simulations it is observed that the performance of designed composite control law is better compared to three-time-scale approach.