A Survey of Modeling and Control Issues for Piezo-electric Actuators

Cao, Yu; Chen, Daniel

doi:10.1115/1.4028055

Cited by 53 publications

(27 citation statements)

References 136 publications

(154 reference statements)

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“…See e.g. Wojewoda et al [28] where the occurrence of hysteresis switching in dry friction oscillators is evidenced in experiments, or Cao-Chen [5] where the effect of hysteresis is discussed in the context of electric actuators.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of limit cycles from a switched equilibrium in planar switched systems

Makarenkov

2019

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 99%

Bifurcation of limit cycles from a switched equilibrium in planar switched systems

Makarenkov

2019

Journal of the Franklin Institute

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“…To address the problem of the hysteresis nonlinearities, many meaningful control approaches have been proposed in other works, which can be roughly classified into 3 categories: charge control, noninverse‐based, and inverse‐based compensations. The charge control methodology is required to strongly depend on the design of the charge amplifier for piezoelectric actuators owing to their highly capacitive characteristics, whereas the noninverse compensation method deals with the effect of unknown hysteresis with the help of various advanced control techniques such as backstepping control, iterative learning control, and internal model–based control, where the hysteresis models are utilized to facilitate the controller design without necessarily constructing their inverses.…”

Section: Introductionmentioning

confidence: 99%

Disturbance observer–based prescribed adaptive control for rate‐dependent hysteretic systems

Zhang

Yan

2017

Intl J Robust & Nonlinear

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Summary In this paper, a disturbance observer–based prescribed adaptive control approach is proposed for ultra‐high‐precision tracking of a class of hysteretic systems with both high‐order matched and mismatched disturbances. Considering the adverse effects of asymmetric and rate‐dependent hysteresis nonlinearities, a polynomial‐based rate‐dependent Prandtl‐Ishlinskii model is first developed to characterize their behaviors, and inverse model based compensation is also constructed. Furthermore, the resulting inverse compensation error is analytically given, and a novel disturbance observer with adaptive control techniques is designed to handle the bounded disturbances, including the inverse compensation error and the high‐order matched and mismatched disturbances. Comparative experiments on a multiaxis nano servo stage are finally conducted to demonstrate the effectiveness of the proposed control architecture, where substantial performance improvement over existing results are achieved on various tracking scenarios.

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“…The electrostatic assumption (due to Maxwell's equations) is widely used to model the single piezoelectric layer which entirely ignores the dynamic effects for the Maxwells's magnetic equations, see i.e. [4,33,34]. In fact, even though it is minor in comparison to the mechanical, the dynamic electromagnetic effects have a dramatic effect on the control of these materials [22,38,39].…”

mentioning

confidence: 99%

“…see [3,5,20]. 4 AHMETÖZKANÖZER dimensions of Ω xy . The layers are indexed from 1 to 3 from the stiff layer to the piezoelectric layer, respectively.…”

mentioning

confidence: 99%

Dynamic and electrostatic modeling for a piezoelectric smart composite and related stabilization results

Özer¹

2018

Evolution Equations &Amp; Control Theory

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A cantilevered piezoelectric smart composite beam, consisting of perfectly bonded elastic, viscoelastic and piezoelectric layers, is considered. The piezoelectric layer is actuated by a voltage source. Both fully dynamic and electrostatic approaches, based on Maxwell's equations, are used to model the piezoelectric layer. We obtain (i) fully-dynamic and electrostatic Rao-Nakra type models by assuming that the viscoelastic layer has a negligible weight and stiffness, (ii) fully-dynamic and electrostatic Mead-Marcus type models by neglecting the in-plane and rotational inertia terms. Each model is a perturbation of the corresponding classical smart composite beam model. These models are written in the state-space form, the existence and uniqueness of solutions are obtained in appropriate Hilbert spaces. Next, the stabilization problem for each closed-loop system, with a thorough analysis, is investigated for the natural B * −type state feedback controllers. The fully dynamic Rao-Nakra model with four state feedback controllers is shown to be not asymptotically stable for certain choices of material parameters whereas the electrostatic model is exponentially stable with only three state feedback controllers (by the spectral multipliers method). Similarly, the fully dynamic Mead-Marcus model lacks of asymptotic stability for certain solutions whereas the electrostatic model is exponentially stable by only one state feedback controller.2010 Mathematics Subject Classification. Primary: 35Q60, 35Q93, 93D15; Secondary: 74F15, 93C20. AHMETÖZKANÖZERThe models of piezoelectric smart composites in the literature all assume the electrostatic assumption for its piezoelectric layer. These models differ by the assumptions for the viscoelastic layer and the geometry of the composite, i.e. see [36]. The models are either a Mead-Marcus (M-M) type or a Rao-Nakra (R-N) type as obtained in [3,15], respectively. The M-M model only describes the bending motion, and the R-N model describes bending and longitudinal motions all together. These models reduce to the classical counterparts once the piezoelectric strain is taken to be zero [19,31]. The active boundary feedback stabilization of the classical R-N model (having no piezoelectric layer) is only investigated for hinged [28] and clamped-free [40] boundary conditions. The exact controllability of the M-M and R-N models are shown for the fully clamped, fully hinged, and clamped-hinged models [12,29]. The exponential stability in the existence of the passive distributed "shear" damping term is investigated for the R-N and M-M models ([1, 42]) .Asymptotic stabilization of piezoelectric smart composite models are investigated in [3,15] for various PID-type feedback controllers and a shear-type distributed damping. The exponential stability of the electrostatic M-M and R-N models for clamped-free boundary conditions has been open problems for more than a decade. Recently, exponential stability of the electrostatic R-N model is shown by using four type feedback controllers [24], two for the...

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A Survey of Modeling and Control Issues for Piezo-electric Actuators

Cited by 53 publications

References 136 publications

Bifurcation of limit cycles from a switched equilibrium in planar switched systems

Bifurcation of limit cycles from a switched equilibrium in planar switched systems

Disturbance observer–based prescribed adaptive control for rate‐dependent hysteretic systems

Dynamic and electrostatic modeling for a piezoelectric smart composite and related stabilization results

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