scholarly journals Rate-Dependent Modeling of Piezoelectric Actuators for Nano Manipulation Based on Fractional Hammerstein Model

Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Liu Yang ◽  
Zhongyang Zhao ◽  
Yi Zhang ◽  
Dongjie Li
Keyword(s):  
Fractional Order ◽  
Dynamic Characteristics ◽  
Autoregressive Model ◽  
Tracking Control ◽  
Piezoelectric Actuators ◽  
Hammerstein Model ◽  
Order Model ◽  
Integer Order ◽  
Rate Dependent ◽  
Rate Correlation

Piezoelectric actuators (PEAs), as a smart material with excellent characteristics, are increasingly used in high-precision and high-speed nano-positioning systems. Different from the usual positioning control or fixed frequency tracking control, the more accurate rate-dependent PEA nonlinear model is needed in random signal dynamic tracking control systems such as active vibration control. In response to this problem, this paper proposes a Hammerstein model based on fractional order rate correlation. The improved Bouc-Wen model is used to describe the asymmetric hysteresis characteristics of PEA, and the fractional order model is used to describe the dynamic characteristics of PEA. The nonlinear rate-dependent hysteresis model can be used to accurately describe the dynamic characteristics of PEA. Compared with the integer order model or linear autoregressive model to describe the dynamic characteristics of the PEA Hammerstein model, the modeling accuracy is higher. Moreover, an artificial bee colony algorithm (DE-ABC) based on differential evolution was proposed to identify model parameters. By adding the mutation strategy and chaos search of the genetic algorithm into the previous ABC, the convergence speed of the algorithm is faster and the identification accuracy is higher, and the simultaneous identification of order and coefficient of the fractional model is realized. Finally, by comparing the simulation and experimental data of multiple sets of sinusoidal excitation with different frequencies, the effectiveness of the proposed modeling method and the accuracy and rapidity of the identification algorithm are verified. The results show that, in the wide frequency range of 1–100 Hz, the proposed method can obtain more accurate rate-correlation models than the Bouc-Wen model, the Hammerstein model based on integer order or the linear autoregressive model to describe dynamic characteristics. The maximum error (Max error) is 0.0915 μm, and the maximum mean square error (RMSE) is 0.0244.

Extended state observer–based fractional order sliding-mode control of piezoelectric actuators

2020 ◽  
Vol 235 (1) ◽  
pp. 39-51
Author(s):  
Shuyou Yu ◽  
Yangyang Feng ◽  
Xiaoping Yang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Piezoelectric Actuators ◽  
State Observer ◽  
Extended State Observer ◽  
Hammerstein Model ◽  
Extended State ◽  
Mode Control ◽  
Rate Dependent

Tracking control of piezoelectric actuators is considered in the article. A Hammerstein model is used to depict the rate-dependent hysteresis characteristics of piezoelectric actuators, in which a Bouc–Wen model is to describe the static hysteresis characteristic, and a linear time-invariant system is to describe its rate-dependent characteristics. An inverse Bouc–Wen model connected in series with the piezoelectric actuator is used to compensate the static hysteresis nonlinearity of piezoelectric actuators. Furthermore, an extended state observer–based fractional order sliding-mode control is designed to deal with higher order unmodelled dynamics and inverse compensation errors. Moreover, the bounds of the estimation error of the extended state observer are estimated, and the convergence of the proposed control strategy is proved. Experimental results show that the proposed scheme can track both single and composite input signals within a certain frequency range. Compared with extended state observer–based conventional sliding-mode controller, the proposed scheme has faster response time and smaller tracking error.

Finite deformation and fractional order viscoelasticity of an auxetic foam

2022 ◽  
pp. 1045389X2110643
Author(s):  
Eugenia Stanisauskis ◽  
Paul Miles ◽  
William Oates
Keyword(s):  
Fractional Order ◽  
Finite Deformation ◽  
Viscoelastic Behavior ◽  
Integer Order ◽  
Relaxation Effects ◽  
Viscoelastic Parameters ◽  
Rate Dependent ◽  
Improve Model ◽  
Model Predictions ◽  
And Performance

