Output Tracking Using Reduced Order SMC for Right-Invertible Systems with Input Saturation

In general, when a system is only right-invertible, it indicates that the number of inputs surpasses both the outputs and states of the system. Over-actuated systems fall into this category. This chapter presents a structured approach to designing a reduced-order Sliding Mode Control for a uncertain non-minimum phase over-actuated systems to track arbitrary reference signals. The method proposed involves a transformation that resolves input redundancy, thus representing the system as a normally-actuated with virtual control inputs. Additionally, unstable zero dynamics are virtually stabilized through another transformation, allowing for the exclusion of stable and virtually stable zero dynamic states from the super-twisting control design. Finally, the computed virtual control magnitude is distributed among all actuators through a redistributed pseudo-inverse type of control allocation, ensuring that the system operates within the limits of actuator saturation.