On backstepping control for a class of multiple uncertain systems with reduced-order ESO

The paper studies the control problem for nonlinear uncertain systems with multiple channel uncertainties, and presents the manifold of a class of second-order systems including unmatched and matched disturbances, which is mainly found in flexible components. The system model is first transformed into a Brunovsky form, where the multiple uncertainties in the system are lumped as one term-equivalent total effects. A backstepping united with a reduced-order ESO control design is proposed, where the intermediate variables need not be measurable, and only the system output is required for the control implementation. Finally, the proposed control structure is equivalent to PID, and its working mechanism is revealed. The use of multiple ESO or iterative learners can be avoided to match plant parameters, leading to reduced computational costs, simpler parameter tuning, and improved convergence as compared to traditional control methods. Finally, the simulation and experimental results illustrate the effectiveness of the proposed method.