Auxetic foams exhibit novel mechanical properties due to their unique microstructure for improved energy-absorption and cavity expansion applications that have fascinated the scientific community since their inception. Given the advancements in material processing and performance of polymer open cell auxetic foams, there is a strong desire to fully understand the nonlinear rate-dependent deformation of these materials. The influence of nonlinear compressibility is introduced here along with relaxation effects to improve model predictions for different stretch rates and finite deformation regimes. The viscoelastic behavior of the material is analyzed by comparing fractional order and integer order calculus models. All results are statistically validated using maximum entropy methods to obtain Bayesian posterior densities for the hyperelastic, auxetic, and viscoelastic parameters. It is shown that fractional order viscoelasticity provides [Formula: see text]–[Formula: see text] improvement in prediction over integer order viscoelastic models when the model is calibrated at higher stretch rates where viscoelasticity is more significant.

Model Predictive Control of General Fractional Order Systems Using a General Purpose Optimal Control Problem Solver: RIOTS

2019 ◽  
Author(s):  
Sina Dehghan ◽  
Tiebiao Zhao ◽  
YangQuan Chen ◽  
Taymaz Homayouni
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Fractional Order ◽  
Predictive Control ◽  
Order System ◽  
Problem Solver ◽  
Fractional Order Systems ◽  
Application Process ◽  
Order Model ◽  
Integer Order

Abstract RIOTS is a Matlab toolbox capable of solving a very general form of integer order optimal control problems. In this paper, we present an approach for implementing Model Predictive Control (MPC) to control a general form of fractional order systems using RIOTS toolbox. This approach is based on time-response-invariant approximation of fractional order system with an integer order model to be used as the internal model in MPC. The implementation of this approach is demonstrated to control a coupled MIMO commensurate fractional order model. Moreover, the performance and its application process is compared to examples reported in the literature.

Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation

2019 ◽  
Vol 22 (2) ◽  
pp. 424-443 ◽  
Author(s):  
Wojciech Przemysław Hunek
Keyword(s):  
Fractional Order ◽  
Control Algorithm ◽  
Mimo System ◽  
Practical Implementation ◽  
Space Systems ◽  
Order Model ◽  
Integer Order ◽  
Fractional Order Model ◽  
State Space Systems ◽  
Systems Simulation

Abstract A new perfect control algorithm dedicated to fractional-order right-invertible systems, i.e. plants with a greater number of input than output variables, is presented in this paper. It is shown that such a control strategy can be particularly applied with regard to practical tasks. Henceforth, the Grünwald-Letnikov difference operator Δα of an assumed order α can be truncated without loss of generality. For that reason, the so-called pole-free perfect control formula can be used to minimize the essential drawback of the Grünwald-Letnikov approach engaged, so as to define the intriguing issue regarding the robust perfect control for non-integer-order right-invertible LTI discrete-time state-space systems. Simulation examples show that the presented method can compete with a classical stable-pole one, for which the actual systems described by a fractional-order model often correspond with an inconvenient asymptotic perfect control solution given by the unlimited original operator Δα. In the end, the possibility of employing of author’s nonunique right inverses dedicated to nonsquare MIMO system matrices is demonstrated, thus giving rise to the introduction of a new powerful tool for robustification of non-integer-order closed-loop perfect control plants as well.

Distributed coordination of fractional order multi-agent systems with communication delays

2014 ◽  
Vol 17 (1) ◽  
Author(s):  
Hong-yong Yang ◽  
Xun-lin Zhu ◽  
Ke-cai Cao
Keyword(s):  
Fractional Order ◽  
Communication Delays ◽  
Distributed Coordination ◽  
Multi Agent Systems ◽  
Order Model ◽  
Agent Systems ◽  
Integer Order ◽  
Dynamical Characteristics ◽  
The Laplace Transform ◽  
Multi Agent

AbstractBecause of the complexity of the practical environments, many distributed multi-agent systems can not be illustrated with the integer-order dynamics and can only be described with the fractional-order dynamics. Under the connected network with directed weighted topologies, the dynamical characteristics of agents with fractional-order derivative operator is analyzed in this paper. Applying the Laplace transform and frequency domain theory of the fractional-order operator, the distributed coordination of fractional-order multi-agent systems (FOMAS) with communication delays is studied, and a critical value of time delay is obtained to ensure the consensus of FOMAS. Since the integer-order model is a special case of fractional-order model, the extended results in this paper are in accordance with that of the integer-order model. Finally, numerical examples are provided to verify our results.

