Reduced Order SMC Design for Output Tracking of Arbitrary Signal

This chapter presents the design of a reduced-order sliding mode controller for output tracking of an arbitrary signal. The controller aims to stabilize the difference between the system’s states and the reference states. A key challenge in reduced-order controller design is dealing with the zero dynamics states within the range space of the control input. To address this issue, a virtual zero placement using a specific transformation is discussed. By overcoming this obstacle, the reduced-order sliding mode controller can achieve stable output tracking despite the presence of unstable zero dynamics. Another challenge involves obtaining a bounded solution for the unstable zero dynamic state with respect to an arbitrary tracking input. Two methods are discussed to address this challenge: a non-causal system inverse and a causal reference tracking method, which involves a stable system center.