Enhanced Disturbance Rejection Approach for Repetitive-Control Systems Based on a Novel Loop-Shaping Design

The equivalent-input-disturbance (EID) approach is widely employed in repetitive control systems to address disturbance issues. However, the EID method faces challenges due to the disturbance estimation error, which is defined as the difference between the EID signal and the EID compensation signal. This study presents an enhanced EID method from the perspective of the design of a disturbance-rejection loop. First, the disturbance-rejection problem is reformulated to design a framework where the EID compensation signal closely matches the EID signal, effectively addressing the disturbance estimation error. Second, a loop is constructed from the EID signal to the EID compensation signal, consisting of only two transfer functions: a model <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G(s)$</tex-math></inline-formula> and a filter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F(s)$</tex-math></inline-formula>. As a result, the developed disturbance-rejection framework is significantly simple. Third, the loop design conditions are specified, requiring the loop magnitude to approach 1 and the loop phase to approach 0. This study provides detailed design procedures for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G(s)$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$F(s)$</tex-math></inline-formula>. Via the developed disturbance-rejection framework, the closed-loop stabilization is achieved. Finally, motor drive experiments and comprehensive comparisons demonstrate the effectiveness and superiority of the method.