An Integrated Model-Data-Based Zero-Phase Error Tracking Feedforward Control Strategy With Application to an Ultraprecision Wafer Stage

In precision motion control, well-designed feedforward control can effectively compensate the reference-induced tracking error. To achieve excellent tracking performance such as nanometer accuracy regardless of reference variations, an integrated model-data-based zero-phase error tracking feedforward control (ZPETFC) strategy is synthesized for precision motion systems with complex and nonminimum phase (NMP) dynamics. The feedforward controller comprises a conventional ZPETFC controller and a gain compensation filter structured with symmetric finite impulse response (FIR) filter. Especially, the conventional ZPETFC is predesigned based on the plant model, and consequently, the feedforward controller is parameterized by the gain compensation filter coefficients, which results in excellent capacity for approximating the inverse behavior of the complex and NMP dynamics. In order to compensate the modeling error in the conventional ZPETFC design and improve the tracking performance, a data-based instrumental-variable method with impulse response experiment is developed to obtain the optimal parameter vector under the existence of noise and disturbances. Furthermore, the ridge estimate method using singular value decomposition is employed to guarantee a fast convergent iteration in the case of ill-conditioned Hessian matrix. The proposed ZPETFC strategy enables a convex optimization procedure with the inherent stability in the iterative tuning process, and is finally implemented on a developed ultraprecision wafer stage. Comparative experimental results demonstrate that the strategy is insensitive to reference variations in comparison with iterative learning control, and outperforms preexisting model-based ZPETFC and data-based FIR feedforward control.