Parallel-Equivalent-Input-Disturbance-Approach-Based Spatial Repetitive Control for Rotating Systems

The repetitive control method is effective for signals with fixed periods but struggles with signals with varying periods. This article introduces a parallel-equivalent-input-disturbance-based (PEID) spatial repetitive control method for rotating systems. The aim is to accurately track position-dependent time-varying periodic reference inputs and effectively reject aperiodic disturbances. First, a proportional–integral observer (PIO) with a relaxation variable is designed to estimate the system state. The state error is used to derive an equivalent input disturbance (EID). A PEID estimator is constructed by paralleling <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{p}$</tex-math></inline-formula> PIO-based EID estimators, enhancing system flexibility and EID estimation accuracy. Next, a spatial internal model is built to create a spatial modified repetitive controller (SMRC). The SMRC includes a low-pass filter for stability and a small correction to the delay constant to improve steady-state tracking accuracy. Then, a composite control input is designed to combine the PEID estimate with the SMRC output through a domain operator to ensure satisfactory tracking and disturbance rejection performance. A digital SMRC implementation is developed using a new data storage technique, allowing synchronous execution of the SMRC and the temporal PEID estimator. Finally, experimental results and comparisons with related methods validate the effectiveness of this approach.