Sliding Mode Control of a Piezoelectric Actuator with Neural Network Compensating Rate-Dependent Hysteresis

Yu, Shuanghe; Alici, Gürsel; Shirinzadeh, Bijan; Smith, Julian Anderson

doi:10.1109/robot.2005.1570674

Cited by 19 publications

(5 citation statements)

References 21 publications

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“…Innovative controllers of piezoelectric actuators involving a large number of methods, usually focused on hysteresis compensation, have been proposed [15]. Inverse hysteresis models, such as the Preisach model, neural network models and phase shifting operators [4,16,17], give decent results for a given frequency, but exhibit poor accuracy when the frequency is varied. These drops in performance are mainly due to a lack of compensation for the dynamical losses.…”

Section: Discussionmentioning

confidence: 99%

High frequency bandwidth polarization and strain control using a fractional derivative inverse model

Guyomar¹,

Ducharne²,

Sebald³

2010

Smart Mater. Struct.

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The present paper proposes an inverse dynamical model based on fractional derivatives in order to simulate the electrical field versus the polarization field E(P) as well as the electrical field versus the mechanical strain E(S) of ferroelectric hysteresis. By considering a fractional derivative term, the frequency bandwidth of the inverse model is greatly increased. As a consequence, the model became suited for the usual inverse model applications, such as adaptive inverse control of piezoelectric actuators, high-speed positioning or high precision positioning. The proposed high-accuracy inverse model rendered it possible to avoid standard feedback mechanisms that usually exhibit restrain frequency bandwidths due mainly to high frequency noise. Starting from a quasi-static inverse model, and based on a simple mechanism related to the dry-friction concept, a polarization fractional derivative term was added in order to take into account the dynamical effects. The order of the fractional derivative was, using a direct model P(E) and experimental data on a large frequency bandwidth (10 −3 Hz < f < 10 2 Hz), found to be equal to 0.5. A quadratic relation was used to link the ferroelectric strain and the polarization field. Moreover, a dynamical strain control based on an inverse dynamic polarization field contribution was proposed. Experimental procedures were developed to verify the accuracy of the polarization as well as of the strain control. Good results were obtained and exposed for sinus and triangular polarization-imposed waveforms. Various frequencies and amplitudes were tested in both cases.

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Section: Discussionmentioning

confidence: 99%

High frequency bandwidth polarization and strain control using a fractional derivative inverse model

Guyomar¹,

Ducharne²,

Sebald³

2010

Smart Mater. Struct.

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“…Substituting the control input (12) in the dynamic model (1), the closed loop dynamic would be obtained. m i Ṡi + η 1 i S i + η 2 i Sgn(S i ) = P i (t) (13) Satisfying the overall stability and sliding condition, η 2 should be more than all disturbances as η 2 i > |P i (t)|.…”

Section: Sliding Mode Robust Control Designmentioning

confidence: 99%

“…In addition, solo neural network based controls are not robust to the inevitable sensor noises problem. Therefore, Yu et al represented a robust neural network control [13].…”

Section: Introductionmentioning

confidence: 99%

Robust control with unknown dynamic estimation for multi-axial piezoelectric actuators with coupled dynamics

Ghafarirad

Rezaei

Zareinejad

et al. 2012

Comptes Rendus. Mécanique

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Piezoelectric actuators are widely used for precise micro-positioning. The ability of fine positioning is strictly under the effect of hysteresis nonlinear behavior. Simultaneous micro-positioning in multi-dimensions has also attracted much attention in recent years. In addition to hysteresis behavior, a nonlinear dynamic coupling exists between the different degrees of freedom in multi-axis piezoelectric actuators. The nonlinear coupling phenomenon is called the Axes Coupling Effect (ACE). A modified Prandtl-Ishlinskii (PI) operator and its inverse are utilized for both the identification and real time compensation of the hysteresis effect in this article. Considering the PI estimation error and probable un-modeled dynamics, a variable structure controller coupled with the neural network is proposed for position tracking. Due to the model-based structure of the proposed controller, the dynamic model of actuator should be identified. Coupling between nonlinear hysteresis behavior and the linear dynamic model causes a complicated identification. The ACE has also an unknown trend. Eliminating the necessity of dynamic parameters and ACE identification, a Radial Basis Function (RBF) neural network approach would estimate the unknown dynamics of the designed controller. Stability of the controller in the presence of estimated unknown dynamics is demonstrated analytically. Experimental results depict that the proposed approach can achieve precise tracking of multi-frequency trajectories and appropriate estimation of unknown dynamics.

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“…Krejci and Kuhnen [12] proved that the inverse hysteretic operator for the Prandtl-Ishlinskii model is unique and input-output stable; and from this statement, an analytic compensator for this model was proposed. Besides, several methods for determining the compensator using different algorithms have been developed [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Compensation For Hysteresis Of a Stacked Pzt Actuatormentioning

confidence: 99%

Compensator design for hysteresis of a stacked PZT actuator using a congruency-based hysteresis model

Nguyen¹,

Choi²

2011

Smart Mater. Struct.

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This paper proposes a rate-independent hysteresis compensator for a stacked PZT (lead zirconate titanate) actuator. From a congruency-based hysteresis (CBH) model which is derived from the inherent properties of this actuator, especially the congruency, a feedforward compensator associated with it is developed. The formulation of the proposed compensator is based on an assumption that the inverse operator also possesses the same properties as the CBH model does. This implies that the compensator also possesses properties such as the wiped-out loop closing between the consecutive control points and congruency. Consequently, the expressions for the compensator can be conducted by exploiting the equations for the CBH model in two cases of monotonic increase and monotonic decrease of input excitation. In order to assess the performance of the compensator, several experiments in both open-loop and closed-loop controls are undertaken. In the open-loop control experiment, the performance of the feedforward compensator using the CBH model is compared with the classical Preisach model-based one in three cases of reference waveforms. In the closed-loop control experiment, the proposed compensator is incorporated into a PID (proportional-integral-derivative) control system and the performance of this integrated system is then evaluated and compared to that of the PID with and without compensator.

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Sliding Mode Control of a Piezoelectric Actuator with Neural Network Compensating Rate-Dependent Hysteresis

Cited by 19 publications

References 21 publications

High frequency bandwidth polarization and strain control using a fractional derivative inverse model

High frequency bandwidth polarization and strain control using a fractional derivative inverse model

Robust control with unknown dynamic estimation for multi-axial piezoelectric actuators with coupled dynamics

Compensator design for hysteresis of a stacked PZT actuator using a congruency-based hysteresis model

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