An Empirical Model of Piezoelectric Stick-slip Actuation of the Kleindiek Mm3a Micromanipulator

The need for precise micro/nano-positioning has arisen in many fields of research and technology. Piezoelectric stick-slip actuators are widely used where precise positioning over a wide range of motion is required. Controlling manipulators that utilize piezoelectric stick-slip actuators is not a trivial task, as these actuators have a discrete stepping nature, with a step size that is influenced by a variety of factors such as actuator loading, temperature, and humidity. Absence of integrated joint sensors in manipulators that use piezoelectric stick-slip actuators (which is typical), as well as difficulty in using vision feedback for closed-loop control, has led to development of open-loop modeling methods to estimate the step size of the actuators. Prior work has failed to characterize and quantify the effects of various parameters on the displacement of such actuators to a degree as to be easily utilized in the control of an actual manipulator. In this thesis, we propose an empirically derived predictive open-loop model for the step size of the prismatic and rotary piezoelectric-stick-slip-actuated joints of a Kleindiek MM3A micromanipulator, based on static and inertial loads due to the mass of the manipulator’s links as well as loads applied to the end-effector. The effects of various parameters on the step size of each joint are quantified and characterized. The results obtained are then fit into a model based on nonlinear regression via joint-specific parameters. Calibration routines are developed to quickly determine the joint-specific parameters for use in the derived predictive step-size model. Using the model obtained, we can predict the step size with an accuracy of 20% (100 nm) for the prismatic joint of the manipulator, and 2% (1μrad) for the rotary joints of the manipulator.