Feedforward control approach to precision trajectory design and tracking: Theory and application to nano-mechanical property mapping using Scanning Probe Microscope

The output tracking problem has been extensively studied. The linear system case has been addressed by B. A. Francis (1976) by converting the tracking problem to a regulator problem. Such an approach was later extended to nonlinear systems by A. Isidori et al. (1990). On the feedforward control side, the stable inversion theory solved the challenging output tracking problem and achieved exact tracking of a given desired output trajectory for nonminimum phase systems (linear and nonlinear). The obtained solution is noncausal and requires the entire desired trajectory to be known a priori. This noncausality constraint has been alleviated through the development of the preview-based inversion approach, which showed the precision tracking can be achieved with a finite preview of the future desired trajectory, and the effect of the limited future trajectory information on output tracking can be quantified. Moreover, optimal scan trajectory design and control method provided a systematic approach to the optimal output-trajectory-design problem, where the output trajectory is repetitive and composed of pre-specified trajectory and unspecified trajectory for transition that returns from ending point to starting point in a given time duration.;This dissertation focuses on the development of novel inversion-based feedforward control technique, with applications to output tracking problem with tracking and transition switchings, possibly non-repetitive. The motivate application examples come from atomic force microscope (AFM) imaging and material property measurements. The raster scanning process of AFM and optimal scan trajectory design and control method inspired the repetitive output trajectory tracking problem and attempt to solve in frequency domain. For the output tracking problem, especially for the AFM, there are several issues that have to be addressed. At first, the shape of the desired trajectory must be designed and optimized. Optimal output-trajectory-design problem provided a systematic approach to design the desired trajectory by minimizing the total input energy. However, the drawback is that the desired trajectory becomes very oscillatory when the system dynamics such as the dynamics of the piezoelectric actuator in AFM is lightly damped. Output oscillations need to be small in scanning operations of the AFM. In this dissertation, this problem is addressed through the pre-filter design in the optimal scan trajectory design and tracking framework, so that the trade off between the input energy and the output energy in the optimization is achieved. Secondly, the dissertation addressed the adverse effect of modeling error on the performance of feedforward control. For example, modeling errors can be caused in process of curve fitting.;The contribution of this dissertation is the development of novel inversion based feedforward control techniques. Based on the inversion-based iterative learning control (S. Tien et al. (2005)) technique, the dissertation developed enhanced inversion-based iterative control and the model-less inversion-based iterative control. The convergence of the iterative control law is discussed, and the frequency range of the convergence as well as the effect of the disturbance/noise to signal ratio is quantified. The proposed approach is illustrated by implementing them to high-speed force-distance curve measurements by using atomic force microscope (AFM). Then the control approach is extended to high-speed force-volume mapping. In high-speed force-volume mapping, the proposed approach utilizes the concept of signal decoupling-superimposition and the recently-developed model-less inversion-based iterative control (MIIC) technique. Experiment of force-volume mapping on a Poly-dimethylsiloxane (PDMS) sample is presented to illustrate the proposed approach. The experimental results show that the mapping speed can be increased by over 20 times.