Fractional-Order-Based Inferential Control

2020 ◽  
pp. 322-341
Author(s):  
Abdul Wahid Nasir ◽  
Idamakanti Kasireddy ◽  
Arun Kumar Singh
Keyword(s):  
Fractional Order ◽  
Order Model ◽  
Model Approximation ◽  
Integer Order ◽  
Inferential Control ◽  
Fractional Differential Operator ◽  
Control Scheme ◽  
And Control ◽  
Primary Variable ◽  
Operating Points

This chapter presents the application of fractional differential operator in modelling and control of a three-tank interacting level process. In cases where the usage of sensors for the measurement of primary variable, which is the level of third tank in present case, is physically or economically not feasible, the measurement of secondary variable (i.e., second tank level) is used to determine the level of third tank for control purpose, known as inferential control scheme. The process is modeled and linearized around the operating points, resulting in third order plant, which is approximated to lower order integer and non-integer model. Both conventional integer order PI (IO-PI) & PID (IO-PID) and fractional order PI (FO-PI) & (FO-PID) controllers are implemented for this inferential control. Extensive simulation studies performed using MATLAB validate the supremacy of non-integer order model and controller over integer order model and controller. Genetic algorithm (GA) is being applied for both, firstly for reduced order model approximation and secondly for controller tuning.

Tracking control of a 3-dimensional piezo-driven micro-positioning system using a dynamic Prandtl–Ishlinskii model

2021 ◽  
pp. 1045389X2110482
Author(s):  
Wei Zhu ◽  
Feifei Liu ◽  
Fufeng Yang ◽  
Xiaoting Rui
Keyword(s):  
Power Amplifier ◽  
Dynamic Characteristics ◽  
Tracking Control ◽  
Feedforward Control ◽  
Positioning System ◽  
Hysteresis Model ◽  
Tracking Accuracy ◽  
Simple Method ◽  
3 Dimensional ◽  
Rate Dependent

A controller composed of a feed-forward loop based on a novel dynamic Prandtl–Ishlinskii (P-I) model and a PID feedback control loop is developed to support a 3-dimensional piezo-driven micro-positioning system for high-bandwidth tracking control. By considering the dynamic characteristics of the power amplifier, the dynamic P-I model can accurately describe the rate-dependent hysteresis of piezoelectric stack actuators (PSAs). To ensure that the hysteresis model is independent of system load, the P-I hysteresis operator in that model characterizes the relationship between the output force and the input voltage of PSAs. The dynamics equation of the mechanical is established by using the cutoff modal method. The feedforward control is designed based on the dynamic hysteresis model to reduce the rate-dependent hysteresis. The PID control is incorporated with the feedforward control to increase the tracking accuracy. Experimental results indicate that the controller can overcome the hysteresis efficiently and preserve good positioning accuracy in 1–100 Hz bandwidth. Just by introducing the dynamic characteristics of the power amplifier, which can be expressed as a first-order differential equation, the P-I model can accurately describe the rate-dependent hysteresis of the PSA, which provides a simple method to describe and control piezoelectric actuators and piezo-driven systems in a wide frequency.

Modeling and Control for GMA Based on Hammerstein Model Structure

2013 ◽  
Vol 668 ◽  
pp. 406-409
Author(s):  
Qing Song Liu ◽  
Zhen Zhang ◽  
J.Q. Mao
Keyword(s):  
Tracking Control ◽  
Hammerstein Model ◽  
Model Structure ◽  
Hysteresis Model ◽  
Modeling And Control ◽  
Feedforward Loop ◽  
Rate Dependent ◽  
Proposed Model ◽  
Magnetostrictive Actuator ◽  
And Control

A rate-dependent hysteresis model for Giant Magnetostrictive Actuator (GMA) is proposed based on Hammerstein model structure. The Generalized Prandtl-Ishlinskii (GPI) model is used to represent nonlinear block in Hammerstein model. The validity of model is examined by comparsion between simulation results and experimental data. Based on the proposed model, a PID feedback controller combined with an inverse compensation in the feedforward loop is used for tracking control. Experimental results show that the control strategy is effective.

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