Stable Inversion of Unstable Zeros for Iterative Learning Control and Application to CNC Machine Tool Precision Tracking Control

Iterative Learning Control (ILC) is an excellent feedforward control method that can effectively suppress repetitive disturbances based on past error information. For motion platforms with good linearity, such as CNC machine tools, ILC design using inverse models remains the most effective. However, the presence of unstable zeros transforms the inverse model into an unstable pole, resulting in unbounded outputs. In discrete systems, unstable zeros primarily arise from: (1) non-collocated placement of actuators and sensors; (2) discretization using zero-order hold. Unstable zeros are common in motion control systems; therefore, this paper addresses these zeros using a time-domain noncausal stable inversion method to avoid phase and magnitude errors associated with conventional frequency-domain methods. Experiments conducted on a CNC machine tool motion stage with unstable zeros in X-axis demonstrate that the proposed method is effective for achieving precise motion control in CNC machine tools.