A modeling-free inversion-based iterative feedforward control for precision output tracking of linear time-invariant systems

In this paper, we propose a modeling-free inversion-based iterative feedforward control (MIIFC) approach for high-speed output tracking of single-input single-output linear time-invariant systems. The recently developed inversion-based iterative learning control (IIC) techniques provide a straightforward manner to quantify and account for the effect of dynamics uncertainty on iterative learning control performance, thereby arriving at rapid convergence of the iterative control input. However, dynamics model and thereby the modeling process are still needed, and the model quality directly limits the performance of the IIC techniques. The main contribution of this paper is the development of the MIIFC algorithm to eliminate the dynamics modeling process, and significantly improve the tracking performance. The disturbance (measurement noise) effect on the tracking precision is addressed in the convergence analysis of the MIIFC algorithm. The allowable disturbance/noise level to guarantee the convergence is quantified in frequency domain, and the noise level can be estimated through the noise spectrum measured before the whole operation. The MIIFC technique is demonstrated by applying it to the output tracking of a piezotube scanner on an atomic force microscope. The experimental results showed that precision output tracking of a frequency-rich desired trajectory with power spectrum similar to a band-limited white noise can be achieved.