Reduced Order SMC Design for Output Tracking in Non-Minimum Phase Systems: A Concept

This chapter addresses the problem of achieving output tracking in non-minimum phase (NMP) systems using reduced order sliding mode control (SMC). Unstable zero dynamics hinders the design of reduced order tracking controllers. However, this problem can be solved through the virtual stabilization of zero dynamics, achieved by decomposing the system in a special coordinate basis (SCB). The design of reduced order control is possible because of the robustness property of SMC, which effectively eliminates the matched disturbance. This chapter details a methodology for designing a reduced order sliding surface with a reduced order state vector, aiming to ensure the asymptotic stability of the entire state vector during sliding motion. This approach eliminates the need for zero dynamics states in the surface and the control design.