A Modified Preisach Model for Hysteresis in Piezoelectric Actuators

Piezoelectric actuators (PEAs) exhibit hystérésis nonlinearity in open-loop operation, which may lead to undesirable inaccuracy and limit system performance. Classical Preisach model is widely used for portraying hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. This paper aims to propose a modified Preisach model that demands relatively few measurements and that describes the detachment. The modified model is implemented by adding a damper in parallel with the classical Preisach model. The parameter of the damper is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Experimental results prove that the proposed modified Preisach model can characterize hysteresis more accurately than the classical model

Hybrid PSO-tuned PID and hysteresis-observer based control for piezoelectric micropositioning stages

Piezo-actuated micropositioning stages consist of a piezoelectric actuator that operates a positioning system. Hysteresis nonlinearity is one of the significant variables limiting the positioning precision of these stages. This paper introduces a technique of developing a hybrid controller for a precise positioning tracking of a piezoelectric micropositioning system. Bouc-Wen nonlinear hysteresis model is utilized to denote the hysteresis nonlinear phenomenon of the piezo-actuated system. A hysteresis observer-based feedforward controller is designed based on Luenberger observer. This feedforward controller is then coupled with a particle swarm optimization (PSO)-based proportional-integral-derivative (PID) feedback controller to form a hybrid controller. A new fitness function is used to compute the optimal PID gains. This fitness function is intended to reduce the overshoot, steady-state error, and the rise and settling times. The findings of this work indicate that using the developed controller structure can significantly decrease the hysteresis effect. In addition, the proposed structure shows the ability to reduce the error is to 0.046% of the maximum displacement range. Such performance demonstrates that the proposed hybrid control structure is efficient for precise micropositioning applications.Piezo-actuated micropositioning stages consist of a piezoelectric actuator that operates a positioning system. Hysteresis nonlinearity is one of the significant variables limiting the positioning precision of these stages. This paper introduces a technique of developing a hybrid controller for a precise positioning tracking of a piezoelectric micropositioning system. Bouc-Wen nonlinear hysteresis model is utilized to denote the hysteresis nonlinear phenomenon of the piezo-actuated system. A hysteresis observer-based feedforward controller is designed based on Luenberger observer. This feedforward controller is then coupled with a particle swarm optimization (PSO)-based proportional-integral-derivative (PID) feedback controller to form a hybrid controller. A new fitness function is used to compute the optimal PID gains. This fitness function is intended to reduce the overshoot, steady-state error, and the rise and settling times. The findings of this work indicate that using the developed controller structure can significantly decrease the hysteresis effect. In addition, the proposed structure shows the ability to reduce the error is to 0.046% of the maximum displacement range. Such performance demonstrates that the proposed hybrid control structure is efficient for precise micropositioning applications

An enhanced physics-based model to estimate the displacement of piezoelectric actuators

Piezoelectric actuators are the foremost actuators in the area of nanopositioning. However, the sensors employed to measure the actuator displacement are expensive and difficult, if not impossible, to use. Mathematical models can map the easy-to-measure electrical signals to the displacements of the actuators as the displacement sensors are replaced with the models. In addition, these models can be used in model-based control system design. Two main groups of mathematical models are used for this purpose: black box and physics-based models. As an advantage, the latter has a much smaller number of parameters reducing computational demand in real-time applications. However, physics-based models suffer from (1) the relatively low accuracy of the models and (2) non-standard and ad-hoc parameter identification methods. In this research, to improve the model accuracy, mathematical structure of a well-known physics-based model, the Voigt model, is enhanced by adding two complementary terms inspired by another model, the Preisach model. Then, a standard method based on the evolutionary algorithms is proposed to identify the model’s parameters. The proposed ideas are substantiated to increase the applicability and accuracy of the model, and they are easily extendable to other physics-based models of piezoelectric actuators. The newly proposed enhanced structure of the Voigt model doubles the estimation accuracy of the original model and results in accuracies comparable with black box models.Narges Miri, Morteza Mohammadzaheri and Lei Che

Modeling and Control of Piezoelectric Actuators

Piezoelectric actuators (PEAs) utilize the inverse piezoelectric effect to generate fine displacement with a resolution down to sub-nanometers and as such, they have been widely used in various micro- and nanopositioning applications. However, the modeling and control of PEAs have proven to be challenging tasks. The main difficulties lie in the existence of various nonlinear or difficult-to-model effects in PEAs, such as hysteresis, creep, and distributive vibration dynamics. Such effects can seriously degrade the PEA tracking control performances or even lead to instability. This raises a great need to model and control PEAs for improved performance. This research is aimed at developing novel models for PEAs and on this basis, developing model-based control schemes for the PEA tracking control taking into account the aforementioned nonlinear effects. In the first part of this research, a model of a PEA for the effects of hysteresis, creep, and vibration dynamics was developed. Notably, the widely-used Preisach hysteresis model cannot represent the one-sided hysteresis of PEAs. To overcome this shortcoming, a rate-independent hysteresis model based on a novel hysteresis operator modified from the Preisach hysteresis operator was developed, which was then integrated with the models of creep and vibration dynamics to form a comprehensive model for PEAs. For its validation, experiments were carried out on a commercially-available PEA and the results obtained agreed with those from model simulations. By taking into account the linear dynamics and hysteretic behavior of the PEA as well as the presliding friction between the moveable platform and the end-effector, a model of the piezoelectric-driven stick-slip (PDSS) actuator was also developed in the first part of the research. The effectiveness of the developed model was illustrated by the experiments on the PDSS actuator prototyped in the author's lab. In the second part of the research, control schemes were developed based on the aforementioned PEA models for tracking control of PEAs. Firstly, a novel PID-based sliding mode (PIDSM) controller was developed. The rational behind the use of a sliding mode (SM) control is that the SM control can effectively suppress the effects of matched uncertainties, while the PEA hysteresis, creep, and external load can be represented by a lumped matched uncertainty based on the developed model. To solve the chattering and steady-state problems, associated with the ideal SM control and the SM control with boundary layer (SMCBL), the novel PIDSM control developed in the present study replaces the switching control term in the ideal SM control schemes with a PID regulator. Experiments were carried out on a commercially-available PEA and the results obtained illustrate the effectiveness of the PIDSM controller, and its superiorities over other schemes of PID control, ideal SM control, and the SMCBL in terms of steady state error elimination, chattering suppression, and tracking error suppression. Secondly, a PIDSM observer was also developed based on the model of PEAs to provide the PIDSM controller with state estimates of the PEA. And the PIDSM controller and the PIDSM observer were combined to form an integrated control scheme (PIDSM observer-controller or PIDSMOC) for PEAs. The effectiveness of the PIDSM observer and the PIDSMOC were also validated experimentally. The superiority of the PIDSMOC over the PIDSM controller with σ-β filter control scheme was also analyzed and demonstrated experimentally. The significance of this research lies in the development of novel models for PEAs and PDSS actuators, which can be of great help in the design and control of such actuators. Also, the development of the PIDSM controller, the PIDSM observer, and their integrated form, i.e., PIDSMOC, enables the improved performance of tracking control of PEAs with the presence of various nonlinear or difficult-to-model effects