Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl-Ishlinskii Approach

Kuhnen, Klaus

doi:10.3166/ejc.9.407-418

Cited by 468 publications

(351 citation statements)

References 5 publications

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“…The converged control in the iteration domain is defined as U ∞ = lim i→∞ U i , and then a necessary and sufficient condition for asymptotic convergence is sense of |U ∞ − U i + 1 | < |U ∞ − U i | is presented for the system as 22,27 ρ(M)<1 (19) where ρ(·) is the spectral radius of a n × n matrix defined as ρ(·) = max λ j (·) , j = 1, 2, ..., n, and λ j (·) is the ith eigenvalue of the matrix.…”

Section: Stability Analysismentioning

confidence: 99%

“…For example, Lai 18 utilized an inversion-based feedforward controller combined with a PID controller to compensate the nonlinearities of a parallel micro-motion stage, and excellent positioning and tracking performances were achieved. Additionally, several analytical models, such as the Prandtl-Ishlinskii model, 19 Preisach model, 20 and Bouc-Wen model, 21 have been proposed and applied in the feedforward controller to compensate the hysteresis of the piezoceramic actuator. The result of the model-based feedforward controller depends on the model accuracy.…”

Section: Introductionmentioning

confidence: 99%

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Contour accuracy improvement of a flexure-based micro-motion stage for tracking repetitive trajectory

Jia

Jiang

et al. 2017

AIP Advances

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Flexure-based micro-motion mechanisms have been widely utilized in modern precision industry due to their inherent merits, while model uncertainty, uncertain nonlinearity, and cross-coupling effect will obviously deteriorate their contour accuracy, especially in the high-speed application. This paper aims at improving the contouring performance of a flexure-based micro-motion stage utilized for tracking repetitive trajectories. The dynamic characteristic of the micro-motion stage is first studied and modeled as a second-order system, which is identified through an open-loop sinusoidal sweeping test. Then the iterative learning control (ILC) scheme is utilized to improve the tracking performance of individual axis of the stage. A nonlinear cross-coupled iterative learning control (CCILC) scheme is proposed to reduce the coupling effect among each axis, and thus improves contour accuracy of the stage. The nonlinear gain function incorporated into the CCILC controller can effectively avoid amplifying the non-recurring disturbances and noises in the iterations, which can further improve the stage’s contour accuracy in high-speed motion. Comparative experiments between traditional PID, ILC, ILC & CCILC, and the proposed ILC & nonlinear CCILC are carried out on the micro-motion stage to track circular and square trajectories. The results demonstrate that the proposed control scheme outperforms other control schemes much in improving the stage’s contour accuracy in high-speed motion. The study in this paper provides a practically effective technique for the flexure-based micro-motion stage in high-speed contouring motion.

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Section: Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Contour accuracy improvement of a flexure-based micro-motion stage for tracking repetitive trajectory

Jia

Jiang

et al. 2017

AIP Advances

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“…These can be classified as operator-based such as Preisach (Mayergoyz, 1991), Prandtl-Ishlinskii and Kransnosel'skii-Pokrovskii models (Brokate, 1996), and differential equations-based such as Duhem and Bouc-Wen models (Coleman and Hodgdon, 1987). Therein, the Prandtl-Ishlinskii (PI) model, a subclass of the Preisach model, is considered meritorious compared to other operator-based models since it is continuous and permits analytical model inversion (Kuhnen, 2003), which could facilitate the design of control/compensation methods (Chen and Su, 2016;Nguyen et al, 2018). The PI model employs a superposition of elementary play or stop operators, and a density function (Brokate and Sprekels, 1996).…”

Section: Introductionmentioning

confidence: 99%

“…The input rate-dependence of the hysteresis nonlinearity has been mostly characterized by introducing a dynamic density function to the classical PI and Preisach models (Li et al, 2014). Kuhnen (2003) employed a summation of weighted nonlinear and memoryless deadband operators to relax symmetry of the classical PI model so as to describe saturation nonlinearities. Another study proposed dissimilar envelop functions under increasing and decreasing inputs to formulate generalized play operators for describing output asymmetry (Valadkhan et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

A Modified Prandtl-Ishlinskii Hysteresis Modeling Method with Load-dependent Delay for Characterizing Magnetostrictive Actuated Systems

Feng

Rakheja

et al. 2018

Mech. Sci.

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Abstract. The actuating precision of a micro-positioning system, driven by a magnetostrictive actuator, is adversely limited by its nonlinearities, particularly the output-input hysteresis, which are further affected by the operating load and input frequency. In this paper, the output-input properties of a magnetostrictive actuated system are experimentally characterized considering a wide range of operating frequencies and loads. The measured data revealed that the hysteresis behaviour is strongly affected with a change of operating load, and a modified Prandtl-Ishlinskii model with load-dependent delay is subsequently formulated to describe the nonlinear characteristics of the magnetostrictive actuated system in terms of major and minor loop hysteresis, and output magnitude and phase responses. The proposed model integrates a load-delay function related to the load mass with the Prandtl-Ishlinskii hysteresis model so as to fully describe the coupled nonlinear delay effects of the system output. The validity of the proposed model is demonstrated through comparisons with the experimental data for a range of operating loads and frequencies. It is shown that the proposed model can accurately describe the load-dependent hysteresis effects of the magnetostrictive actuated system up to certain input frequencies.

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“…Several inverse hysteresis models have been proposed in past several years, e.g. Kuhnen [1] constructed inverse hysteresis model based on modified PI operator. Hu and Ben Mrad [2] proposed a discrete-time compensation algorithm for hysteresis based on first-order reversal functions.…”

Section: Introductionmentioning

confidence: 99%

A neural networks based model of inverse hysteresis

Tan

Shen

2011

Physica B: Condensed Matter

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Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl-Ishlinskii Approach

Cited by 468 publications

References 5 publications

Contour accuracy improvement of a flexure-based micro-motion stage for tracking repetitive trajectory

Contour accuracy improvement of a flexure-based micro-motion stage for tracking repetitive trajectory

A Modified Prandtl-Ishlinskii Hysteresis Modeling Method with Load-dependent Delay for Characterizing Magnetostrictive Actuated Systems

A neural networks based model of inverse hysteresis

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