A new strongly predefined time sliding mode controller for a class of cascade high-order nonlinear systems

Many real-time systems can be described as cascade space-state models of different orders. In this paper, a new predefined controller is designed using a Strongly Predefined Time Sliding Mode Control (SPSMC) scheme for a cascade high-order nonlinear system. The proposed control scheme based-on SMC methodology is designed such that the system states reach zero within a determined time prior to performing numerical simulation. Moreover, Fixed Time Sliding Mode Control (FSMC) and Terminal Sliding Mode Control (TSMC) schemes are presented and simulated to provide a comparison with the proposed predefined time scheme. The numerical simulation is performed in Simulink/MATLAB for the proposed SPSMC and the other two existing methods on two examples: second and of third order to demonstrate the effectiveness of the proposed SPSMC method. The trajectory tracking of the ship course system is addressed as an example of a second-order system. Synchronization of two chaotic systems, Genesio Tesi and Coullet, is considered as an example of a third-order system. Also, by using two performance criteria, a thorough comparison is made between the proposed predefined time scheme, SPSMC, and the two no predefined time schemes, FSMC and TSMC.