Quantitative Analysis on Tracking Error Under Different Control Architectures and Feedforward Methods

In this paper, we present quantitative analysis on tracking error in two kinds of two degree-of-freedom (DOF) control architectures under different stable-inversion feedforward methods such as zero-phase-error tracking control (ZPETC), zero-magnitude-error tracking control (ZMETC), non-minimum-phase-zero-ignored tracking control (NMZITC). Research shows that tracking error is approximately proportional to a specific order derivative of reference trajectory with specific feedforward and feedback controller in specific control architecture. Further compensation of tracking error requires extra feedforward terms related to the derivatives of reference trajectory like velocity and acceleration feedforward. Stable-inversion feedforward methods are naturally non-casual, but can also be implemented as causal ones. However, research shows that non-causal and causal implementation will lead to different tracking error and require different extra compensation. The quantitative analysis on tracking error can not only explain the generation of tracking error but also give rise to a feedforward tuning algorithm by the shape of tracking error. Experiment on an ultra-precision motion system well validates the theoretical analysis and feedforward tuning algorithm.