Repetitive Learning of Backstepping Controlled Nonlinear Electrohydraulic Material Testing System

This paper develops repetitive and iterative learning control design and analysis for back stepping controlled nonlinear systems. To precisely track periodic or finite duration trajectories for nonlinear systems, back stepping control is first designed to render closed loop stability and, in theory, asymptotic tracking performance. However, due to the sensitivity to the unmodelled dynamics plant variations, asymptotic tracking performance is usually not feasible. Thus, repetitive or learning control is applied over the back stepping controlled system to restore asymptotic tracking performance. This approach is applied to an electrohydraulic material testing system, in which the material specimen present substantial nonlinear force and displacement relationship. It will be shown that the back stepping control employs both feedback and feedforward actions to render linearized I/O plant and thus the outer loop repetitive and learning control design can be based on the compensated linear system. Experimental results will be given to demonstrate the effectiveness of the proposed approach.