Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators

In the paper, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. The actuator dynamics are initially modeled using the homogenized energy model (HEM) framework. This provides a comprehensive high-fidelity model, which can be inverted and implemented in real time for certain control regimes. To improve efficiency, we additionally discuss the development of data-driven models and focus on the implementation of a surrogate model based on a dynamic mode decomposition (DMD). Finally, we detail the design and implementation of a PI controller on the surrogate and high-fidelity models.

A Multi-Axial Electromechanically-Coupled Homogenized Energy Model for Ferroelectric Materials

In this paper, we discuss the development and implementation of a 3-D electromechanically coupled homogenized energy model (HEM) for ferroelectric materials. A stochastic-based methodology is introduced and applied to problems involving large scale switching of ferroelectric and ferroelastic materials. Switching criteria for polarization variants are developed using density distributions in three dimensions to accommodate both electrical and mechanical loading and their coupled response. The theory accommodates non-proportional loading and major/minor loop hysteresis. Such formulations are known to accelerate computations for real-time control of nonlinear and hysteretic actuators. The proposed formulation maintains superior computational efficiency in the three dimensional case through the application of density formulations that are based on internal distributions of stress and electric field to produce a distribution of polarization switching events over a range of applied fields and stresses.

Model Development for PZT Bimorph Actuation Employed for Micro-Air Vehicles

In the paper, we discuss the development of a model for PZT bimorph actuators used to power micro-air vehicles including Robobee. Due to highly dynamic drive regimes required for the actuators, models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in these regimes. We employ the homogenized energy model (HEM) framework to model the actuator dynamics and numerically we illustrate the capability of the model to characterize the inherent hysteresis. This provides a comprehensive model, which can be inverted and implemented for certain control regimes.

Model-Based Adaptive Sliding Mode Control Design for Magnetostrictive Actuator

Giant magnetostrictive actuator (GMA) has been used in precise position, active vibration control etc. for its merits of large output force and displacement. At low drive level, GMA presents linear relation between displacement and input current, while nonlinear appears when applied moderate or high drive level. This paper addresses the development of model-based adaptive sliding mode control designs for GMA operating in nonlinear and hysteretic regimes. Homogenized energy model in combination with a quadratic moment rotation model for magnetostriction is adopted in this paper to describe hysteresis of GMA, and its inverse model is employed as a inverse filter before GMA system to compensate the hysteresis and nonlinear. The proposed control law guaranteed global stability of the control system with certain accuracy in tracking desired trajectories. Simulation result verified the correctness and effectiveness of the extracted control method.

Sliding Mode Control for Inverse Compensated Hysteretic Smart Systems

Ferroelectric (e.g., PZT), ferromagnetic (e.g., Terfenol-D) and ferroelastic (e.g., shape memory alloy (SMA)) materials offer unique capabilities for a range of present and emerging control applications. To fully realize the capabilities these materials offer, model-based control designs must account for the nonideal effects (e.g., creep, rate-dependent hysteresis, and constitutive nonlinearities) that the materials exhibit. In this paper, we employ the homogenized energy model (HEM) to characterize rate-dependent hysteresis behavior, construct an approximate inverse algorithm to compensate the material nonlinearities, and combine this with a sliding mode controller to accommodate uncertainties in the model. We illustrate this in the context of an actuator employing the ferroelectric material PZT but note that the general framework is also applicable to magnetic and shape memory alloy transducers. Through numerical examples, we illustrate the effectiveness of the HEM inverse-based sliding mode design for tracking a reference trajectory in the presence of modeling and inversion errors.

Homogenized Energy Model and Markov Chain Monte Carlo Simulations for Macro Fiber Composites Operating in Broadband Regimes

Macro Fiber Composites (MFCs), comprised of PZT fibers, are being considered for a variety of applications due to their flexibility and relatively low production costs. Like other PZT actuators, MFCs also exhibit hysteresis and constitutive nonlinearities that must be characterized in models and control designs to achieve the full potential. Here we use an Euler-Bernoulli beam model coupled with the homogenized energy strain model to predict the structural/hysteretic response of a thin cantilever beam with an MFC patch attached during a series of frequency sweep experiments. Optimization routines are employed to optimized both MFC parameters and beam parameters using a subset of displacement data. The posterior probability distribution of each model parameter is estimated using Markov Chain Monte Carlo simulations. Finally, we present model predictions with quantified uncertainties.

The Homogenized Energy Model for Characterizing Magnetization and Strains in Ferromagnetic Materials

Ferromagnetic materials exhibit rate-dependent hysteresis, creep and constitutive nonlinearities due to their inherent domain structure. For model-based control applications, these non-linear attributes must be incorporated in a models in a manner that facilitates model calibration and real-time control implementation. In this paper, we present a homogenized energy model for these materials. This is a multiscale framework that quantifies energy at the domain level and then employs stochastic homogenization techniques to provide macroscopic models that are highly efficient to implement. The accuracy of models will be validated using a variety of experimental data.