Sensorless Quasi-static Piezoelectric Actuator for Micro-Robotics

Research interest into the miniaturisation of micro-robots has soared in recent years due to the availability of suitable integrated actuators. The reduction in size of these components is achieved through the implementation of Self-Sensing Actuation (SSA). This approach foregoes the need for external sensors which increase the encumbrance of micro-robots. The SSA approach is all the more relevant with piezoelectric actuators due to the reversible properties of piezoelectricity. The present thesis endeavours to explore the topic of piezoelectric SSA by applying a focus on the fundamental theory supporting the approach. It would then be possible to determine how a piezoelectric actuator could be tailored for SSA, particularly at the quasi-static ranges of frequencies that characterise robotic manipulation tasks.

A general model describing the piezoelectric actuator as a system with electro-mechanical inputs and outputs has been formulated: the inputs are the force and the voltage, resulting in a displacement and accumulated electrical charge as outputs. It is shown that all piezoelectric actuators follow this model form, which can be summarised through the description of three parameters: the stiffness, the capacitance, and a coefficient named beta. The latter describes the electro-mechanical coupling between charge accumulation and force, and is the most critical characteristic when aiming for high precision SSA. It is then demonstrated through dynamic modelling of piezoelectric actuators using bond graph models that the performance of the position and force sensorless estimation is intimately tied to these three actuator characteristics. Since these are a function of the actuator's design parameters, the self-sensing performance may be drastically improved at the design level.

By deriving design guidelines from an actuator design study based on an analytical model, a SSA demonstration prototype is developed. A batch of piezoelectric benders are manufactured with sub-mN sensorless estimation accuracies in mind. A test environment supporting these actuators is designed with the specific goals of determining their parameters experimentally, and of providing the grounds for the testing of diverse SSA implementations. After a measurement campaign providing a statistical appreciation for the parameters of the actuator batch, a calibrated self-sensing implementation approach is discussed. With this approach, it is shown that force estimation accuracies of 0.25 mN for durations of up to 60 s are within the grasp of these actuators tailored to SSA. Longer durations that guarantee high estimation accuracies would be acquired by focusing more research effort into the delicate task of measuring minute electrical charges.

In light of some inconsistencies between model predictions and experimental data, an updated model is proposed: the error of the beta coefficient and the stiffness are reduced to 3% and 12% respectively. From this model describing parameters with non-monotonic characteristics, a multi-objective optimisation study is proposed to simultaneously optimise an actuator design for high sensitivity and low estimation error. The resulting piezoelectric actuator design provides a beta coefficient of -4.62nC/mN, corresponding to a sensitivity increase of 52% compared the previously fabricated actuator, and a sensitivity increase by a factor of 9.5 compared to a commercial actuator of similar morphology.