Physical-model-based control of a piezoelectric tube for nano-scale positioning applications

Piezoelectric tubes exhibit a highly resonant mode of vibration which, if uncontrolled, limits the maximum scan rate in nano-scale positioning applications. Highly resonant systems with collocated sensor/actuator are often controlled using resonant shunt dampers. Unfortunately, in the configuration used here, this approach is not possible due the non-minimum phase property arising from the presence of a right-half plane zero. This problem is solved by: (i) interpreting the resonant shunt damper in the context of physical-model-based control (PMBC) and (ii) extending the PMBC approach to handle non-minimum phase systems. The resultant controller combines the physical insight of the resonant shunt damper with the ability to control the non-minimum phase piezoelectric tube. A digital implementation of the controller was experimentally evaluated and found to successfully eliminate the resonant mode of vibration during an accurate and fast scan using a piezoelectric tube actuator

Physical-model-based control of a piezoelectric tube scanner

A piezoelectric tube is shown to have linear, but non-minimum phase dynamics. The main impediment to the actuation of this piezoelectric tube is the presence of a low-frequency resonant mode which causes mechanical vibrations. A physical-model-based control method is extended to non-minimum phase systems in general and successfully applied to damp the resonant mode; leading to a vibration-free actuation of the piezoelectric tube

A closed-loop approach to reducing scan errors in nanopositioning platforms

Piezoelectric stack-actuated parallel-kinematic nanopositioning platforms have their first resonant mode at relatively low frequencies and also suffer from nonlinearities such as hysteresis and creep, resulting in a typically low-grade positioning performance. Closed- loop control algorithms have shown the potential to eliminate these problems and achieve robust, repeatable nanopositioning. In this work, the performance of three commonly used damping controllers is compared based on their closed-loop noise characteristics. The best one is combined with an integrator to produce accurate raster scans of large areas while imparting substantial damping to the system and minimizing inherent nonlinearities. A scanning resolution of approximately 8nm, over a 100μm × 100μm area is achieved

Reduced order models for a two-dimensional diffusion system

In this paper, a two-dimensional heat diffusion system modelled by a partial differential equation (PDE) is considered. Finite order approximations are constructed first by a direct application of the standard finite difference approximation (FD)scheme. Using standard tools, the constructed FD approximate models are reduced to computationally simpler models. Further, alternative approximate models are proposed using the asymptotic limits of the FD approximations. Numerical experiments suggest that the proposed alternative approximations are more accurate than the FD approximation

High-performance control of piezoelectric tube scanners

In this paper, a piezoelectric tube of the type typically used in scanning tunneling microscopes (STMs) and atomic force microscopes (AFMs) is considered. Actuation of this piezoelectric tube is hampered by the presence of a lightly damped low-frequency resonant mode. The resonant mode is identified and damped using a positive velocity and position feedback (PVPF) controller, a control technique proposed in this paper. Input signals are then shaped such that the closed-loop system tracks a raster pattern. Normally, piezoelectric tubes are actuated using voltage amplifiers. Nonlinearity in the form of hysteresis is observed when actuating the piezoelectric tubes at high amplitudes using voltage amplifiers. It has been known for some time that hysteresis in piezoelectric actuators can be largely compensated by actuating them using charge amplifiers. In this paper, high-amplitude actuation of a piezoelectric tube is achieved using a charge amplifier